MRI method for calculating a proton density fat fraction

Abstract

The present invention relates to a method of calculating a proton density fat fraction, PDFF, from a water and fat separated magnetic resonance imaging, MRI, based on fat-referenced lipid quantification in a region of interest (ROI) and using determination of a reference tissue. The method comprises the step of determining: F.Math.β.sub.f/R, wherein F is the fat signal in the ROI provided from the MRI, β.sub.f is a function providing a ratio between T1 saturation values of the fat signals in the reference tissue and in the ROI; and R is a representation of the sum of fat and water signals on an intensity scale where the saturation of each of the fat and water signals equals the saturation of fat in the reference tissue.

Claims

1. A method of calculating a proton density fat fraction, PDFF, from a water, W, and fat, F, separated magnetic resonance imaging, MRI, based on fat-referenced lipid quantification in a region of interest (ROI) and using determination of a reference tissue, the method comprising the step of determining PDFF as: $\frac{F.Math.{\beta }_f}{R}$ wherein F is the fat signal in the ROI provided from the MRI, β.sub.f is a function providing a ratio between T1 saturation factors of the fat signals in the reference tissue and in the ROI; and R is a representation of the sum of the unsaturated fat and water signals after this sum has been saturated by the saturation factor for fat in the reference tissue.

2. A proton density fat fraction, PDFF, calculation apparatus comprising: a receiver configured to receive a water, W, and fat, F, separated magnetic resonance imaging, MRI; and a processor configured to, based on the received water and fat separated MRI, and based on fat-referenced lipid quantification in a region of interest (ROI) and using determination of a reference tissue, determine the PDFF as $\frac{F.Math.{\beta }_f}{R}$ wherein F is the fat signal in the ROI provided from the MRI, β.sub.f is a function providing a ratio between T1 saturation factors of the fat signals in the reference tissue and in the ROI; and R is a representation of the sum of the unsaturated fat and water signals after this sum has been saturated by the saturation factor for fat in the reference tissue.

3. Method according to claim 1, wherein R provides a quota between F.sub.ref and PDFF.sub.ref such that the method comprises the step of determining PDFF as: $\frac{F}{F_{\mathrm{ref}}}.Math.{\beta }_f.Math.{\mathrm{PDFF}}_{\mathrm{ref}}$ wherein F.sub.ref is the fat signal in the reference tissue; and PDFF.sub.refis the PDFF of the reference tissue provided by a separate experiment of the reference tissue or by a predetermined constant.

4. The method according to claim 1, wherein the T1 saturation factors of the fat signal in the reference tissue and in the ROI are equal, providing β.sub.f=1.

5. The method according to claim 3, wherein the PDFF is determined from a fat-referenced two-point Dixon acquisition without previous correction for T.sub.2* relaxation effects, and wherein the water signal in the reference tissue, W.sub.ref, is low such that a resulting value when W.sub.ref is multiplied with a resulting T.sub.2* relaxation effect provides an approximation that the water signal in the ROI equals an observed water signal in the ROI, W.sub.2PD, being a reconstruction of the water signal from the MRI in the ROI using two-point Dixon acquisition, providing the PDFF to be calculated as $\frac{F_{2\mathrm{PD}}-W_{2\mathrm{PD}}.Math.\frac{e^{-T_{\mathrm{ip}}/T_{2w}^{*}}-e^{-T_{\mathrm{op}}/T_{2w}^{*}}}{2}}{F_{2\mathrm{PD},\mathrm{ref}}}.Math.{\beta }_f.Math.{\mathrm{PDFF}}_{\mathrm{ref}}$ wherein F.sub.2PD is the observed fat signal in the ROI, being a reconstruction of the fat signal from the MRI in the ROI using two-point Dixon acquisition; T.sub.ip is a constant of the echo time of the in-phase (IP) component comprising water plus fat signal of the water and fat signals from the MRI in the ROI; T.sub.2*.sub.w is the T.sub.2* relaxation effect of water in the ROI resulting from the two-point Dixon analysis; T.sub.op is a constant of the echo time of the out-of-phase (OP) component comprising the difference between the water and fat signals from the MRI in the ROI; and F.sub.2PD, ref is the observed fat signal of the reference tissue, being a reconstruction of the fat signal from the MRI in the reference tissue using two-point Dixon acquisition.

