Targeted magnetic resonance imaging (tMRI) of small changes in the T₁ and spatial properties of normal or near normal appearing white and gray matter in disease of the brain using divided subtracted inversion recovery (dSIR) and divided reverse subtracted inversion recovery (drSIR) sequences

Introduction

In the first study of multiple sclerosis (MS) with magnetic resonance imaging (MRI) in 1981, an intermediate inversion time (TI) T₁-weighted inversion recovery (IR) pulse sequence was used to produce high contrast visualization of lesions with increased T₁s (1). This was followed by the use of long repetition time (TR), long echo time (TE) T₂-weighted spin echo (T₂-wSE) sequences in 1982 and 1983 to show lesions in MS and other diseases with high contrast as a result of their increased T₂s (2-5).

In 1984, a Gadolinium based contrast agent (GBCA) was used with intermediate TI (TI_i) T₁-weighted IR sequences to provide high contrast in lesions as a result of the reduction in T₁ produced by the GBCA (6).

In 1985, the short TI IR (STIR) sequence was described (7). For concurrent increases in T₁ and T₂ in lesions in disease, this sequence displayed synergistic contrast in which the contributions to lesion contrast from both the increases in T₁ and T₂ were complementary. This resulted in high contrast visualization of abnormalities in diseases of the brain and body.

In the same paper (7), the double IR (DIR) sequence was described in which two IR sequences with different TIs were multiplied together. The DIR sequence was used to simultaneously suppress signal from fat and cerebrospinal fluid (CSF). In addition, as with the STIR sequence, concurrent increases in the T₁ and T₂ of lesions produced high synergistic contrast. In 1994, the DIR sequence was used to suppress signal from white or gray matter in the brain, as well as CSF. In lesions with concurrent increases in T₁ and T₂, the sequence provides synergistic T₁ and T₂ contrast in gray or white matter respectively (8).

The T₂-fluid attenuated inversion recovery (T₂-FLAIR) sequence was described in 1992. It used a long TI (TI_l) to suppress CSF signal and a long TE to increase T₂ contrast since, for concurrent increases in T₁ and T₂ in lesions, the T₁ contrast is opposed to the T₂ contrast. The increased T₂-weighting provided by the long TE is used to overcome this, and render the sequence T₂-weighted for most lesions (9).

IR sequences including TI_i IR sequences such as magnetization prepared-rapid acquisition gradient echo (MP-RAGE), GBCA enhanced TI_i IR acquisitions, STIR and T₂-FLAIR are key components of present day MRI protocols for the study of MS in the brain and spinal cord (10) as well as for tumors (11) and other diseases of the brain (12).

In 2010, in addition to the DIR sequence, another multiplied IR (MIR) sequence, magnetization prepared 2 rapid acquisition gradient echo (MP2RAGE), was described (13) and this has been used to visualize MS lesions in the brain and spinal cord with performance superior to conventional sequences (14,15). The MP2RAGE sequence uses changes in T₁ twice to generate synergistic T₁ contrast from two IR images with different TIs. The images are multiplied together, and the product is normalized by dividing it by the sum of the squares of the signals from both IR images. The sequence contrast is optimized for composite white-gray matter, white matter-CSF, and gray matter-CSF contrasts and uses two widely separated fixed TIs. This provides sensitivity to differences in T₁ in normal and abnormal tissue over a wide domain of T₁ values.

Subtracted IR (SIR) sequences with different TI_s were described in 2017 and 2018 (16,17). The SIR sequence provides images with increased T₁ dependent contrast compared with single IR sequences for T₁s between the nulling values for the two TIs of the IR sequences. The TIs of the two IR sequences were narrowly separated and were varied depending on the tissue(s) of interest.

Variants of the fluid and white matter suppression (FLAWS) sequence in which two IR images with different TIs are subtracted, and then divided by the sum of the two images were described in 2019 and 2021 (18,19). These FLAWS high contrast (FLAWS-hc) and FLAWS-hc opposite (FLAWS-hco) sequences use two widely separate fixed TIs and provided T₁ contrast over a wide domain of T₁ values.

In four previous papers published in 2020 and 2022, a formalism was described to understand the signal, contrast and weighting of MRI pulse sequences using the concepts of tissue property filters (TP-filters) and the central contrast theorem (CCT) (20-23). This approach uses a quantitative definition of sequence weighting to understand the contrast produced by commonly used clinical sequences as well as more complex sequences. Combinations of two or more IR sequences were generalized as the multiplication, addition, subtraction, and/or division of IR (MASDIR) group of sequences. Contrast in these sequences was mathematically modeled using TP-filters and the CCT.

In modeling contrast produced by MASDIR sequences, two particularly interesting sequences were identified. These were forms of the divided SIR (dSIR) sequence in which two magnitude IR images with different TIs were subtracted and divided by the sum of the two images, and a variant of this, the divided reverse SIR (drSIR) sequence, in which the subtraction of the two IR images is performed in the reverse order. Both sequences employ differences or changes in T₁ on 3–4 occasions to generate synergistic T₁ contrast. The middle domain (mD) of the dSIR and drSIR sequences includes T₁s between the nulled T₁s of the original two IR sequences. When narrow mD versions of the dSIR and drSIR sequences were used, small changes in T₁ produced 5–15 times the contrast seen with conventional MP-RAGE sequences. This was particularly well suited to demonstrating contrast due to small changes in T₁ in normal or near normal appearing white matter (as shown with conventional T₂-wSE and T₂-FLAIR sequences). Using narrow mD dSIR sequences in cases of MS, extensive abnormalities were demonstrated in areas of normal appearing white matter [e.g., Fig. 31-35 in (23)].

Narrow mD dSIR and drSIR sequences are very sensitive to small changes in T₁ within the narrow mD. This differs from MP2RAGE, FLAWS-hc, and FLAWS-hco sequences which are generally less sensitive to small changes in T₁ than narrow mD dSIR and drSIR sequences in the mD, but are sensitive to changes in T₁ over a wider domain of T₁ values.

The term targeted MRI (tMRI) is used to describe sequences which are focused on a particular tissue and specific changes in one or more tissue properties (TPs) of that tissue such as T₁ and T₂. In this paper, the dSIR and drSIR sequences are targeted at small changes in T₁ from normal in normal or near normal appearing white or gray matter. This requires use of TIs targeted at the nulling TIs of normal white and gray matter as well as different TIs to match the sign and size of changes in T₁ expected in disease. This is different to MP2RAGE, FLAWS-hc, and FLAWS-hco sequences which use fixed TIs for all tissues and are not targeted at a specific tissue or specific changes in the T₁ of that tissue in disease.

In addition to the production of high contrast from small changes in tissue T₁ using narrow mDs described above, dSIR and drSIR sequences can produce high signal, often high contrast boundaries between tissues and fluids. (The term “tissues” is used to include tissues and fluids in the rest of this paper unless otherwise specified.)

dSIR and drSIR images are normalized, and are largely independent of mobile proton density (ρ_m) and T₂ (which both cancel out in the dSIR and drSIR signal equations), and are therefore essentially T₁ maps. In the mD, image signal is, to a first approximation, proportional to T₁.

The drSIR sequence is very sensitive to small reductions in T₁ produced by GBCAs and the sequence can be used with three-dimensional (3D) isotropic acquisitions and rigid body registration to eliminate misregistration between pre- and post-GBCA images, and show GBCA enhancement in normal and diseased tissue.

The high signal boundaries of dSIR and drSIR sequences can be used with rigid body registration to show small changes in spatial properties (e.g., site, shape, size and surface) of normal anatomical structures and lesions over time in serial studies. This is in addition to changes in T₁.

The availability of T₁ measurements and sharply defined boundaries with dSIR and drSIR sequences makes them well suited to quantification of T₁ without or with GBCA enhancement, as well as the spatial properties of normal tissues and lesions.

The purpose of this article is to explain the background underpinning the use of dSIR and drSIR sequences to target small changes in the T₁ and spatial properties of normal (or near normal) white matter or gray matter of the brain, describe implementation of the sequences and illustrate their use in clinical cases.

Theory

The spin echo (SE) sequence (univariate model)

The usual explanation of image signal and contrast with the SE sequence utilizes a simplified version of the Bloch equations. This initially follows longitudinal magnetization (M_Z) over time TR and, after the application of a 90° pulse, then follows transverse magnetization (M_XY) over time TE (Figure 1). Contrast between two tissues such as P with a shorter T₁ and T₂, and Q with a longer T₁ and T₂, is shown by the vertical difference in M_XY at the time of data collection TE, as shown by the vertical blue arrow on the right in Figure 1. M_Z becomes M_XY as a result of the 90° pulse used in the SE sequence.

Figure 1 Plot of M_Z/M_XYvs. time for the SE sequence for two tissues P (with a shorter T₁ and T₂) and Q (with a longer T₁ and T₂). T₁-dependent contrast (first negative blue arrow on left), and overall T₁ and T₂ contrast (second = third positive blue arrows in center and on right) are shown. TR, repetition time; TE, echo time; SE, spin echo.

The voxel signal S for a SE sequence is derived from the simplified Bloch equations where:

S=Kρm(1−e−t'/T1)e−t''/T2[1]

K is a scaling function, ρ_m is mobile proton density, t' is the variable time for the initial part of the sequence, and t" is the variable time for the latter part of the sequence. T₁ and T₂ are time constants. Eq. [1] describes ρ_m in the first segment, recovery of longitudinal magnetization (M_Z) over time in the second segment (which is in parentheses), and decay of transverse magnetization (M_XY) over time in the third segment. The equations in the second and third segments are of the forms y = 1 − e^−x and y = e^−x, respectively where x is a variable.

It is useful to replace the variables t' and t" in Eq. [1] respectively by the constant times of the SE sequence TR and TE, and to treat the two time constants T1 and T₂ in Eq. [1] as variables. This changes Eq. [1] to:

S=Kρm(1−e−TR/T1)e−TE/T2[2]

or:

S=KSρm⋅ST1⋅ST2[3]

where the signals for the three segments Sρm, ST1, and ST2 are given by:

Sρm=ρm[4]

ST1=1−e−TR/T1[5]

ST2=1−e−TE/T2[6]

The second and third segments in Eq. [2] are of the forms y = 1 − e^−1/x and y = e^−1/x respectively, since T₁ and T₂ are now variables. These forms are quite different from the forms y = 1 − e^−x and y = e^−x shown in the second and third segments of the Bloch equations in Eq. [1].

The three segments in Eqs. [2-6] have the features of a linear or exponential high pass filter for ρ_m [depending on whether the X axis is linear or natural logarithmic (ln)], a low pass filter for T₁ (i.e., low values of T₁ pass) and a high pass filter for T₂ (i.e., high values of T₂ pass) (Figures 2-4).

Figure 2 SE sequence. ρ_m-filter with ln ρ_m X axis. It is an exponential filter. The positive increase in ρ_m from P to Q (horizontal green arrow) Δln ρ_m = Δρ_m/ρ_m is multiplied by the positive slope of the filter (red line) to give positive contrast (vertical blue arrow). ΔSρm=Cab. SE, spin echo.

Figure 3 SE sequence. T₁-filter with a ln T₁ X axis. It is a low pass filter. The positive increase in T₁ from P to Q (horizontal green arrow) ΔlnT1=ΔT1/T1 is multiplied by the negative slope of the filter (red line) to give negative contrast (vertical blue arrow). ΔST1=Cab. ΔST1 may be positive or negative. ΔlnT1 may also be positive or negative. SE, spin echo.

Figure 4 SE sequence. T₂-filter with a ln T₂ X axis. It is a high pass filter. The positive increase in T₂ from P to Q (horizontal green arrow) ΔlnT2=ΔT2/T2 is multiplied by the positive slope of the filter (red line) to give positive contrast (vertical blue arrow). ΔST2=Cab. SE, spin echo.

The signal levels on images are given by Eqs. [2-6] for Sρm, ST1, and ST2, and correspond to the signal or brightness of tissues seen on images.

Eqs. [2-6] can be plotted using ln X axes. When using a linear axis, changes in x (i.e., changes in ρ_m, T₁, or T₂) are absolute differences in TPs. When using a ln X axis as in Figures 2-4, small changes in x (i.e., Δln ρ_m, Δln T₁, and Δln T₂) represent fractional changes in TPs because for small differences in x, Δln x = Δx/x.