6. The method according to claim 5, wherein the T.sub.2* relaxation effect value is determined in a separate experiment.

7. The method according to claim 5, wherein the T.sub.2* relaxation effect value is set as a constant based on a population mean.

8. The method according to claim 1, wherein the water and fat separated imaging is a spoiled gradient echo water-fat separated image reconstruction, and wherein β.sub.f is the quota of $\sin \left(\alpha \right)\frac{1-e^{-T_R/T_{1f,\mathrm{ref}}}}{1-\cos \alpha \left(1-e^{-T_R/T_{1f,\mathrm{ref}}}\right)}\mathrm{and}\sin \left(\alpha \right)\frac{1-e^{-T_R/T_{1f,\mathrm{ROI}}}}{1-\cos \alpha \left(1-e^{-T_R/T_{1f,\mathrm{ROI}}}\right)},$ wherein α is the effective flip angle in the MRI acquisition, T.sub.R is the repetition time, T.sub.1f,ref is the T1 value for the fat signal in the reference tissue, and T.sub.1f,ROI is the T1 value for the fat signal in the ROI.

9. The method according to claim 3, wherein the F.sub.ref is determined as a weighted interpolation of the fat signal in the reference tissue.

10. The method according to claim 1, wherein R is defined as F.Math.β.sub.f+W.Math.β.sub.w , and wherein the T1 saturation factor of the fat signal in the reference tissue and in the ROI is equal, providing β.sub.f=1, providing the method comprising the step of determining PDFF as $\frac{F}{F+W.Math.{\beta }_w}$ wherein W is the water signal in the ROI provided by the MRI; and β.sub.w is a function providing a ratio between the T1 saturation factor of the fat signal in the reference tissue and the T1 saturation factor of the water signal in the ROI.

11. The method according to claim 10, wherein β.sub.w is determined in a separate experiment by determining $\underset{{\beta }_w}{\min }\left(\underset{\mathrm{Measurements}}{.Math.}{\left(\frac{F}{F+W.Math.{\beta }_w}-{\mathrm{PDFF}}_{\mathrm{ex}}\right)}^2\right)$ wherein PDFF.sub.ex is the proton density fat fraction measured in a separate experiment.

12. The method according to claim 11, wherein PDFF.sub.ex is provided by a separate 2-point Dixon experiment.

13. The apparatus according to claim 2, wherein R provides a quota between F.sub.ref and PDFF.sub.ref such that the method comprises the step of determining PDFF as: $\frac{F}{F_{\mathrm{ref}}}.Math.{\beta }_f.Math.{\mathrm{PDFF}}_{\mathrm{ref}}$ wherein F.sub.ref is the fat signal in the reference tissue; and PDFF.sub.ref is the PDFF of the reference tissue provided by a separate experiment of the reference tissue or by a predetermined constant.

14. The apparatus according to claim 2, wherein the T1 saturation factors of the fat signal in the reference tissue and in the ROI is equal, providing β.sub.f=1.

15. The apparatus according to claim 13, wherein the processor is configured to determine PDFF from a fat-referenced two-point Dixon acquisition without previous correction for T.sub.2* relaxation effects, and wherein the water signal in the reference tissue, W.sub.ref, is low such that a resulting value when W.sub.ref is multiplied with a resulting T.sub.2* relaxation effect provides an approximation that the water signal in the ROI equals an observed water signal in the ROI, W.sub.2PD, being a reconstruction of the water signal from the MRI in the ROI using two-point Dixon acquisition, providing the PDFF to be determined by the processor as $\frac{F_{2\mathrm{PD}}-W_{2\mathrm{PD}}.Math.\frac{e^{-T_{\mathrm{ip}}/T_{2,w}^{*}}-e^{-T_{\mathrm{op}}/T_{2,w}^{*}}}{2}}{F_{2\mathrm{PD},\mathrm{ref}}}.Math.{\beta }_f.Math.{\mathrm{PDFF}}_{\mathrm{ref}}$ wherein F.sub.2PD is the observed fat signal in the ROI, being a reconstruction of the fat signal from the MRI in the ROI using two-point Dixon acquisition; T.sub.ip is a constant of the echo time of the in-phase (IP) component comprising water plus fat signal of the water and fat signals from the MRI in the ROI; T.sub.2*.sub.w is the T.sub.2* relaxation effect of water in the ROI resulting from the two-point Dixon analysis; T.sub.op is a constant of the echo time of the out-of-phase (OP) component comprising the difference between the water and fat signals from the MRI in the ROI; and F.sub.2PD,ref is the observed fat signal of the reference tissue, being a reconstruction of the fat signal from the MRI in the reference tissue using two-point Dixon acquisition.

16. The apparatus according to claim 15, wherein the T.sub.2* relaxation effect value is determined in a separate experiment.

17. The apparatus according to claim 15, wherein the T.sub.2* relaxation effect value is set as a constant based on a population mean.

18. The apparatus according to claim 2, wherein the water and fat separated imaging is a spoiled gradient echo water-fat separated image reconstruction, and wherein β.sub.f is the quota of $\sin \left(\alpha \right)\frac{1-e^{-T_R/T_{1f,\mathrm{ref}}}}{1-\cos \alpha \left(1-e^{-T_R/T_{1f,\mathrm{ref}}}\right)}\mathrm{and}\sin \left(\alpha \right)\frac{1-e^{-T_R/T_{1f,\mathrm{ROI}}}}{1-\cos \alpha \left(1-e^{-T_R/T_{1f,\mathrm{ROI}}}\right)},$ wherein α is the effective flip angle in the MRI acquisition, T.sub.R is the repetition time, T.sub.1f,ref is the T1 value for the fat signal in the reference tissue, and T.sub.1f,ROI is the T1 value for the fat signal in the ROI.

19. The apparatus according to claim 13, wherein the F.sub.ref is determined as a weighted interpolation of the fat signal in the reference tissue.

20. The apparatus according to claim 2, wherein R is defined as F.Math.β.sub.f+W.Math.β.sub.w, and wherein the T1 saturation factor of the fat signal in the reference tissue and in the ROI is equal, providing β.sub.f=1, providing the processor to be configured to determine PDFF as $\frac{F}{F+W.Math.{\beta }_w}$ wherein W is the water signal in the ROI provided by the MRI; and β.sub.w is a function providing a ratio between the T1 saturation factor of the fat signal in the reference tissue and the T1 saturation factor of the water signal in the ROI.

21. The apparatus according to claim 20, wherein β.sub.w is determined in a separate experiment by determining $\underset{{\beta }_w}{\min }\left(\underset{\mathrm{Measurements}}{.Math.}{\left(\frac{F}{F+W.Math.{\beta }_w}-{\mathrm{PDFF}}_{\mathrm{ex}}\right)}^2\right)$ wherein PDFF.sub.ex is the proton density fat fraction measured in a separate experiment.

22. The apparatus according to claim 21, wherein PDFF.sub.ex is provided by a separate 2-point Dixon experiment.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will in the following be described in more detail with reference to the enclosed drawings, wherein:

(2) FIG. 1 shows a schematic block view of a method according to an embodiment of the present invention;

(3) FIG. 2 shows a schematic block view of a method according to an embodiment of the present invention; and

(4) FIG. 3 shows a schematic block view of a PDFF calculation apparatus according to an embodiment of the present invention.