Figure 2 shows a ρ_m-filter in which the positive change in ρ_m Δln ρ_m from P to Q along the X axis (horizontal green arrow) is multiplied by the positive slope of the ρ_m-filter (red line) to give the positive change in signal ΔSρm from P to Q along the Y axis (vertical blue arrow). The change in signal ΔSρm is the absolute contrast C_ab.

With the T₁-filter shown in Figure 3, the positive change in T₁ Δln T₁ from P to Q along the X axis (horizontal green arrow) is multiplied by the negative slope of the T₁-filter (red line) to produce a negative change in signal ΔST1 from P to Q along the Y axis (vertical blue arrow). The negative change ΔST1 is the negative contrast C_ab.

The equation for C_ab for small changes in ΔT₁ and ΔST1 using a linear X axis is:

Cab=ΔST1=∂ST1∂T1⋅ΔT1[7]

where ∂ST1∂T1 is the first partial derivative of the T₁-filter with respect to T₁, which is the slope of the T₁-filter, ∙ = multiplied, and ΔT₁ is the change in T₁ using a linear X axis.

Using a ln X axis, as in Figure 3 and noting that ΔlnT1=ΔT1T1 for small changes in T₁, and that dyd(lnx) =xdydx, where x is a variable, Eq. [7] becomes:

Cab=ΔST1=∂ST1∂lnT1⋅ΔT1T1[8]

where ∂ST1∂lnT1 is the slope of the T₁-filter. This is the first partial derivative of the T₁-filter with respect to lnT1 (when using a ln X axis). ∙ = multiplied, and ΔT1T1 is the fractional change in T₁ as shown in Figure 3.

For the T₂-filter (Figure 4), the positive change in T₂ ΔlnT2=ΔT2T2 from P to Q along the X axis (horizontal green arrow) is multiplied by the positive slope of the T₂-filter (red line) and this results in the positive change in signal ΔST2 from P to Q along the Y axis and positive contrast Cab=ΔST2.

Putting the second derivative of the T₁- and T₂-filters to zero yields the T₁ or T₂ value where the slope of the T₂-filter, and therefore the contrast, is highest. For the T₁- and T₂-filters, the slope is greatest at TR = T₁ and TE = T₂ when using a ln X axis, and at TR = 2T₁ and TE = 2T₂ when using a linear X axis.

For fractional contrast C_fr = ΔS/S (rather than absolute contrast C_ab = ΔS), Eqs. [7,8] are divided by ST1 and ST2 respectively for non-zero values of ST1 and ST2.

So, for T₁ using a ln X axis:

Cfr=1ST1∂ST1∂lnT1⋅ΔT1T1[9]

and for T₂ using a ln X axis:

Cfr=1ST2∂ST2∂lnT2⋅ΔT2T2[10]

The SE sequence (multivariate model)

TP-filters can be considered separately [i.e., a univariate model for each TP (i.e., ρ_m, T₁, and T₂) alone, as in the previous section], or be combined in a multivariate model of the SE sequence as in this section. The multivariate model in Figure 5 shows the contributions to contrast of the change in each TP and the corresponding sequence weighting for each TP i.e., ρ_m, T₁, and T₂ (vertical blue arrows for each TP). The overall contrast (vertical blue arrow on the right) is the algebraic sum of the contrasts produced by each TP.

Figure 5 SE sequence with combination of ρ_m-, T₁-, and T₂-filters (multivariate model). Increases in Δρ_m/ρ_m, ΔT₁/T₁, and ΔT₂/T₂ (horizontal green arrows) are multiplied by the slopes of their respective TP-filters (red lines) to produce positive, negative, and positive ρ_m, T₁, and T₂ contrasts from their respective TP-filters (vertical blue arrows with each filter). The overall fractional contrast (vertical blue arrow on right) is the algebraic sum of the fractional contrasts produced by each of the three TP-filters (blue arrows with ρ_m-, T₁-, and T₂-filters). SE, spin echo; TP, tissue property.

From Eqs. [3-6] for small change in Δρ_m, ΔT₁, and ΔT₂, and using a ln X axis, the product rule from differential calculus gives:

ΔS=∂Sρm∂lnρmST1ST2⋅Δρmρm+Sρm∂ST1∂lnT1ST2⋅ΔT1T1+SρmST1∂ST2∂lnT2⋅ΔT2T2[11]

Normalizing Eq. [11] by dividing it by S and using Eq. [3], for non-zero values of S, Sρm, ST1, and ST2, C_fr is given by:

Cfr=ΔSS=1Sρm∂Sρm∂lnρm⋅Δρmρm+1ST1∂ST1∂lnT1⋅ΔT1T1+1ST2∂ST2∂lnT2⋅ΔT2T2[12]

Thus, the contributions of the TPs to the overall fractional contrast C_fr are, for each TP, its sequence weighting multiplied by the fractional change in the TP.

This can be expressed as:

Cfr=∑TP1STP∂STP∂lnTP⋅ΔTPTP[13]

where 1/S_TP S_TP/∂ln TP is the sequence weighting for the TP which is the slope of the TP-filter. ΔTP/TP is the fractional change in the TP. The TPs are ρ_m, T₁, and T₂ for the SE sequence. Eq. [13] is one form of the CCT of MRI. Using a ln X axis, it states that the contrast for each TP is the normalized first partial derivative with respect to ln TP multiplied by the fractional change in TP. The total fractional contrast C_fr is the algebraic sum of the contributions to contrast from each TP.

When a single TP such as T₁ is used, the contributions to T₁ contrast from the different parts of the sequence need to be of the same sign to achieve overall contrast. With two different TPs, such as T₁ and T₂, their fractional contrasts also need to be of the same sign to achieve overall synergistic contrast. If one TP contrast is negative and the other is positive a reduction in overall C_fr results.

The IR sequence

The IR sequence has an additional T₁-filter (segment) to those of the SE sequence shown in Figure 6. This IR T₁-filter is:

ST1=(1−2e−TI/T1)[14]

Figure 6 IR T₁-filters with phase-sensitive (A) and magnitude reconstruction (B) using ln T₁ axes. (A) A low pass T₁-filter; (B) a notch T₁-filter. (A) Both positive and negative values for ST1 whereas in (B) negative values are “reflected” across the X axis and become positive. The maximum slopes of the T₁-filters are shown as red lines, and are negative in both cases. IR, inversion recovery.

where ST1 is the signal from the T₁-filter, TI in the inversion time and T₁ is the longitudinal relaxation time. The IR T₁-filter is shown in phase-sensitive (ps) reconstructed form in Figure 6A where it is a low pass filter, and in magnitude (m) reconstructed form in Figure 6B where it is a notch filter.

When TI is increased, the T₁-filter shifts to the right as shown for the m form of the IR T₁-filter in Figure 7. Figure 7A (left) shows the IR T₁-filter with a short TI (TI_s) (e.g., the STIR sequence) for the brain where gray matter (G) has a higher signal than white matter (W). The slope of the T₁-filter between W and G is strongly positive.

Figure 7 The long TR IR sequence. T₁-filters for TI_s (A), TI_i (B), and TI_l (C) values. The positions of W and G are the same for each (TI). TI is increased from TI_s (A) to TI_i (B) and increased further to TI_l (C). The increase in T₁ from W to G (horizontal green arrows) is multiplied by the relevant slopes of the T₁-filters (red lines) and produces strongly positive, strongly negative, and mildly negative contrast in (A-C) respectively (vertical blue arrows), as TI is increased from left to right. TI_s, short TI; TI, inversion time; TI_i, intermediate TI; TI_l, long TI; W, white matter; G, gray matter; TR, repetition time; IR, inversion recovery.

When TI is increased to a TI_i as in Figure 7B (center) the T₁-filter is shifted to the right. W and G are fixed in the same position on the ln X axis, and W now has a higher signal than G. The slope of the T₁-filter between W and G is strongly negative.

When TI_l is increased further with a long TI_l, the filter is displaced further to the right, as in Figure 7C (right). W has a slightly higher signal than G, and the slope of the T₁-filter between them is negative but of smaller size than in Figure 7B. The sequence weighting of the T₁-filter, which is the slope or first partial derivative of the filter, is highly positive in (Figure 7A), highly negative in (Figure 7B) and slightly negative in (Figure 7C) using a TI_s (Figure 7A), a TI_i (Figure 7B), and a TI_l (Figure 7C) respectively.

Note that when the IR sequence TR is much greater than T₁, the other T₁-filter (1 − e^−TR/T1) becomes ~1 and the principal determinant of T₁ contrast is the (1 − 2e^−TI/T1) T₁-filter.

MASDIR sequences

Classification of MASDIR sequences

A classification of MASDIR sequences is shown in Table 1. They are separated into: (i) multiplied, (ii) added, (iii) subtracted, and (iv) divided groups (left column). More than one of the arithmetical operations (multiplication, addition, subtraction, and division) may be performed in a single sequence.

• MIR sequences: MIR sequences include the DIR and MP2RAGE sequences as described in the “Introduction” section;
• Added IR (AIR) sequences: one type of AIR sequence adds two magnitude (m) reconstructed sequences with different TIs and can be used with subtraction and division [see the (iv) section below];
• SIR sequences: the SIR and reverse rSIR sequences are included in this group. The SIR sequence uses the subtraction: shorter TI image minus longer TI image, and the rSIR sequence uses the reverse (r) subtraction: longer TI image minus shorter TI image;
• Divided IR (dIR) sequences (dSIR and drSIR): a central issue with division of IR sequences is the behavior of the T₁-filter if, or when, the denominator takes a value of zero. This potentially leads to infinite values of the T₁-filter. Even if zero values are avoided, there may be uncertain values when the denominator approaches zero and division becomes unreliable as a consequence of noise and/or artifacts.

The problem can largely be avoided in the case of two magnitude IR images with different TIs (e.g., SIR and rSIR images) by making the denominator the addition (or sum) of the signals from the two images. Because the T₁-filters have different TIs, when using magnitude reconstruction addition of them in the denominator is non-zero.

When the numerator is two SIR images, division normalizes the sequence so that to a first approximation, the effects of ρ_m and T₂ are eliminated. As a result, dSIR and drSIR images are essentially T₁ maps.

The bipolar dSIR T1-filter

Two magnitude IR T₁-filters with different TIs (TI_s and TI_i) are shown in Figure 8A. They are subtracted (TI_s minus TI_i) to give the SIR T₁-filter in Figure 8B. The SIR T₁-filter has a steep positive slope in the X axis region between the T₁s corresponding to the two nulling TIs, i.e., in the mD. Subtraction of the negative slope of the TI_i T₁-filter from the positive slope of the TI_s T₁-filter produces a synergistic near doubling of the positive slope in the mD of the SIR T₁-filter. The width of the mD is determined by the difference in TI between the two filters, ΔTI. Small ΔTIs give a narrow mD and large ΔTIs give a wide mD. ΔTI is the difference between the two TIs i.e., first reference, baseline or targeted tissue TI (mostly the nulling TI of the normal tissue) and the second TI chosen to match the targeted change in the sign and size of T₁. By convention ΔTI is taken as the second TI minus the first TI and may be positive or negative. ΔTI is positive for dSIR T₁-filters which have a positive slope and is negative for drSIR T₁-filters which have a negative slope (see later). If ΔTI is the same sign as the change in T₁ (ΔT₁) contrast is positive. If ΔTI and ΔT₁ are of opposite sign, contrast is negative. With the dSIR T₁-filter targeted at normal appearing white matter and small increases in T₁, ΔTI is the longer TI chosen to allow for an increase in T₁ in disease, minus the shorter TI nulling normal white matter. Thus ΔTI is positive and so is ΔT₁. This results in positive contrast.

Figure 8 SIR and AIR T₁-filters. T₁ is shown along the X axis in ms. (A) The TI_s T₁-filter (pink) and TI_i T₁-filter (blue); (B) the subtraction (STIs−STIi) IR or SIR T₁-filter; (C) the addition (STIs+STIi) IR or AIR T₁-filter. In (B) the slope of the curve in the mD is about double that of the STIs T₁-filter [pink in (A)]. In (C) the signal at T₁=0 is doubled to 2.0, and the signal in the mD is reduced to about 0.20 in the nearly linear, slightly downward sloping central part of the AIR T₁-filter (i.e., in the mD). TI_s, short TI; TI, inversion time; TI_i, intermediate TI; SIR, subtracted inversion recovery; AIR, added inversion recovery; IR, inversion recovery; mD, middle domain.

The two T₁-filters in Figure 8A can also be added as an AIR T₁-filter which is shown in Figure 8C. There are higher signals and higher slopes outside of the mD. Within the mD there is a generally low signal with a nearly linear slightly downward sloping curve.

Figure 9A shows the dSIR T₁-bipolar filter in which the SIR T₁-filter in Figure 8B is divided by the AIR T₁-filter in Figure 8C. The dSIR T₁-bipolar filter shows a very high positive slope in its mD. The sloping mD in Figure 8B (the SIR T₁-filter) was divided by the fractional value mD in the AIR T₁-filter to greatly increase the slope shown in the mD of the dSIR T₁-filter.

Figure 9 dSIR T₁-bipolar filter (A), comparison of the STIs T₁-filter with the SIR T₁-filter (B), and comparison of the STIs T₁-filter with the dSIR T₁-bipolar filter (C) for an increase in T₁ (ΔT₁) in the mD. T₁ is shown along the X axis in ms. In (A) division of the subtraction (STIs−STIi) T₁-filter by the addition (STIs+STIi) AIR T₁-filter gives (STIs−STIi)/(STIs+STIi) or SIR/AIR which is the dSIR T₁-bipolar filter. The dSIR T₁-bipolar filter shown in (A,C) has maximum and minimum values of 1 and −1 respectively and has a steeply positive slope in its mD. (B) The increase in signal (i.e., contrast) for the increase in T₁ within the mD (positive horizontal green arrow, ΔT₁) is about 0.20 for the STIs T₁-filter and about 0.42 for the SIR T₁-filter. This represents an increase in positive contrast for the SIR T₁-filter compared to the STIs T₁-filter of about two (right vertical pink and blue arrows). (C) The contrast produced by in the STIs T₁-filter by the change in T₁ (positive horizontal green arrow, ΔT₁) is about 0.20 as also shown in (B), and the contrast produced by the dSIR T₁-bipolar filter is 2.0 representing an increase in positive contrast of about 10 times (right vertical pink and blue arrows). TI_s, short TI; TI, inversion time; TI_i, intermediate TI; dSIR, divided subtracted inversion recovery; SIR, subtracted inversion recovery; AIR, added inversion recovery; mD, middle domain.

Figure 9B compares the contrast from the TI_s T₁-filter, STIs (pink) which is that of a conventional IR sequence such as MP-RAGE, to that from a SIR T₁-filter (blue). For the same positive change in T₁ (positive horizontal green arrow in the mD, ΔT₁) the vertical pink and blue arrows on the right show that the positive contrast produced by the SIR T₁-filter is about double that produced by the STIs T₁-filter.

Figure 9C compares the contrast produced by a TI_s T₁-filter, STIs (pink) to that from a dSIR T₁-bipolar filter (blue). For the same positive change in T₁ (positive horizontal green arrow in the mD, ΔT₁) the dSIR T₁-bipolar filter generates about 10 times the positive contrast produced by the STIs T₁-filter (vertical pink and blue arrows on the right). This follows directly from the CCT i.e., increasing the slope of the T₁-filter increases the contrast produced by the same change in T₁, ΔT₁.

As the second TI is moved closer to the first TI, the magnitude of ΔTI decreases, the dSIR T₁-bipolar filter becomes steeper in its mD, and the T₁ dependent contrast generated increases for the same change in T₁ (providing the change is within the mD). This is documented in Table 2. In this table, ΔTI is negative. As its magnitude decreases from 90% to 13% of the initial TI, the ratio of the contrast produced by the dSIR T₁-bipolar filter to that produced by the conventional IR T₁-filter increases from 5 to 20.

Figure 9C also shows sequence targeting. The T₁ X axis has low, middle and high domains separated by the vertical dashed lines. The T₁-filter of the conventional IR sequence (pink) has a mostly non-zero slope and is sensitive to changes in T₁ in all three domains including T₁ values from near zero to the maximum value of T₁ shown.

The dSIR T₁-bipolar filter (blue) has a generally similar slope to the conventional IR T₁-filter in the first domain and in the third domain (though of opposite sign there). In the mD however, the slope of the dSIR T₁-bipolar filter is about 10 times higher than that of the conventional IR filter. As a result, the positive contrast produced by it is 10 times greater for the same change in T₁. This increase in positive contrast is confined to the mD. To exploit the increased contrast, TI_s need to be chosen to place the mD of the dSIR T₁-bipolar filter in a position to target the change in T₁. To do this for normal white matter, the first TI of the dSIR T₁-bipolar filter needs to correspond to the normal value of T₁ of white matter to achieve nulling. The second TI needs to be chosen to target the sign and size of the change in T₁ that is expected. In Figure 9C the dSIR T₁-bipolar filter is targeted firstly to null normal tissue, and secondly to produce positive contrast from the positive change in T₁ from normal (positive horizontal green arrow, ΔT₁). The size of ΔTI is sufficient to include the change in T₁ i.e., the extent of the horizontal green arrow.

If the change in T₁ (ΔT₁) is negative as in Figure 10 (negative horizontal green arrow, ΔT₁), and ΔTI is positive (as for the dSIR T₁-bipolar filter), the resulting contrast is negative (vertical blue arrow on the right). It is about 10 times the size of the contrast produced by the conventional IR sequence (vertical pink arrow on right).

Figure 10 dSIR T₁-bipolar filter shown in Figure 9C (blue) and STIs T₁-filter (pink) for a decrease in T₁ (not an increase in T₁ as in Figure 9C). T₁ is shown along the X axis in ms. The decrease in T₁ (negative horizontal green arrow, ΔT₁) results in negative contrast for both the conventional IR T₁-filter (negative vertical pink arrow) and the dSIR T₁-bipolar filter (negative vertical blue arrow). The contrast is opposite in sign to what is seen in Figure 9C. The negative contrast is about 10 times greater for the dSIR T₁-bipolar filter compared with the conventional IR T₁-filter. TI_s, short TI; TI, inversion time; TI_i, intermediate TI; dSIR, divided subtracted inversion recovery; IR, inversion recovery.

The bipolar drSIR T₁-filter

Figure 11A shows the same two magnitude IR T₁-filters with signals STIs and STIi as in Figure 8A. In Figure 11B the r subtraction rSIR T₁-filter is shown (i.e., STIi minus STIs). This has a negative slope in the mD. Figure 11C shows addition of the two original IR T₁-filters to give the AIR T₁-filter. Figure 12A shows the rSIR T₁-filter in Figure 11B divided by the AIR T₁-filter in Figure 11C which gives the drSIR T₁-bipolar filter. This has a steep negative slope in the mD and a negative ΔTI. Figure 12B shows a comparison of the STIi T₁-filter (pink) with the rSIR T₁-filter (blue) for a decrease in T₁ as may be seen with hemorrhage, iron accumulation and GBCA administration (negative horizontal green arrow, ΔT₁). The positive contrast produced by the rSIR T₁-filter is about twice that of the STIi T₁-filter (vertical pink and blue arrows on right). Figure 12C shows a comparison of the STIi T₁-filter (pink) with the drSIR T₁-bipolar filter (blue) for the same negative change in T₁ (negative horizontal green arrow, ΔT₁). The positive contrast produced by the drSIR T₁-bipolar filter is about 10 times greater than that obtained with the STIi T₁-filter (vertical pink and blue arrows on right). In this case, the drSIR T₁-bipolar filter is targeted to produce positive contrast from the negative change in T₁.

Figure 11 rSIR and AIR T₁-filters. T₁ is shown along the X axis in ms. (A) The TI_s (pink) and TI_i (blue) T₁-filters; (B) the subtraction (STIi−STIs) or rSIR T₁-filter; (C) the addition (STIs+STIi) or AIR T₁-filter. In (B) the slope of the filter in the mD is negative and about double that of the STIi T₁-filter. In (C) the signal at T₁=0 is doubled to 2.0, and the signal in the mD it is reduced to about 0.20 as shown in the nearly linear slightly downward sloping central part of the AIR T₁-filter (i.e., in the mD). TI_s, short TI; TI, inversion time; TI_i, intermediate TI; rSIR, reverse subtracted inversion recovery; AIR, added inversion recovery; mD, middle domain.

Figure 12 drSIR T₁-bipolar filter (A), comparison of the STIi T₁-filter with the rSIR T₁-filter (B), and comparison of the STIi T₁-filter with the drSIR T₁-bipolar filter (C) for a decrease in T₁ in the mD. T₁ is along the X axis in ms. In (A) division of the subtraction rSIR (STIi−STIs) T₁-filter by the AIR T₁-filter gives (STIi−STIs)/(STIs+STIi) or rSIR/AIR which is the drSIR T₁-bipolar filter. The drSIR T₁-bipolar filter in (A,C) has maximum and minimum values of 1 and −1 respectively and has a steeply negative slope in its mD. In (B) the increase in signal (i.e., contrast) for the decrease in T₁ within the mD (negative horizontal green arrow, ΔT₁) is about 0.20 for the STIi T₁-filter (positive vertical pink arrow) and about 0.42 for the rSIR T₁-filter (vertical blue arrow). This represents an increase in contrast for the rSIR T₁-filter compared with the STIs T₁-filter of about two (right vertical pink and blue arrows). In (C) for the same decrease in T₁ (negative horizontal green arrow, ΔT₁) the contrast with the STIi T₁-filter is about 0.20 as in (B) (vertical pink arrow), and the contrast with the drSIR T₁-bipolar filter is 2.0 (vertical blue arrow) representing an increase in positive contrast of about 10 times. TI_s, short TI; TI, inversion time; TI_i, intermediate TI; drSIR, divided reverse subtracted inversion recovery; rSIR, reverse subtracted inversion recovery; AIR, added inversion recovery; mD, middle domain.

If the change in T₁ (ΔT₁) is positive, as in Figure 13, then the negative ΔTI of the drSIR T₁-bipolar filter, coupled with the positive ΔT₁ means that the contrast is negative (vertical blue arrow on right). It is about 10 times the size of the negative contrast produced by the conventional IR sequence (vertical pink arrow on right).

Figure 13 drSIR T₁-bipolar filter (blue) and conventional IR T₁-filter (pink) as shown in Figure 12C, but with an increase in T₁, not the decrease in T₁ shown in Figure 12C. T₁ is shown along the X axis in ms. The increase in T₁ (positive horizontal green arrow, ΔT₁) results in negative contrast for both the conventional IR T₁-filter (negative vertical pink arrow) and the drSIR T₁-bipolar filter (negative vertical blue arrow). This contrast is of the opposite sign to what is seen in Figure 12C. With the drSIR T₁-bipolar filter, the negative contrast is about 10 times greater than with the conventional IR T₁-filter. TI_s, short TI; TI, inversion time; TI_i, intermediate TI; drSIR, divided reverse subtracted inversion recovery; IR, inversion recovery.

Synergistic contrast MRI (scMRI)

Synergistic contrast arises in two main ways:

• A single TP can be used twice or more in a sequence to increase contrast. For example, changes in T₁ can be used in the T₁ dependent TR segment of an IR sequence as well as the T₁ dependent TI segment. Changes in T₁ are also used twice in the SIR sequence when employing the subtraction: TI_s T₁-filter minus TI_i T₁-filter. T₁ changes are also used twice in the rSIR T₁-filter with the reverse subtraction. The synergistic T₁ contrast from the SIR and rSIR sequences can be increased further by using T₁ changes 3–4 times by employing division with them as for the dSIR and drSIR sequences;
• Two or more different TPs can also be used to produce synergistic contrast as was first described with the STIR sequence in 1985 (7). Clinical pulse sequences have a basic structure consisting of ρ_m, T₁, and T₂-filters as seen in SE sequences. There are additional options which can be added such as those for T₁ dependent inversion pulses and apparent diffusion coefficient (D*) sensitization. In many circumstances ρ_m is a minor determinant of contrast and T₁, T₂, and D* are major determinants.

The most common change in TPs in disease is concurrent increases in ρ_m, T₁, T₂. In this situation with the SE sequence, the contrast developed by an increase in T₁ is negative while the contrast developed by an increase in T₂ is positive, so that simultaneous increases in T₁ and T₂ produce opposed contrast and the net, or overall, contrast is reduced. To avoid this problem, T₁-weighted SE sequences use a short TE to minimize the opposed T₂ contrast, and T₂-weighted SE sequences use a long TR to minimize the opposed T₁ contrast. The dominant source of contrast in the resulting sequences is then a single TP, i.e., T₁ or T₂ and the sequences are described as T₁-weighted or T₂-weighted respectively. T₁ and T₂ are each used only once to create contrast in both sequences, and so the sequences are not synergistic for T₁ and T₂ contrast.