DESCRIPTION OF EMBODIMENTS

(5) The present invention will be described more fully hereinafter according to preferred embodiments of the invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

(6) Signal Model

(7) In spoiled gradient echo water-fat separated image reconstruction after taking T.sub.2* and lipid spectrum effects into account, the water (W) and fat (F) signals can be represented by the following equations:

(8) $\begin{array}{cc}W=W_{\mathrm{unsat}}.Math.\sin \left(\alpha \right)\frac{1-e^{-T_R/T_{1w}}}{1-\cos \alpha \left(1-e^{-T_R/T_{1w}}\right)}=W_{\mathrm{unsat}}.Math.s_w\mathrm{and}& \left[\mathrm{equation}1\right]\\ F=F_{\mathrm{unsat}}.Math.\sin \left(\alpha \right)\frac{1-e^{-T_R/T_{1f}}}{1-\cos \alpha \left(1-e^{-T_R/T_{1f}}\right)}=F_{\mathrm{unsat}}.Math.s_f,& \left[\mathrm{equation}2\right]\end{array}$
where W.sub.unsat and F.sub.unsat are the unsaturated water and fat signals, and s.sub.w and s.sub.f are the water- and fat-saturation factors that are dependent on the local flip angle α, the repetition time TR and the tissue dependent T.sub.1 values, T.sub.1w and T.sub.1f, for water and fat. Note that the exact value of a is unknown as it is dependent on prescan performance and on the characteristics of the radiofrequency pulse profile.

(9) To quantify the fat content of a tissue, the unsaturated F.sub.unsat is insufficient as it is dependent on a range of unknown factors, besides the number of fat protons. Proton density fat fraction (PDFF) is a quantitative fat-content technique that is invariant to these unknown factors. In PDFF imaging F.sub.unsat is calibrated using a unsaturated in-phase signal reference, IP.sub.unsat=F.sub.unsat+W.sub.unsat, e.g. PDFF is defined as:

(10) 0$\begin{array}{cc}\mathrm{PDFF}=\frac{F_{\mathrm{unsat}}}{I{P}_{\mathrm{unsat}}}.& \left[\mathrm{equation}3\right]\end{array}$

(11) Because the multiplicative factors are identical in F.sub.unsat and IP.sub.unsat, PDFF is the fraction of MRI visible fat protons in relation to the sum of MRI visible fat and water protons. Furthermore, as PDFF is based on the unsaturated MRI signals, the acquisition parameters must be set such that s.sub.w≈s.sub.f, e.g. by choosing a low flip angle. Alternatively, additional images need to be collected to determine the ratio between and s.sub.w and s.sub.f.

(12) An alternative quantitative technique is fat-referenced MRI where F is calibrated using a fat signal F.sub.ref (Romu et al., 2011; Dahlqvist Leinhard et al., 2008). The benefit is that this measurement is invariant to the water and fat saturations given that F.sub.ref is affected by the same s.sub.f as F. However, the fat-referenced signal corresponds to the number of fat protons in the measurement point relative to the number of fat protons in the reference, and is thus not identical to PDFF. To translate the fat-reference signal to PDFF, assume that there exists an in-phase reference, R, which saturates with a fat saturation factor, s.sub.f,R, e.g.:
R=IP.sub.unsats.sub.f,R.Math.  [equation 4]

(13) Then, the PDFF equation can be expressed as:

(14) $\begin{array}{cc}\mathrm{PDFF}=\frac{F_{\mathrm{unsat}}}{I{P}_{\mathrm{unsat}}}=\frac{F}{R}\frac{s_{f,R}}{s_f}=\frac{F}{R}{\beta }_f,& \left[\mathrm{equation}5\right]\end{array}$
where the factor

(15) $\begin{array}{cc}{\beta }_f=\frac{s_{f,R}}{s_f},& \left[\mathrm{equation}6\right]\end{array}$
corrects for any difference in saturation between the measured fat signal and the reference. Also note that if the saturation of R is similar to that of the fat signal, then β.sub.f≈1.
Relating the Fat-Referenced Signal to PDFF

(16) In fat-referenced lipid quantification, a signal reference is acquired from regions of pure adipose tissue within the subject and interpolated over the complete image volume (Romu et al., 2011; Dahlqvist Leinhard et al., 2008). To convert the fat-referenced signal to PDFF, let F.sub.ref represent the fat signal of the reference tissue, and set the saturation of R to the saturation level of F.sub.ref, i.e. s.sub.f,ref=s.sub.f,R. Thus, the PDFF of the reference tissue is equal to F.sub.ref.Math.R.sup.−1, so R=F.sub.ref.Math.PDFF.sub.ref.sup.−1, and eq. 5 describing PDFF in the measurement point can therefore be reformulated as (see FIGS. 1 and 2):