In particular circumstances, such as certain forms of the STIR and the DIR sequences, the T₁ contrast produced by an increase in T₁ is positive, and so is the T₂ contrast produced by an increase in T₂. The effects of concurrent increases in T₁ and T₂ are therefore synergistic, and typically result in high positive lesion contrast.

The synergistic contrast produced above from (i) a single TP, and/or (ii) two or more different TPs can be supplemented by increasing or decreasing signals from normal tissues and/or fluids. There may be little contrast between high signal lesions and high signal fat, long T₂ tissues, or fluids. Reduction in the normal signal from these tissues or fluids [using the same or different TPs as those used to create the original synergistic contrast in (i) and/or (ii)] can increase the contrast between the high signal lesions and the zero or low signal suppressed tissues and/or fluids.

Contrast at tissue boundaries

In the previous sections of this paper, contrast between two pure voxels each containing a pure sample of a different tissue has been considered, but there has been no reference to the location of the voxels, contrast at boundaries between two voxels, or contrast within transitional regions between the two pure voxels where there are mixed voxels containing mixtures of the two different tissues (i.e., there are partial volume effects).

In general terms, contrast detectability at boundaries between two pure voxels with different values of S can be related to contrast C_ab = ΔS or C_fr = ΔS/S divided by the distance Δx between the two pure voxels. Boundaries are more detectable when contrast is high and Δx is low, and less detectable in the opposite situation, where contrast is low and Δx is high.

In boundary regions between two pure tissues P and Q it is useful to define the tissue fraction (f) which is the proportion of the second tissue Q in a mixed voxel which contains a mixture of both tissues. The proportion of the other tissue P in the mixed voxel is then (1 − f).

The T₁ of a mixture of the two tissues (P and Q) in a voxel can be expressed as a function

T1P,Q=Γ(T1P,T1Q,f)[15]

where T_1P,Q is the T₁ of the mixture, T_1P is the T₁ of P, and T_1Q is the T₁ of Q.

It is also useful to consider ∂f∂x the change in tissue fraction with distance x. This may be gradual and correspond to a low value of ∂f∂x, or be abrupt and correspond to a higher value of ∂f∂x.

Using the chain rule from differential calculus, normalized contrast over distance for T₁ is given by:

1ST1⋅ΔSΔx≈1ST1⋅dSdx=1ST1⋅∂ST1∂T1⋅∂T1∂f⋅∂f∂x[16]

where 1ST1⋅ΔSΔx is the change in fractional contrast with distance x, ST1 is the T₁-filter signal, dSdx is a measure of detectable contrast at a boundary, ∂ST1∂T1 is the first partial derivative of ST1 with respect to T₁, i.e., the sequence weighting, ∂T1∂f is the change in T₁ with tissue fraction (f), and ∂f∂x is the change in f with distance x (Table 3).

Thus, contrast at a boundary depends on the sequence weighting, the change in T₁ with tissue fraction and the change in tissue fraction with distance. The change in tissue fraction with distance may be abrupt in one plane, but gradual in another plane.

At a boundary between two pure tissues, the T₁s of mixed voxels typically span the range of T₁ values between those of the two pure tissues. If the T₁-bipolar filter has a narrow mD so that a T₁ value between those of white and gray matter produces a peak of the T₁-bipolar filter S_W,G, as in Figure 14A, this results in a high signal narrow line at the boundary between white and gray matter. This high signal boundary is inside the brain and is obtained using a narrow mD. If a wide mD is used as in Figure 14B, the peak signal S_G,CSF occurs at a T₁ between those of gray matter and CSF where there are mixtures of gray matter and CSF in voxels. As a result, the high signal boundary appears outside the brain. A boundary inside the brain is shown in Figure 15 and one outside the brain is shown in Figure 16.

Figure 14 This figure shows a narrow mD T₁-bipolar filter in (A) and a wide mD T₁-bipolar filter in (B). (A) A narrow mD dSIR T₁-bipolar filter (blue) with a mD extending from W to a T_1W,G between W and G (blue), and a white matter nulled IR T₁-filter e.g., MP-RAGE (pink). The peak signal (S_W,G) with the dSIR T₁-bipolar filter appears between W and G along the X axis (in ms) where there is a partial volume effect between W and G producing a T_1W,G with a value of T₁ between those of W and G. This results in a high signal S_W,G in (A) and corresponds to the high signal boundary between W and G shown in Figure 15. (B) A wide mD dSIR T₁-bipolar filter with a mD extending from W to beyond G (blue) and a white matter nulled T₁-filter e.g., MP-RAGE (pink). The peak signal S_G,CSF with the dSIR T₁-bipolar filter appears between G and CSF at a T₁ which is higher than that of G and corresponds to a partial volume effect between G and CSF (the T₁ of CSF is off the X axis to the right). This results in a high signal between G and CSF S_G,CSF in (B), and corresponds to the high signal at the junction between cortical G and CSF just outside the brain shown in Figure 16. W and G are in the same position in (A,B). W, white matter; G, gray matter; CSF, cerebrospinal fluid; mD, middle domain; dSIR, divided inversion recovery; IR, inversion recovery; MP-RAGE, magnetization prepared-rapid acquisition gradient echo.

Figure 15 Narrow mD dSIR image with the first TI nulling W and the second TI less than that needed to null G. Narrow high signal boundaries are seen between W and G as well as between W and CSF (white arrows). mD, middle domain; dSIR, divided subtracted inversion recovery; TI, inversion time; W, white matter; G, gray matter; CSF, cerebrospinal fluid.

Figure 16 Wide mD dSIR image of the brain using a wide mD with the first TI nulling W and the second TI longer than that needed to null cortical G (TI_s =350 ms, TI_i =800 ms, ΔTI =−130% at 3T). High signal boundaries are seen just outside of the brain between G and CSF (white arrows). mD, middle domain; dSIR, divided subtracted inversion recovery; TI, inversion time; W, white matter; G, gray matter; TI_s, short TI; TI_i, intermediate TI; CSF, cerebrospinal fluid.

The width of boundaries seen on dSIR images can be changed by changing the width of the mD. Change from a narrow mD (Figure 17A) to an intermediate mD (Figure 17B) widens the peak region of the T₁-bipolar filter and increases the width of the boundary. Figure 18 shows a comparison of an image obtained with a narrow mD (Figure 18A) with one obtained using an intermediate mD (Figure 18B). The white matter gray matter boundaries are narrow in Figure 18A and intermediate in Figure 18B (compare the paired white arrows in Figure 18A,18B).

Figure 17 This figure shows a narrow mD T₁-bipolar filter in (A) and an intermediate mD T₁-bipolar filter in (B). In (A) a narrow mD dSIR T₁-bipolar filter (blue) with the first TI nulling W and the second TI nulling a T_1W,G between W and G resulting from a mixture of the two tissues is shown. T₁ is shown along the X axis in ms. The pink T₁-filter is that from a white matter nulled IR sequence e.g., MP-RAGE. The signal S_W,_G is from a mixture of W and G with a T₁ between those of W and G, and is greater than that of the signal from W S_W, and G S_G. It corresponds to the line between W and G seen inside the cortex in Figure 18A. In (B) an intermediate mD dSIR T₁-bipolar filter with the first TI nulling W and the second TI nulling a mixture of W and G with a T₁ between W and G with a higher value than the T₁ for nulling the mixture of W and G in (A) is shown. The signal from the mixture S_W,_G in (B) is greater than that of S_W and S_G. The dSIR T₁-bipolar filter in (B) is wider than the dSIR T₁-bipolar filter in (A) and this corresponds to the wider boundaries between W and G, and between W and CSF seen in Figure 18B compared with Figure 18A. W and G are in the same position as in Figure 18A,18B. W, white matter; G, gray matter; mD, middle domain; dSIR, divided inversion recovery; TI, inversion time; IR, inversion recovery; MP-RAGE, magnetization prepared-rapid acquisition gradient echo; CSF, cerebrospinal fluid.

Figure 18 This figure shows a narrow mD dSIR image in (A) and an intermediate mD dSIR image in (B) in a patient with small vessel disease in white matter. In (A) a narrow mD dSIR image (TI_s =540 ms, TI_i =640 ms, ΔTI =18% at 3T) (with about 15 times amplification of contrast) is compared to a standard IR sequence such as MP-RAGE. (B) shows an intermediate mD dSIR image (TI_s =540 ms, TI_i =840 ms, ΔTI =56%). In (A) the slope of the T₁-filter is high, and the high signal boundaries between white matter and gray matter, and between white matter and CSF are narrow (white arrows). In (B) where the slope of the T₁-bipolar filter is lower and its peak is wider, the high signal boundaries between white matter and gray matter, and between white matter and CSF are wider compared to (A) [see corresponding pairs of white arrows in (A,B)]. mD, middle domain; dSIR, divided inversion recovery; IR, inversion recovery; MP-RAGE, magnetization prepared-rapid acquisition gradient echo; TI_s, short TI; TI, inversion time; TI_i, intermediate TI; CSF, cerebrospinal fluid.

In using a dSIR sequence with white matter nulled by the first TI, when the second TI is increased and approaches that for nulling gray matter, the contrast between the high signal boundary and gray matter is reduced. When the second TI becomes the same as that for nulling gray matter, the high signal boundary merges with gray matter. To create a high contrast boundary with gray matter (as well as with white matter) in this situation, the second TI needs to be significantly shorter than the TI which nulls gray matter.

The high signal boundaries between white matter and gray matter on dSIR and drSIR images are characteristic of this type of imaging. Their presence provides validation of the use of T₁-bipolar filters to describe the signal and contrast behavior of the dSIR and drSIR sequences.

T₁ maps

The signals S_s and S_i for two long TR IR magnitude T₁-filters with TI_s and TI_i as shown in Figures 8A,11A are respectively given by:

STIs=1−2e(−TIS/T1)[17]

and

STIi=1−2e(−TIi/T1)[18]

Performing the subtraction: magnitude of the IR signal |STIs| in Eq. [17] minus magnitude of the IR signal |STIi| in Eq. [18] gives the signal of the SIR filter SSIR which is equal to −STIs−STIi i.e.,:

SSIR=2e(−TIS/T1)+2e(−TIi/T1)−2[19]

Addition of the magnitudes of the two IR signals |STIS| and |STIi| in Eqs. [17,18] S_AIR is equal to −STIS+STIi i.e.,:

SAIR=2e(−TIS/T1)−2e(−TIi/T1)[20]

Division of the signal of the subtraction T₁-filter S_SIR in Eq. [17] by the signal of the addition T1-filter S_AIR in Eq. [18] gives the signal of the S_dSIR T₁-filter:

SdSIR=e(−TIS/T1)+2e(−TIi/T1)−1e(−TIS/T1)−e(−TIi/T1)[21]

While this expression is accurate, it does not provide easy insight into the properties of the dSIR T₁-filter. To do this, a linear equation of the form y = mx + c between the end points of the mD can be produced by fitting a straight line between the first and last points of the mD (i.e., first point x = TI_s/ln 2 and y = −1, and last point x = TI_i/ln 2 and y = + 1). It is an approximation to the dSIR T₁-filter in the mD, so S_dSIR in the mD is given by:

SdSIR≈ln4ΔTIT1−ΣTIΔTI[22]

where ∆TI = TI_i − TI_s (i.e., second longer TI minus first shorter TI which is positive) and ΣTI = TI_s + TI_i. The convention for ΔTI is to define it by the subtraction: second TI minus first TI so ∆TI is positive for dSIR T₁-bipolar filters and negative for drSIR T₁-bipolar filters. The sign of ∆TI depends on whether the second TI is greater or less than the first TI. Note that because ΔTI is positive, and the slope ln4ΔTI in Eq. [22] is positive (e.g., Figure 9C) the contrast is positive.

The same approach applies to the drSIR T₁-bipolar filters where the first point is x = TI_i/ln 2 with y = −1, and the second point is x = TI_s/ln 2 with y = 1. S_drSIR in the mD is given by:

SdrSIR≈ln4ΔTIT1−ΣTIΔTI[23]

where ΔTI = the second TI, TI_s − the first TI, TI_i which is negative, and ΣTI=TIs+TIi. Since ΔTI is negative, the slope ln4ΔTI in Eq. [23] is negative (e.g., Figure 12C) and the contrast is positive.

The expressions in Eqs. [22,23] capture four key features of the dSIR and drSIR T₁-bipolar filters, firstly, the near linear change in signal with T₁ in the mD, secondly, the T₁-bipolar filters have slopes equal to ln4ΔTI, and thirdly, the T₁-bipolar filters show high contrast sensitivity for small changes in T₁ when the size of ∆TI is small (since ΔSdSIR≈ln4ΔTIΔT1 and ΔSdrSIR≈ln4ΔTIΔT1). As ΔTI decreases in magnitude, amplification of contrast increases (Table 2). Fourthly the equations can be used to map T₁ in the mD since for S_dSIR and S_drSIR:

T1≈ΔTIln4SdSIR−ΣTIln4[24]

T1≈ΔTIln4SdrSIR−ΣTIln4[25]

The S_dSIR and S_drSIR maps typically show high contrast and high spatial resolution (e.g., Figure 19).

Figure 19 Narrow mD dSIR image/T₁ map (TI_s =540 ms, TI_i =640 ms, ΔTI =18%, TR =6,000 ms) in a patient with small vessel disease showing T₁ values within the mD on the gray-scale at the right. Image dimensions in voxels are shown along the X and Y axes of the image. The T₁ gray-scale covers the mD which is within white matter. The gray-scale shows T₁ values over a range of 144 ms with the dark low signal representing the shorter normal T₁ value of white matter of 780 ms (i.e., 540/ln 2 ms) and higher signal representing abnormal increased T₁ values of white matter up to the maximum of 924 ms (i.e., 640/ln 2 ms). The full display gray-scale ranges from +1 to −1 and linearly covers a 144 ms difference in T₁. With conventional T₁ maps of the brain and CSF the gray-scale range typically covers 2,000–4,000 ms. Thus, there is much greater display sensitivity to differences in T₁ in the mD with the dSIR image than with conventional T₁ maps. Lesions with T₁ values greater than the maximum in the mD (i.e., greater than 924 ms) “overshoot” and have a mid-gray center (where T₁ values shown on the gray-scale are unreliable) and are surrounded by high signal boundaries. T₁ mapping is only valid in the mD. If the TR is short, the values may be low and need correction. In this case, the source images were obtained using a long TR IR sequence. mD, middle domain; dSIR, divided inversion recovery; TI_s, short TI; TI, inversion time; TI_i, intermediate TI; CSF, cerebrospinal fluid; TR, repetition time; IR, inversion recovery.

The linear approximation is only valid in the mD. Also, it is assumed that TR is long otherwise T₁ values may require correction for incomplete recovery of longitudinal magnetization during TR. It is also assumed that the nulling of the baseline tissue is accurate.

GBCA enhancement

The effect of GBCA is to decrease T₁ (i.e., produce a negative ΔT₁) so, in order to see positive contrast enhancement, drSIR sequences are used as shown in Figures 11,12.

The baseline tissue may be normal or abnormal. In the latter case, its T₁ may be prolonged and so the initial TI may need to be lengthened to correspond to this and thus be greater than that for normal tissue.

There is interest in both the image contrast produced by the GBCA and the specific effect of the agent itself. The image contrast may be demonstrated by appropriate choice of ΔTI. The specific effect of the agent can be found from the subtraction: post minus pre with the same IR sequence i.e., the baseline nulling sequence.

It is possible to choose several TIs so that image contrast increases can be observed in several tissues simultaneously.

The process of intravenous injection of a GBCA usually displaces the head between pre and post GBCA acquisitions relative to the scanner. 3D isotropic acquisitions with rigid body registration are a preferred way to deal with the resulting misregistration.

The focus is on subtle GBCA contrast enhancement including the types that delayed and double dose contrast agent regimes have been used for. It may also be possible to use lower doses of GBCAs.

Dynamic contrast enhancement and modeling of GBCA distribution may be improved by having greater sensitivity to T₁ shortening produced by smaller quantities of GBCAs early in the enhancement process.

GBCA enhancement may be seen in CSF using the T₂-FLAIR sequence as a baseline, but inflow of CSF during TI may produce shortening of the effective T₁ of CSF and be a confounder. This can be addressed with a thicker slice, or non-slice selective inversion pulses (24).

Serial studies

In general terms, there is no special premium in clinical MRI in demonstrating high contrast lesions with even greater contrast. The emphasis with MASDIR sequences is on demonstrating contrast in situations where there are only small changes in TPs and, as a consequence, little or no contrast is seen with conventional sequences. The emphasis is therefore on imaging regimes which detect small changes in TPs. Ideally these can allow disease to be monitored over time to follow its natural history and the effects of treatment.

Increased sensitization in the mD is produced by a decreased width of the mD and decreased magnitude of ΔTI. This is particularly appropriate for detecting small changes in T₁ from normal to abnormal in specific tissues. These changes may be seen in earlier stages of disease as well as in more subtle forms of disease.

In addition to contrast due to differences or changes in T₁ as above, magnetic resonance (MR) images may show differences in signal (or contrast), due to differences in the spatial properties of tissues e.g., their size, site, shape and surface. This applies to normal and abnormal tissues.

The changes from normal in signal and space seen in a single image may vary over time in serial studies as part of the natural history of the disease and/or the result of therapy. In situations where the changes in signal and/or space are small, rigid body registration can accurately align images obtained on two or more examinations so that genuine changes can be distinguished from artefactual differences due to variation in slice alignment at the different examinations (i.e., misregistration).

This has been performed with 3D isotropic spoiled gradient echo (GE) sequences, and a system of interpreting subtracted images has been described (25). MASDIR sequences using 3D MP-RAGE or brain volume (BRAVO) type data acquisitions with rSIR or drSIR image processing offer increased sensitivity to changes in T₁ compared with spoiled GE sequences. They also offer high signal boundaries to improve detection of changes in the spatial properties of tissues. This option is not available with spoiled GE sequences.

A major advantage with serial studies is that the patient may act as her/his own control with the initial images providing a baseline to recognize small changes in T₁ and/or image spatial properties on subsequent examinations using registration. These might not be recognizable on a single image seen in isolation.

Quantitation

The fact the dSIR and drSIR images can directly provide values of T₁ in the mD is valuable for quantitation. This can include decrease in T₁ due to GBCA enhancement. In addition, the high signal boundaries are of value in quantifying spatial properties of normal tissues and lesions such as the volume of lesions or parts of them (as well as changes in volumes) in serial studies.

Summary of key concepts affecting the understanding and use of rSIR and drSIR sequences

Targeting

• In this work, tMRI is typically aimed at small changes in T₁ and the spatial properties from normal in single tissues;
• The tissues of interest are normal or near normal appearing white or gray matter;
• The changes in T₁ and spatial properties may arise from disease of the brain or other causes (e.g., physiological changes, contrast agents and drugs);
• The normal or near normal appearances of white or gray matter are usually those shown with MP-RAGE, T₂-wSE, and/or T₂-FLAIR sequences;
• For small changes in T₁ from normal, narrow mD dSIR and drSIR sequences can usefully produce contrast up to about 15 times greater than that generated by conventional MP-RAGE sequences, and so make the effects of small changes in T₁ visible on dSIR and drSIR images when they are not seen on conventional images;
• The dSIR and drSIR sequences need to be targeted to the T₁ of the normal tissue for nulling as well as the sign and size of the change in T₁ being sought. This is done by appropriate choice of their TIs, i.e., the nulling TI and the difference in TI, ΔTI are matched to the change in T₁, ΔT₁.

Mathematical modeling

• The modeling employs TP-filters which are plots of signal against TP or ln TP for segments of sequence or sequences;
• The contrast generated by a small change in a TP is the change in that TP multiplied by the slope of its TP-filter. The overall fractional contrast produced by a sequence is the algebraic sum of the contrasts generated by each TP in that sequence. This is expressed as the CCT. It is derived from the Bloch and Torrey equations using the product rule of differential calculus;
• The single TP T₁ is used 3–4 times to generate synergistic T₁ contrast with the dSIR and drSIR T₁-filters;
• The bipolar T₁-filters of the dSIR and drSIR sequences are used to describe the targeting, signal, contrast, boundaries, T₁ mapping and GBCA enhancement of the two sequences;
• The contrast at boundaries (change in signal ΔS with distance x) is the product of the sequence weighting (slope of the T₁-filter), the change in T₁ with tissue fraction (f) and the change in f with distance x. This follows from the chain rule of differential calculus;
• In the mD of the dSIR and drSIR T₁-filters, there is a near linear relationship between signal and T₁ so dSIR and drSIR images can be calibrated as T₁ maps in the mD. When the magnitude of the difference in TI (ΔTI) is decreased, contrast amplification is increased until the stage is reached where images become noise and/or artefact limited.

Radiology

• Contrast: contrast can be targeted at normal or normal appearing white or gray matter and can be produced where it is particularly needed i.e., for improving visualization of subtle disease where there are only small changes in T₁ from normal, so that contrast is not shown, or only poorly shown, with conventional sequences;
• Boundaries: the dSIR sequence can produce high signal, often high contrast boundaries between white and gray matter, between white matter and CSF, between cortical gray matter and CSF, as well as between normal and abnormal tissues;
• T₁ maps: because of the normalization of signals with dSIR and drSIR images, ρ_m and T₂ effects are largely eliminated so dSIR and drSIR images are essentially T₁ maps. There is a near linear relationship between signal and T₁ in the mD which can provide direct reading of T₁ values in areas of interest;
• GBCA enhancement: the narrow mD drSIR sequence is highly sensitive to reductions in T₁ produced by GBCAs;
• Serial studies: using rigid body registration of isotropic 3D images, changes in T₁ can be demonstrated. On registered images, the high signal boundaries produced by the dSIR and drSIR sequences can also be used to demonstrate changes in the spatial properties (e.g., size, shape, site, surface) of normal structures and lesions over time in serial MR examinations;
• Quantitation: dSIR and drSIR images provide direct measurement of T₁ in the mD. This can be extended to GBCA enhancement including modeling of its distribution. T₁ measurements can be supplemented by quantitation of spatial features using the high signal boundaries produced by dSIR and drSIR sequences.

Implementation of dSIR and drSIR sequences and their failure modes

Implementation

The source sequences for dSIR and drSIR images are typically conventional two-dimensional (2D) IR fast SE (FSE) and 3D IR GE (e.g., 3D MP-RAGE, BRAVO, or 3D fast field echo) sequences which are available on most clinical MR systems. The TEs are typically short e.g., 5–10 ms for FSE and 1–5 ms for GEs (Table 4). Comparable or slightly higher spatial resolution conventional sequences were performed for comparison using the same types of data acquisition.

In targeting the source IR images, the initial task is to select the tissue of primary interest and determine the TI needed to null it (Figure 20). The choice of TI may be based on a knowledge of tissue T₁s and nulling TIs, experience with similar cases and recognition of the technical factors which change the nulling TI as well as conditions which change the T₁ of tissues to be nulled [see Tab. 8 in (23)].

Figure 20 Targeting of dSIR (A) and drSIR (B) T₁-bipolar filters for small changes in T₁ from normal. T₁ is shown along the X axis in ms. In (A) the dSIR T₁-bipolar filter nulls normal white matter with a T₁ W_N using the first TI, and is targeted for the location and the size of the mD using the second longer TI for a small increase in the normal white matter T₁ from W_N to W_A (positive horizontal green arrow). ΔTI is positive. This produces positive contrast (blue arrow on right). In (B) the drSIR T₁-bipolar filter nulls normal white matter with T₁ W_N using the first TI. The location and size of the mD is targeted for a small decrease in the white matter T₁ from W_N to W_A (negative horizontal green arrow) using the second shorter TI. ΔTI is negative. This produces positive contrast (blue arrow on right). dSIR, divided subtracted inversion recovery, W_N, white normal; G_N, gray normal; W_A, white abnormal; drSIR, divided reverse subtracted inversion recovery; TI, inversion time; mD, middle domain.

In general, at least initially, it is worth testing to ensure that the tissue of interest is nulled and, if there is doubt, when seeking changes that increase T₁ use a TI slightly less than the expected value. Errors in this direction generally have a benign effect on contrast.