(17) $\begin{array}{cc}\mathrm{PDFF}=\frac{F}{R}{\beta }_f=\frac{F}{F_{\mathrm{ref}}}{\beta }_f.Math.{\mathrm{PDFF}}_{\mathrm{ref}},& \left[\mathrm{equation}7\right]\end{array}$
where F.Math.F.sub.ref.sup.−1 is the fat-referenced signal, e.g. the raw fat signal calibrated by the interpolated fat reference signal. This is further illustrated in FIGS. 1 and 2.

(18) The consequence of Eq. 7 is that the calibrated fat signal in the fat-referenced analysis can be converted to PDFF by adjusting for the PDFF in the adipose reference tissue and for any difference in fat saturation relative to the reference. Furthermore, if the fat saturation is similar to the reference, then the fat-referenced PDFF can be computed as:

(19) $\begin{array}{cc}\mathrm{PDFF}=\frac{F}{F_{\mathrm{ref}}}{\mathrm{PDFF}}_{\mathrm{ref}}.& \left[\mathrm{equation}8\right]\end{array}$
Adjusting for Effects Occurring in Two-Point Dixon (2PD) Imaging

(20) In 2PD analysis, using simplistic reconstruction of the fat and water image components after phase-sensitive reconstruction of the OP image, the observed fat signal is given by

(21) $\begin{array}{cc}{F}_{2\mathrm{PD}}=\frac{\mathrm{IP}-\mathrm{OP}}{2}=F.Math.\frac{e^{-T_{\mathrm{ip}}/T_{2,f}^{*}}.Math.d_{\mathrm{ip}}+e^{-T_{\mathrm{op}}/T_{2,f}^{*}}.Math.d_{\mathrm{op}}}{2}+W.Math.\frac{e^{-T_{\mathrm{ip}}/T_{2,w}^{*}}-e^{-T_{\mathrm{op}}/T_{2,w}^{*}}}{2}=F.Math.t_f^{+}+W.Math.t_w^{-},& \left[\mathrm{equation}9\right]\end{array}$
where t.sub.f.sup.+ is a function of the fat T.sub.2*-relaxation, T.sub.2,f*, the spectral dispersion of fat, d, and the echo times T.sub.op and T.sub.ip. Similarly, t.sub.w.sup.− describes the crosstalk caused by the water signal as a function of T.sub.2,w* and the echo times T.sub.op and T.sub.ip. Similarly, the observed water signal is given by

(22) $\begin{array}{cc}{W}_{2\mathrm{PD}}=\frac{\mathrm{IP}+\mathrm{OP}}{2}=F.Math.\frac{e^{-T_{\mathrm{ip}}/T_{2,f}^{*}}.Math.d_{\mathrm{ip}}-e^{-T_{\mathrm{op}}/T_{2,f}^{*}}.Math.d_{\mathrm{op}}}{2}+W.Math.\frac{e^{-T_{\mathrm{ip}}/T_{2,w}^{*}}+e^{-T_{\mathrm{op}}/T_{2,w}^{*}}}{2}=F.Math.t_f^{-}+W.Math.t_w^{+}.& \left[\mathrm{equation}10\right]\end{array}$

(23) Solving for the PDFF in Eq. 8, with the corresponding signal estimated using two-point Dixon imaging, gives

(24) $\begin{array}{cc}{\mathrm{PDFF}}_{2\mathrm{PD}}=\frac{\frac{F_{2\mathrm{PD}}-W_{2\mathrm{PD}}.Math.t_w^{-}}{t_f^{+}}}{\frac{F_{2\mathrm{PD},\mathrm{ref}}-W_{\mathrm{ref}}.Math.t_{w,\mathrm{ref}}^{-}}{t_{f,\mathrm{ref}}^{+}}}.Math.{\mathrm{PDFF}}_{\mathrm{ref}}.& \left[\mathrm{equation}11\right]\end{array}$