The next decision is the expected sign of the change in T₁ i.e., positive or negative. This determines whether the second TI used is higher (increase in T₁) or lower (decrease in T₁ than the nulling TI. After this, a decision needs to be made on the magnitude of the difference in TI i.e., ΔTI. Smaller TIs give higher amplification of contrast but if the change in T₁ takes it outside the mD this results in overshoot. ΔTI determines the width of the mD which may be narrow, intermediate or wide. For white matter, using a dSIR sequence and seeking an increase in T₁ with a longer second TI, a narrow ΔTI is about 20% to 40%, an intermediate ΔTI is about 40% to 60%, and a wide ΔTI is about 80% or more. The objective is to match the position and size of the mD to the position, sign and size of the change in T₁ so that the sequence is correctly targeted.

When targeting white matter, the choice of narrow, intermediate or wide mD also determines the location of high signal boundaries. If the second TI is less than that needed to null cortical gray matter, the high signal boundary will be within the brain between white matter and cortical gray matter. If the second TI is greater than that needed to null cortical gray matter the boundary will be outside of the brain at the junction between cortical gray matter and CSF.

For other tissues the location and width of the high signal boundaries follows from the same considerations as in Figures 14,17. Narrow boundaries are found with small magnitudes of ΔTI and narrow mDs. Wider boundaries are found with larger magnitudes of ΔTI and wider mDs.

The image processing uses the images acquired with the two different TIs, and does the subtraction: shorter TI image minus longer TI image to give SIR images and the reverse subtraction: longer TI image minus shorter TI image to give rSIR images. The two original images are then added to give an AIR image which is used in the denominator to divide the SIR and rSIR images to give dSIR and drSIR images respectively. This is performed for both 2D and 3D images.

For GBCA enhancement there is usually displacement of the patient’s head between pre and post contrast images relative to the MR system, so 3D isotropic GE acquisitions are used, and rigid body registration is used to align the pre and post images and allow subtraction without misregistration. drSIR sequences are used and the initial nulling TI for contrast enhancement may need to be prolonged if a lesion with an increased T₁ is being studied, or shortened if a lesion with a decreased T₁ is being studied (Figure 21). Subtractions performed after GBCA administration may be targeted at (i) image contrast and (ii) specific effects of the GBCA.

Figure 21 Targeting of drSIR T₁-bipolar filters for GBCA enhancement in lesions with an increase in T₁ (A) and a decrease in T₁ (B). T₁ is shown along the X axis in ms. In (A) the lesion in white matter has increased its T₁ from W_N to W_Apre (upper positive horizontal green arrow). The drSIR T₁-bipolar filter is targeted at a decrease in T₁ due to GBCA enhancement from W_Apre to W_Apost (lower negative horizontal green arrow). ΔTI is negative. This produces positive contrast (vertical blue arrow on right). In (B) the lesion in white matter has decreased its T₁ from W_N to W_Apre (upper negative horizontal green arrow). The drSIR T₁-bipolar filter is matched for a further decrease in T₁ with GBCA enhancement from W_Apre to W_Apost (lower negative horizontal green arrow). ΔTI is negative. This produces positive contrast (vertical blue arrow on right). Thus, tMRI for GBCA enhancement may require the use of additional longer and shorter TIs to bracket the expected reduction in T₁. drSIR, divided reverse subtracted inversion recovery; W_Apost, white abnormal post-enhancement; W_N, white normal; W_Apre, white abnormal pre-enhancement; G_N, gray normal; GBCA, Gadolinium based contrast agent; tMRI, targeted magnetic resonance imaging; TI, inversion time.

In serial studies performed at different times, in addition to changes in signal and contrast there may be changes in space (e.g., change in site, shape, size and surface of normal tissues or lesions as with growth or regression of a tumor). If the changes are relatively small, rigid body registration can also be used to precisely align images obtained at different times. This is often the situation with dSIR and drSIR images when they are used for detection of small changes in T₁ and/or spatial properties. If changes are large, non-rigid body registration may be needed. This is less precise than rigid registration, but if the changes are large, image interpretation is usually straightforward.

Failure modes

Failure modes need to be recognized, preferably at an early stage so the rest of the examination is not compromised.

• The commonest problem is failure to null the normal tissue of primary interest. Usually, the TI is too long and this reduces the contrast produced on dSIR images when nulling white matter and seeking an increase in T₁ in disease. The precise value of TI for nulling can vary for technical reasons e.g., with field strength, the value of TR, the recovery time, the efficiency of the B₁ pulse, B₁ homogeneity, data collection (GE vs. FSE) use of fast recovery and fat saturation. The T₁ of the tissue to be nulled can vary with subject age, location in the brain etc. Cancellation lines are seen at the boundary between two tissues on magnitude images when the longitudinal magnetization of one tissue is positive and the other is negative. They occur when white matter is being nulled if the TI being tested for nulling is too long so that the 90° pulse and sampling is too late. The white matter longitudinal magnetization (M_z) is then positive (not zero as it would have been if the white matter had been nulled) and gray matter M_z is negative. If the TI is too short, both the white and gray matter have negative M_zs. As a result, there is signal on magnitude images, but no cancellation line between the two tissues;
• It is also possible to choose the wrong sign for the change in T₁ in disease e.g., be set up for an increase in T₁ and the disease produces a decrease in T₁;
• The mD may be too narrow leading to signals which overshoot the mD of the dSIR or drSIR sequences. This occurs when the changes in T₁ are greater than expected. With dSIR sequences set up for an increase in T₁, it typically results in a high signal around the lesion with intermediate signal inside the boundary;
• The mD may be too wide leading to low contrast for the change in T₁;
• The boundary location and width may be inappropriate. If the first TI is chosen to null white matter, and the second TI is chosen to null gray matter, the boundary between the two may be isointense with gray matter and so may not be apparent;
• Misregistration is usually obvious, with for example high and low signals at lateral ventricular boundaries. Correction of misregistration with 2D images may be possible to a reasonable degree with shifting of the second image by a few voxels and/or fractions of a voxel. Rigid body registration of isotropic 3D images is usually a more satisfactory solution;
• Partial volume effects from high signal boundaries may simulate lesions particularly with 2D acquisitions using a thick slice e.g., 3–4 mm compared with the typical 1 mm slice thickness of 3D acquisitions;
• Errors in T₁ may arise from:
  • inaccurate tissue nulling;
  • use of a short TR;
  • measurement outside of the mD;
• It may be useful to label accurate T₁ values in the mD on images by color, or use a mask to separate them from inaccurate T₁ values outside of the mD;
• The MP-RAGE sequence has limitations on the TI needed to achieve white matter nulling imposed by the minimum TR which are not found with the BRAVO sequence. Increasing the TR may resolve the problem by making shorter TIs accessible.

Examples

Application of these principles can be seen in a case of MS (Figure 22) which compares a T₂-wSE image (Figure 22A) with a narrow mD dSIR image (Figure 22B). This image (Figure 22B) is targeted to null normal white matter and produce high positive contrast from small increases in white matter T₁ from normal. No abnormality is seen in (Figure 22A) but three focal lesions are seen in (Figure 22B) (long thin arrows). One is in white matter; another is at the junction between white and gray matter (anterior); and the other is at the junction between white and gray matter but mostly in gray matter (left). Localization of lesions is helped by the well defined high signal white matter gray matter boundaries. High signal is seen in the corticospinal tracts (short thin arrows). Normal white matter is seen laterally and has a low signal (dark) appearance in (Figure 22B) (thick arrows). Intermediate signal is seen in the more medial normal superior longitudinal fasciculi in (Figure 22B).

Figure 22 Case of MS. Comparison of 2D T₂-wSE (A) and narrow mD dSIR (B) images using similar spatial resolutions and slice thicknesses. The narrow mD dSIR sequence is targeted to null normal white matter and produce high positive contrast from small increases in T₁ from the normal T₁ of white matter. No abnormality is seen on the T₂-wSE image but three focal lesions are seen on the dSIR image (long thin arrows). The corticospinal tracts are also abnormal (short thin arrows). The normal superior longitudinal fasciculi are of intermediate signal in (B). More peripheral white matter appears dark and much of it is normal in (B) (thick arrows). Thus, the lateral peripheral normal appearing white matter in (A) is mostly normal in (B). A high signal boundary is seen between white matter and cortical gray matter as well as at the white matter-CSF boundary around the lateral ventricles. T₂-wSE, T₂-weighted spin echo; mD, middle domain; dSIR, divided subtracted inversion recovery; MS, multiple sclerosis; 2D, two-dimensional, CSF, cerebrospinal fluid.

Figure 23 is a higher slice in the same case as in Figure 22 where a T₂-wSE image is compared with a narrow mD dSIR image. No abnormality is seen on the T₂-wSE image (Figure 23A) but a focal lesion is seen on the dSIR image (long thin arrow) (Figure 23B). The corticospinal tracts are also seen (short thin arrows). There are areas of increased signal in most of the white matter in (Figure 23B) (thick arrows). Only about 5–10% of the white matter has a low signal (dark) and appears normal. High signal boundaries are seen between white and gray matter.

Figure 23 Same case of MS as in Figure 22 shown at a higher level. Comparison of T₂-wSE (A) and narrow mD dSIR (B) images. The narrow mD dSIR sequence is targeted to null normal white matter and produce high positive contrast from small increases in T₁ from the normal T₁ in white matter. A focal lesion that is not seen on the T₂-wSE image is seen on the dSIR image (long thin arrow) and other abnormalities are seen in the corticospinal tracts (short thin arrows). The white matter appears normal on the T₂-wSE image (A) but most of it has a high signal and appears abnormal on the narrow mD dSIR image (B) (thick arrows). Only about 5–10% of the white matter in (B) has a normal dark appearance. The normal appearing white matter in (A) mostly appears abnormal in (B). High signal boundaries are seen between white matter and cortical gray matter. T₂-wSE, T₂-weighted spin echo; mD, middle domain; dSIR, divided subtracted inversion recovery; MS, multiple sclerosis; CSF, cerebrospinal fluid.

In Figure 22 most of the normal appearing white matter on the T₂-wSE image (Figure 22A) shows as normal tissue with a dark (low) signal appearance in Figure 22B (thick arrows). In Figure 23, most of the normal appearing white matter in Figure 23A shows abnormal high signal in Figure 23B (thick arrows). Even in retrospect it is not possible to decide whether the normal appearing white matter in Figures 22A,23B will appear normal or abnormal on the corresponding narrow mD dSIR images.

In another case of MS, no abnormality is seen on the T₂-FLAIR image (Figure 24A) in the thalamus, but a focal lesion is seen in the thalamus using an intermediate mD dSIR sequence (thin white arrow) (Figure 24B). The intermediate mD dSIR sequence is targeted to null white matter and produce positive contrast from increases in T₁ over a broader domain than in Figures 22B,23B. Figure 24B which used an intermediate mD shows less lesion contrast in white matter than Figures 22B,23B which used narrow mDs.

Figure 24 Case of MS examined at 1.5T. T₂-FLAIR (A) and intermediate mD dSIR (B) images. White matter is nulled and the sequence is sensitive to increases in T₁ over an intermediate T₁ domain. The boundary line between white matter and gray matter is isointense with gray matter. A lesion is seen in the left thalamus in (B) (long thin arrow) but not seen on the T₂-FLAIR image (A). White matter lesions are much less obvious on the intermediate mD image (B) than on the narrow mD images shown in previous Figures 22B,23B. T₂-FLAIR, T₂-fluid attenuated inversion recovery; mD, middle domain; dSIR, divided subtracted inversion recovery; MS, multiple sclerosis.

Figure 25 shows narrow mD dSIR images in a normal, gender, ethnicity and socio-economically matched 49-year-old control (left column), and a 51-year-old patient with methamphetamine dependency for 20 years followed by an abstinence period of 120 days (right column). In the control images, most white matter appears normal with a low signal (dark) (left column), but in the patient most white matter appears abnormal with a high signal (light) (right column). There is only a small amount of normal white matter (dark) present on the patient’s images (thin white arrows, right column).

Figure 25 This shows 2D narrow mD dSIR images in the gender, ethnicity, and socioeconomic status matched 49-year-old normal control (left column) and in the 51-year-old male with a 20-year history of methamphetamine dependency, abstinence period 120 days (right column). The narrow mD sequences are targeted to null normal white matter and highlight contrast produced by small increases in the T₁ of normal white matter. The narrow mD dSIR images in the control show normal white matter as low signal (dark). The dSIR images in the methamphetamine patient (right column) show widespread high signal (light) in white matter with only small areas of normal dark white matter (long thin arrows). Normal high signal boundaries are seen between white matter and gray matter in both sets of dSIR images but are more obvious in the normal control. They are partly obscured by the abnormal high signal in white matter in the patient. Contrast is seen between some normal central white matter in superior longitudinal fasciculi (light) in the normal control and more peripheral normal white matter (dark) (left column). mD, middle domain; dSIR, divided subtracted inversion recovery; 2D, two-dimensional.

In the normal control, there is contrast between more peripheral normal white matter (dark) (left column) and more central normal white matter of the superior longitudinal fasciculi (mid-gray).

Figure 26 compares a T₂-FLAIR image (Figure 26A) with a narrow mD dSIR image (Figure 26B) in the 51-year-old patient. No abnormality is seen on the T₂-FLAIR image (i.e., it shows normal appearing white matter) but extensive high signal abnormalities are seen in white matter on the narrow mD dSIR image. There are only small areas of normal low signal (dark) white matter on this image (thin arrows).

Figure 26 Methamphetamine dependency patient. Comparison of 2D T₂-FLAIR (A) and narrow mD dSIR (B) images with similar spatial resolutions in the 51-year-old patient with a 20-year history of methamphetamine dependency whose images are shown in Figure 25. There is normal appearing white matter on the T₂-FLAIR image (A) but on the narrow mD dSIR image (B) there are extensive areas of higher signal in about 90% of the white matter of the centrum semiovale. Only small areas of more normal lower signal are seen in this white matter (long thin arrows) (B). Thus, most of the normal appearing white matter in (A) appears abnormal in (B). High signal boundaries are seen between white matter and gray matter on the narrow mD dSIR image (B). T₂-FLAIR, T₂-fluid attenuated inversion recovery; mD, middle Domain; dSIR, divided subtracted inversion recovery; 2D, two-dimensional.

Figure 27 shows comparison of 3D T₂-FLAIR images (left column) and 3D intermediate mD dSIR images (right column) in another patient with methamphetamine dependency. Focal lesions are seen in white matter on both the T₂-FLAIR and intermediate mD dSIR images (thin arrows). The intermediate mD dSIR images are less sensitive to change in white matter than the narrow mD dSIR images shown in Figure 25 (right column) and Figure 26B. The comparison illustrates the benefits of using a narrow mD to achieve high lesion contrast compared with using an intermediate mD where the lesion contrast is lower and about the same as that seen on the T₂-FLAIR image.

Figure 27 Coronal 3D T₂-FLAIR (left column) and 3D intermediate mD dSIR (right column) images with similar spatial resolutions and slice thicknesses in a 50-year-old male with a 25-year history of methamphetamine dependency and an abstinence period of 80 days. The T₂-FLAIR and intermediate mD dSIR images show similar changes in the white matter (white arrows). The sensitivity of the intermediate mD dSIR images to change in white matter is much less than that of the narrow mD dSIR images shown in Figures 25,26. T₂-FLAIR, T₂-fluid attenuated inversion recovery; mD, middle domain; dSIR, divided subtracted inversion recovery; 3D, three-dimensional.

Discussion

The use of dSIR and drSIR sequences described in this paper follows directly from the CCT. Increased sequence weighting (higher slope of the T₁-bipolar filter in the mD) is used to compensate for the small change in T₁ (ΔT₁) which may be present in normal appearing tissues but be insufficient to produce contrast with the lower slope T₁-bipolar filters of conventional sequences. The region of the T₁-bipolar filter which has the steepest slope is the mD, and this needs to be narrow for high contrast amplification. This is not a problem when the objective is to image small changes in T₁ which can easily be accommodated within a narrow mD. Detection of small changes in T₁ in normal appearing tissues is therefore a very appropriate application for targeted narrow mD dSIR and drSIR sequences.

Targeting

All MRI examination are targeted to a lesser or greater extent. Even whole-body MRI includes sequences sensitive to only a few TPs (Table 5). The term tMRI is usually applied to sequences focused on specific tissues, their TPs and changes in these TPs in disease (e.g., #4–7 in Table 5). This is greater targeting than that of typical conventional T₁-wSE and IR sequences in which there is sensitivity to changes in T₁ over a relatively broad T₁ domain as shown by the slopes of their filters. They typically have a maximum slope centrally but lesser slopes extending out on either side to flat plateaus at low and high values of T₁ where there is less sensitivity to changes in T₁ (Figures 3,6). Narrow mD dSIR and drSIR sequences are highly sensitive to small changes in T₁ in the mD (Figures 9,11). dSIR and drSIR sequences are generally less sensitive to changes in T₁ outside of the mD. Larger changes in T₁ in the domains outside of the mD can usually be shown with conventional sequences.

dSIR and drSIR T₁-bipolar filters

The dSIR and drSIR T₁-bipolar filters provide keys to understanding the targeting, signal, contrast, boundaries, T₁ mapping and GBCA enhancement seen on the dSIR and drSIR images. dSIR and drSIR T₁-bipolar filters are univariate for T₁ (i.e., dependent on T₁ but not on ρ_m or T₂) and are comprehensive i.e., only a T₁ TP-filter is needed to interpret dSIR and drSIR images unlike, for example, SE and T₂-FLAIR images where three different TP-filters (ρ_m, T₁, and T₂) are needed to understand them.

As the magnitude of ΔTI and the matched change in T₁ ΔT₁ become smaller, the small change approximation of differential calculus used in the CCT, and the linear approximation used for T₁ mapping both become more accurate. Ultimately, however, the images become signal and/or contrast limited. In addition, as the changes between serial examinations become smaller, rigid body registration becomes more accurate.

Normal tissues

The normal tissues and fluids of primary interest are white matter, cortical gray matter, central gray matter and CSF. Normal white matter may be subdivided into 20 or more categories (26), and cortical gray matter into 4–6 categories. Central gray matter includes many nuclei with varying degrees of organic iron associated with them. The iron shortens T₁ and T₂ but to a first approximation, only the T₁ shortening is relevant with dSIR and drSIR sequences.

It is very helpful to know the T₁s of normal tissues. Since dSIR and drSIR images are T₁ maps and their signals in the mD can be linearly scaled to be T₁ values. The order of tissue signal or brightness directly follows from their T₁ values. Even if the nulling TI is not exact, the order of tissues in the mD (apart from those near the null point) is usually well preserved. Nulling of white matter can be targeted at the shortest T₁ of the relevant normal white matter tissues.

Identification of normal white matter is based on anatomical location, signal in relation to other normal white matter, symmetry, and studies of normal subjects of the same age with the same technique.

The cortex may be more easily visualized with the drSIR sequence for increases in T₁. This makes the boundary between cortex and CSF low signal. Increases in T₁ produce negative contrast in this situation.

Normal appearing tissues

The usual approach to imaging normal appearing tissues such as white and gray matter seen with T₁- and T₂-weighted conventional sequences is to use TPs other than T₁ and T₂ such as magnetization transfer and diffusion, or metabolites using MR spectroscopy. In this paper, the approach to imaging normal appearing white and gray matter is different. A TP (T₁) used with conventional sequences is employed. Small changes in T₁ not seen using conventional T₁-weighted IR sequences are then targeted with dSIR and drSIR sequences.

Contrast

The most prominent feature of dSIR and drSIR images is their high soft tissue contrast. This may be much greater than that seen with conventional highly T₁-weighted IR sequences such as MP-RAGE. White matter nulled IR sequences of this type are often used to maximize contrast as in the determining anatomy in the thalamus (27), but much higher contrast is available with dSIR and drSIR sequences.

Boundaries

The high signal, often high contrast boundaries of dSIR and drSIR are a characteristic feature of these images. Boundary creation of this type can, in principle, be applied to any pair of tissues with different T₁s, subject to noise and/or artefact limitations when the difference in T₁ between the tissue is small and the magnitude of the corresponding ΔTI is small. The objective is to obtain maximum signal from a partial volume affected voxel with a T₁ between those of the two tissues of interest. The approach can be applied to normal tissues to define anatomy, and to normal and abnormal tissues to define lesion boundaries. The sharply defined boundaries of the dSIR and drSIR inages may create the impression that they are of higher spatial resolution than comparable T₂-wSE and T₂-FLAIR images.

dSIR and drSIR images as T1 maps

Within the mD it is possible to use a linear approximation to produce T₁ maps. The function becomes more linear as the ΔTI and mD are reduced (see Figure 14A with a narrow mD and compared with Figure 14B with a wide mD).

In comparison with conventional multi-TI T₁ mapping, dSIR and drSIR images/T₁ maps:

• require no additional acquisition;
• are usually higher spatial resolution than the multiple TI acquisitions used with conventional T₁ mapping;
• are targeted at the T₁s of interest in the mD rather than the whole range of T₁s seen on the image and have a narrower range of maximum and minimum values. Rather than values for very long T₁ CSF and short T₁ tissues providing the upper and lower limits of the display gray-scale range as with conventional T₁ maps, dSIR and drSIR images use the same gray-scale for a smaller range of T₁ values and so have higher contrast resolution (i.e., change in the gray scale for the same change in T₁);
• may have reduced partial volume effects because of attenuation of signals towards zero in tissues and fluids outside the mD;
• utilize the analytic solutions in Eqs. [24,25]. These provide an alternative to the fitting procedures used in conventional T₁ mapping.

GBCA enhancement

• GBCA enhancement may be seen in normal tissue (e.g., white matter) where the initial TI is the same for other studies as well as in abnormal tissues (typically with an increase in T₁) where the initial nulling TI needs to be increased so that the lesion is nulled pre-enhancement and positive contrast can be seen with the reduction in T₁ post contrast using a drSIR sequence;
• The blood brain barrier plays a critical role in disease detection where disruption results in increased GBCA concentration;
• 3D isotropic acquisition with rigid body registration is usually necessary to obtain subtracted images that are not artefacted because of the different locations of pre and post images in the subject;
• Post minus pre GBCA subtractions can be targeted at (a) enhanced lesion contrast by using different TIs, and (b) specific identification of GBCA effects using the same TI;
• Quantitation of T₁ change on drSIR images can be directly related to GBCA concentration.

Serial studies

The situations that arise in serial examinations include those seen with tumors and other lesions where there may be changes in T₁ but also changes in site, size, shape, surface etc. which is manifest as differences at lesion boundaries.

The primary interest with dSIR and drSIR images is not in large changes between examinations, which are usually obvious with conventional sequences, but small changes in T₁ and/or the spatial features of tissues. In this situation, rigid body registration may allow accurate registration and recognition of boundaries.

Changes in T₁ may affect the location of boundaries without change in space. Detailed studies may be necessary to determine whether or not this is a significant confounding factor, and how to deal with it.

Quantitation

This exploits the direct measurement of T₁ and the high contrast boundaries produced by dSIR and drSIR sequences. Radiomics and artificial intelligence may benefit from the clarity and analytic form of dSIR and drSIR images.

Cancellation lines

With magnitude reconstructed IR sequences, cancellation lines arise in voxels with mixed tissues where the positive M_z from shorter T₁ tissues is balanced by the negative M_z from longer T₁ tissues so there is no net M_z and therefore no signal after the 90° pulse. Within the brain, when nulling white matter, there is no shorter T₁ tissue present with a positive M_z and so all tissues and fluids including gray matter and CSF have zero or negative M_zs and there is no cancellation line. When using a TI longer than that needed to null white matter, but shorter than that needed to null gray matter, there are voxels with mixtures of white matter (positive M_z) and gray matter (negative M_z). When the proportions balance in mixed tissue voxels there is no net M_z and a cancellation line arises at the boundary between white and gray matter. As TI is increased this occurs up until the TI necessary to null gray matter after which, with further increases in TI, both white and gray matter have positive M_zs. However, voxels with a mixture of white or gray matter and CSF may show positive M_z for one or both of these tissues, and negative M_z for CSF, leading to net zero M_z in voxels at the boundaries between them and CSF so cancellation lines occur at the junction between white or gray matter and CSF.

The subtraction: TI_s image (nulling white matter) minus TI_i image (nulling a T₁ between white and gray matter), and subsequent division with the dSIR sequence has the cancellation line with zero signal (0) on the longer TI image turned into a high signal (+1) boundary between white and cortical gray matter in voxels with a mixture of white and cortical gray matter just inside cortical gray matter (e.g., Figure 15).