(25) Furthermore, since F.sub.2PD,ref»W.sub.ref.Math.t.sub.w,ref.sup.− in adipose tissue and assuming similar T.sub.2* effects F.sub.2PD and F.sub.2PD,ref, i.e. t.sub.f.sup.+≈t.sub.f,ref.sup.+, Eq. 11 can be approximated to:

(26) $\begin{array}{cc}{\mathrm{PDFF}}_{2\mathrm{PD}}=\frac{F_{2\mathrm{PD}}-W_{2\mathrm{PD}}.Math.t_w^{-}}{F_{2\mathrm{PD},\mathrm{ref}}}.Math.{\mathrm{PDFF}}_{\mathrm{ref}}=\frac{F_{2\mathrm{PD}}-0.5.Math.W_{2\mathrm{PD}}.Math.\left(e^{-T_{\mathrm{ip}}/T_{2,w}^{*}}-e^{-T_{\mathrm{op}}/T_{2,w}^{*}}\right)}{F_{2\mathrm{PD},\mathrm{ref}}}.Math.{\mathrm{PDFF}}_{\mathrm{ref}},& \left[\mathrm{equation}12\right]\end{array}$
where T.sub.2,w*, and PDFF.sub.ref are the only unknowns.
Quantification of PDFF in T.sub.1-Saturated Dixon Imaging

(27) Two different implementations for PDFF quantification in T.sub.1-saturated Dixon imaging can be used.

(28) Implementation 1. Fat-Referenced Dixon Imaging with Correction for Effects of T.sub.2* Relaxation and Adipose Tissue Water Concentration.

(29) Assuming T.sub.1-saturated 2PD, such that the PDFF is given by Eq. 12. Furthermore, the values of T.sub.2,w* and PDFF.sub.ref in Eq. 12 can either be determined on an individual level in a separate experiment, or assumed to be constant and set to a population mean.

(30) Implementation 2. Water-Referenced T.sub.2*-Corrected Dixon Imaging with T.sub.1-Saturation Correction Based on Fat-Referenced Dixon Imaging.

(31) If the saturation ratio between fat and water, β.sub.w=s.sub.f/s.sub.w, is known, the PDFF from a T.sub.1-saturated Dixon acquisition, corrected for T.sub.2* and spectral dispersion effects, is given by

(32) $\begin{array}{cc}\mathrm{PDFF}=\frac{F}{F+W.Math.{\beta }_w}.& \left[\mathrm{equation}13\right]\end{array}$

(33) The saturation ratio β.sub.w can then be determined based on a separate PDFF experiment, such as the fat referenced PDFF.sub.2PD, by minimizing the following expression with respect to β.sub.w,

(34) 0$\begin{array}{cc}\underset{{\beta }_w}{\min }\left({.Math.}_{\mathrm{All}\mathrm{subjects}}{\left(\frac{F}{F+W.Math.{\beta }_w}-{\mathrm{PDFF}}_{2\mathrm{PD}}\right)}^2\right).& \left[\mathrm{equation}14\right]\end{array}$
which minimizes the observed differences between PDFF in the water-referenced acquisition and PDFF.sub.2PD from the fat-referenced T.sub.2*-corrected 2PD acquisition.
FIG. 3 illustrates a PDFF calculation apparatus 10 receiving input from an MRI source 20, the input being a water and fat separated MR imaging. The PDFF calculation apparatus 10 comprises a receiver 12 and a processor 14. The receiver is configured to receive the input from the MRI source 20. The processor is configured to determine the PDFF according to a method as described above. The receiver 12 may also receive input in the form of a PDFF of a reference tissue to be used in the determination by the processor.

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(36) In the drawings and specification, there have been disclosed preferred embodiments and examples of the invention and, although specific terms are employed, they are used in a generic and descriptive sense only and not for the purpose of limitation, the scope of the invention being set forth in the following claims.