The subtraction: TI_s image (nulling white matter) minus long TI image (nulling a T₁ between those of cortical gray matter and CSF) and subsequent division with the dSIR image leads to the cancellation line between cortical gray matter and CSF on the longer TI image becoming a high signal boundary in voxels with a mixture of cortical gray matter and CSF just outside the brain (e.g., Figure 16).

This also applies to lesions which have longer T₁s than the nulling T₁ of the second TI sequence. This results in high signal boundaries between normal and abnormal tissue around the lesion with a lower signal within this boundary inside the lesion.

The same general approach applies to the dSIR sequence. The section on contrast at tissue boundaries in this paper provides the mathematical formalism for understanding the contributions to contrast in this situation using T₁-filters, changes in tissue f with T₁ and changes in f with distance (x).

Technical features

• The sequences used to create dSIR and drSIR images (2D IR FSE and 3D IR GE) are widely available on standard MRI systems and usually require no special implementation. The sequences require adjustment of their TIs to correspond to the increases in tissues T₁s with increasing B₀. The coding required to add, subtract and divide IR images can written in MATLAB or other similar packages. Rigid body registration packages are widely available e.g., in FSL (fMRIB software library);
• dSIR and drSIR sequences can benefit from interleaving the two different TI acquisitions in a single sequence;
• There are also likely to be benefits in scan time from the use of sense, compressed sense and artificial intelligence;
• Ultra low field imaging e.g., at 0.064T may be feasible with adaption to the short T₁s of white matter and gray matter (275 and 330 ms, respectively, in adults) (28);
• Denoising either independently or combined with deep learning may be a significant benefit.

Synthetic dSIR and drSIR images

From Eq. [14] and Figures 9,12, it is possible to calculate synthetic dSIR and drSIR images from T₁ maps produced from other sources such as MP2RAGE, MR fingerprinting and actual flip angle-ultrashort TE (UTE) (29). These provide flexibility for targeting and generating contrast using different TIs.

It is also possible to make narrower mD synthetic dSIR and drSIR images from wider mD dSIR and drSIR images. This can provide a series of progressively smaller magnitude ΔTI images to optimize contrast for different ΔT₁s within the mD of the wider dSIR or drSIR image.

Comparison with other sequences

The DIR sequence has partially opposed but net positive T₁-weighting as well as positive T₂-weighting so that for increases in T₁ and T₂ positive synergistic contrast results.

Clinical comparisons of dSIR and drSIR sequences are usually made with MP-RAGE, T₂-wSE (both with a single use of T₂) and/or T₂-FLAIR sequences. The latter has opposed T₁ and T₂ contrast but with increased T₂-weighting due to the use of a longer TE than the conventional T₂-wSE sequences. As a general rule, non-synergistic (e.g., single use of a TP) and opposed contrast sequences do not show contrast due to small changes in T₁ in lesions as well as specifically targeted highly synergistic sequences such as narrow mD dSIR and drSIR sequences.

The FLAWS (18,19) sequence began as separate white matter nulled and CSF nulled IR images. Later developments included division by a single image as the FLAWS division (FLAWS-div) sequence, and division of two subtracted images by the sum of them as the FLAWS-hc and FLAWS-hco images. They are similar to dSIR and drSIR sequences but use wide mDs and are sensitive to changes in T₁ over a broad T₁ domain. They also use two fixed widely spaced TIs. Unlike narrow mD dSIR and drSIR sequences, they are not targeted at small changes in T₁ in specific tissues. The wide mDs of the FLAWS-hc and FLAWS-hco sequences mean that they generally show lower contrast than that seen in the mD of narrow mD dSIR and drSIR sequences. The FLAWS-hc and FLAWS-hco sequences do not have T₁-bipolar filters. Their T₁-filters are essentially monotonic (Figure 1) (19). Also, they do not show high signal white matter gray matter boundaries as seen with narrow and intermediate mD dSIR and drSIR sequences.

Tissue targets

Emphasis has been placed on normal white or gray matter as the baseline, reference or nulled tissue. Within gray matter there are specific targets of importance including cortical gray matter and central gray matter nuclei. There are also mixed white and gray matter structures such as the hippocampus, thalamus, brainstem and striate cortex. The T₁ values of central gray matter tissues extend from shorter than white matter for the globus pallidus to about that of cortical gray matter. It is possible to use a wide mD to cover all gray matter to ascertain T₁s for nulling purposes. It is then possible to focus on specific targets within central gray matter using specific nulling TIs. Disease of central gray matter can result in increases or decreases in T₁.

The complex anatomy and small size of some gray matter nuclei and mixed white and gray matter structures favor the use of thin slice isotropic 3D acquisitions.

In terms of disease, the emphasis to date has been on white matter diseases such as MS which is generally regarded as a neuroinflammatory disease. It could include other diseases which have components of neuroinflammation [in addition to methamphetamine toxicity (30)], such as traumatic brain injury, Alzheimer’s disease and Parkinson’s disease. Myalgic encephalitis/chronic fatigue syndrome and long coronavirus disease (COVID) are other possibilities. Diffuse relatively low grade neuroinflammation may produce relatively subtle changes in T₁ that only become apparent with dSIR and drSIR sequences.

The increased sensitivity to small T₁ changes, may also help to disentangle demyelination and remyelination processes which often coexist within chronic MS lesions (31).

Different types of white matter disease may be studied, as well as diffusely abnormal white matter (DAWM) seen with conventional sequences (32). The focus could also include cortical gray matter diseases such as focal cortical dysplasia in the workup of epilepsy, as well as discrete cortical demyelinating plaques in MS and other neuroinflammatory diseases.

The high signal white matter gray matter boundaries seen with narrow mD dSIR sequences should allow better characterization of subtle patterns of vasogenic edema associated with neuroinflammatory, neurodegenerative and metabolic conditions. The boundaries may serve as direct or indirect biomarkers (33).

The dSIR and drSIR sequences might also assist with the characterization of different patterns of vascular white matter hyperintensities, and allow determination of predictive stroke recovery profiles. dSIR and drSIR sequences (especially at high field and with some form of contrast enhancement) may also allow evaluation of the glymphatic system in the various inflammatory and degenerative diseases in which abnormal CSF clearance is being increasingly recognized as a contributory factor (34).

Counter-intuitive features, sticking points, and answers to frequently asked questions

Some counter-intuitive features, sticking points and answers to frequently asked questions associated with dSIR and drSIR sequences are listed below:

• The graphics used to explain contrast with T₁-filters differ from the approaches conventionally used to explain T₁ contrast. Instead of a positively sloped exponential recovery for T₁ (Figure 1), the T₁-filter has a negative slope (Figure 3). Likewise, instead of an exponential decay of T₂ (Figure 1), the T₂-filter has a positive slope (Figure 4). The graphics appear contradictory unless it is recognized that the variable along the X axis is time with the conventional approach, and either T₁ or T₂ with the T₁ or T₂-filters;
• The concept of nulling signals from both normal and abnormal tissues in order to increase their visibility is counterintuitive. This is then followed first by subtraction of the remaining signal, and then by division of this, and appears likely to just result in noise. It generally requires modeling of the contrast using T₁-filters approach to understand how this can be productive (Figures 8-13 );
• In general terms, increase in contrast of up to about 15 times over conventional T₁-weighted IR sequences seems improbable. This high amplification is only for small changes in T₁ in the mD, and is not across the board. However, if this amplification is correctly targeted at small changes in T₁, it may be exactly what is needed to produce high contrast from these changes;
• The conventional teaching on partial volume effects between two tissues is that these result in signals intermediate between those of the two tissues. Production of high contrast boundaries from partial volume effects with signals much greater than that of either of the contributing tissues appears counterintuitive. It is useful to refer to the dSIR and drSIR T₁-bipolar filters to explain this as in Figures 14-18 ;
• dSIR images appear similar to highly T₂-weighted images such as T₂-wSE and T₂-FLAIR in terms of the sign of white matter gray matter contrast, and high signals from lesions, but dSIR images are highly T₁-weighted, not T₂-weighted. The use of dSIR T₁-bipolar filters explains how this is possible and the drSIR T₁-bipolar filter shows how the contrast can be reversed to produce more conventional T₁-weighted appearances of the brain;
• CSF signals in brain images are usually very low as with T₁-wSE, TI_i IR and T₂-FLAIR images, or very high as with T₂-wSE images. The dSIR and drSIR images usually show CSF as intermediate signal which does not fit either category. Again, the dSIR and drSIR T₁-bipolar filters explain how this comes about;
• It is often assumed that advanced mathematics is required to understand MR contrast. The contrast behavior described in this paper can be understood using primary school arithmetic and secondary school algebra, geometry and calculus together with math teaching apps (e.g., WolframAlpha). The equations necessary for this are included in the text;
• The descriptive terms used to describe TP-filters are derived from resistance inductance, capacitance (RLC) filters in electronics which have similar shapes and functional descriptions such as low pass, high pass and notch. The terms are borrowed and analogous. Their use does not imply that an electronic model is being employed to understand contrast (20);
• The use of T₁ 3–4 times to generate synergistic contrast with the dSIR and drSIR sequences comes from the numerator where T₁ is used twice to increase the slope of the SIR filter in the mD, and in the denominator where T₁ is used twice as an addition which can be regarded as a single or double use of T₁. The latter increases the slope of the dSIR and drSIR T₁-bipolar filters in the mD and thus the size of the T₁ contrast that is generated by changes in T₁ in the mD;
• T₂-wSE and T₂-FLAIR utilize changes in T₂ to produce contrast but dSIR and drSIR sequences use changes in T₁. Often there are concurrent changes in T₁ and T₂ in disease so either or both of T₁ and T₂ can be exploited to produce contrast;
• In an historical context, the IR sequences necessary to produce dSIR and drSIR images have existed on clinical MR systems for at least 40 years (1). However, it is probable that the noise and artefacts present on MR systems at these earlier times would have limited the useful amplification that could have been attained had they been implemented;
• The ease of implementation of dSIR and drSIR techniques which use sequences that are already on systems seems unusual for a significant advance in clinical imaging;
• The dSIR and drSIR sequences are specifically T₁-weighted rather than conventionally T₁-weighted as with SE sequences of the brain. These conventional sequences also have ρ_m-weighting and may actually be T₂-weighted when imaging the Achilles tendon (23);
• The dSIR and drSIR sequences can, in principle, be used at any static field strength but amplification may be more noise and/or artifact limited at low and ultra-low field strengths;
• The principles are also applicable to other organs besides the brain.

TP-filters and CCT apps

Understanding the contrast behavior of the dSIR and drSIR sequences can be greatly facilitated by use of interactive Apps based on T₁-filters. These demonstrate contrast, allow comparisons to be made, and make it possible to simulate contrast behavior almost in real time.

Conclusions

The dSIR and drSIR sequences can produce an order of magnitude increase in contrast and be targeted at normal or near normal white matter or gray matter in a wide range of disease of the brain where subtle abnormalities in T₁ are present. A particular example is chronic neuroinflammation. This is associated with many diseases but it may be low grade and produce relatively small changes in T₁ and T₂, and therefore may not produce contrast that is apparent using conventional sequences (35).

Validation of the findings obtained with dSIR and drSIR sequences by comparison with other MRI techniques and other forms of imaging as well as histology will be necessary.

The dSIR and drSIR sequences have the potential to produce a substantial advance in clinical MRI by providing unequivocal demonstration of abnormalities that are not seen, or only poorly seen with conventional sequences. The dSIR and drSIR sequences can also produce more certainty about the absence of disease in normal appearing tissues than conventional sequences.

Acknowledgments

The authors wish to thank Dr. Nivedita Agarwal (Head of Neuroradiology, Research Institute Eugenio Medea, Lombardy, Italy) for providing the image used in Figure 19.

Funding: This study was supported by NIH (Nos. RF1AG075717, R01AR062581, R01AR068987, R01AR079484, and R21AR075851); the VA Clinical Science Research & Development Service (No. I01CX002211); GE Healthcare (Nos. A-31, A-32, and A-33) as well as from Kānoa, New Zealand and Trust Tairāwhiti, New Zealand.

Footnote

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-23-232/coif). JD serves as an unpaid editorial board member of Quantitative Imaging in Medicine and Surgery. MNJP is a scientific and technical adviser to Magnetica, Brisbane, Australia. GMB is a clinical consultant to Magnetica, Brisbane, Australia. The other authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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