AN ANALYSIS METHOD OF DYNAMIC CONTRAST-ENHANCED MRI

Abstract

The present invention discloses an analysis method for dynamic contrast-enhanced magnetic resonance image. Firstly, the time-series signal of vascular contrast agent concentration, AIF, of biological individual is obtained from DCE-MRI time-series data. Secondly, perform the nonlinear least sum of square fitting by using the full Shutter-Speed model (SSM.sub.full) and the simplified vascular Shutter-Speed model (SSM.sub.vas) on the DCE-MRI time-series signal of each pixel, and the fitting results of DCE-MRI time-series signal are obtained. Thirdly, the corrected Akaike Information Criterion (AIC.sub.C) score is used to comparing the DCE-MRI time-series signal fitting results to select the optimal model. If the optimal model is SSM.sub.full, distribution maps of five physiological parameters. K.sup.trans, p.sub.b p.sub.o, k.sub.bo, and k.sub.io, are produced after fitting; if the optimal model is SSM.sub.vas, distribution maps of three physiological parameters, K.sup.trans, p.sub.b, and k.sub.bo, are produced after fitting. Finally, perform error analysis on the k.sub.io and k.sub.bo, resulting the final distribution maps of k.sub.io and k.sub.bo along with distribution maps of parameters K.sup.trans, p.sub.b, p.sub.o. This method can improve the estimation accuracy of K.sup.trans, p.sub.b, p.sub.o, k.sub.bo and k.sub.io.

Claims

1: An analysis method for dynamic contrast-enhanced magnetic resonance images (DCE-MRI), which is characterized by the analysis steps described below: (1) obtaining the biological individual's vascular contrast agent concentration as a function of time from the time-series DCE-MRI data; (2) according to the time-series signal of vascular contrast agent concentration in step (1), fitting the DCE-MRI time-series signal of each pixel by the nonlinear least sum of square algorithm using the Full Shutter-Speed model (SSM.sub.full) and the Simplified Shutter-Speed model (SSM.sub.vas) respectively, and obtaining the DCE-MRI signal fitting results of SSM.sub.full model and SSM.sub.vas model of each pixel; (3) using corrected Akaike information criterion (AIC.sub.c) to score and compare the DCE-MRI signal fitting results of the SSM.sub.full model and the SSM.sub.vas model in each pixel, according to the score from the corrected Akaike information criterion evaluating the SSM.sub.full model and the SSM.sub.vas model in each pixel, selecting the optimal model from the SSM.sub.full model and the SSM.sub.vas model for each pixel; (4) carrying out fitting according to the optimal model selected in step (3); if the optimal model being SSM.sub.full model, producing distribution maps of five groups of physiological parameters produced after fitting; the five groups of physiological parameters being the contrast agent (CA) volume transfer constant between blood plasma and extravascular-extracellular space (K.sup.trans), intravascular water mole fraction (p.sub.b), extravascular-extracellular water mole fraction (p.sub.o), the vascular water efflux rate constant (k.sub.bo) and the cellular water efflux rate constant (k.sub.io); if the optimal model being SSM.sub.vas model, due to p.sub.o and k.sub.io not being considered as estimated parameters, obtaining only distribution maps of three groups of physiological parameters after fitting; the three groups of physiological parameters being K.sup.trans, p.sub.b and k.sub.bo. (5) performing error analysis on the k.sub.io and k.sub.bo obtained in step (4) and only reserving the pixel results with 95% confidence interval in the range of [0 s.sup.−1 20 s.sup.−1] or the lower limit of 95% confidence interval greater than 5 s.sup.−1, resulting the final k.sub.io and k.sub.bo parametric distribution maps and the K.sup.trans, p.sub.b, p.sub.o parametric distribution map.

2: The dynamic contrast-enhanced magnetic resonance image (DCE-MRI) analysis method of claim 1, wherein the basic assumption of SSM.sub.full model in Step (2) is that water molecules are in three compartments of the vascular space, extravascular-extracellular space and intracellular space and water exchange happens between vascular and extravascular-extracellular spaces and between extravascular-extracellular and intracellular spaces and no water exchange happens between vascular and intracellular spaces.

3: The dynamic contrast-enhanced magnetic resonance images (DCE-MRI) analysis method of claim 2, wherein the SSM.sub.full model's fitting parameters are K.sup.trans, p.sub.b, p.sub.o, k.sub.bo and k.sub.io.

4: The dynamic contrast-enhanced magnetic resonance image (DCE-MRI) analysis method of claim 1, wherein the basic assumption of the SSM.sub.vas model in step (2) is that water molecules are in three compartments of vascular space, extravascular-extracellular space and intracellular space and water exchange processes happen between vascular and extravascular-extracellular spaces and there is no water exchange process between vascular and intracellular space, wherein the SSM.sub.vas model ignores the effect on the magnetic resonance signal induced by the water exchange process between extravascular-extracellular space and intracellular space and the intercellular water molar fraction.

5: The dynamic contrast-enhanced magnetic resonance image analysis method of claim 4, wherein the SSM.sub.vas model includes three fitting parameters are K.sup.trans, p.sub.b and k.sub.bo, and p.sub.o and k.sub.io are fixed at 0.2 and 1000 s.sup.−1, respectively.

6: The dynamic contrast-enhanced magnetic resonance image analysis method of claim 1, wherein in step (3), if the difference between the corrected Akaike information criterion scores of the SSM.sub.full model and the corrected Akaike information criterion (AIC.sub.c) score of the SSM.sub.vas model of a pixel is no more than −10, the optimal model is the SSM.sub.full model for this pixel; if the difference between the corrected Akaike information criterion score of the SSM.sub.full model and the corrected Akaike information criterion (AIC.sub.c) score of the SSM.sub.vas model of a pixel is more than −10, then the optimal model is the SSM.sub.vas model for this pixel.

7: The analysis method of dynamic contrast-enhanced magnetic resonance image of claim 6, wherein the corrected Akaike information criterion (AIC.sub.c) score is calculated as follows: $\mathrm{AI}{C}_c=-2\log L+2K\frac{N}{N-K-1}$ wherein K is the number of the estimated model parameters, and K=4 for SSM.sub.vas model and K=6 for SSM.sub.full model, N is the number of measurements in DCE-MRI, and log L is the maximized log likelihood.

8: The analysis method of dynamic contrast-enhanced magnetic resonance image of claim 1, wherein in step (5), the 95% confidence interval of k.sub.bo or k.sub.io in the error analysis is determined by fixing the k.sub.bo (or k.sub.io) value, and then fitting all the remaining parameters via the nonlinear least sum of square method, and then changing the k.sub.bo or k.sub.io value in the [0 s.sup.−1 20 s.sup.−1] interval in small step size and repeating the fitting until: ${\chi }^2\ge {\chi }_0^2\left[1+\frac{K}{N-K}F\left(K,N-K,0.95\right)\right]$ wherein χ.sup.2 is the reduced chi-squared value from the fitting with the parameter of k.sub.bo or k.sub.io, χ.sub.0.sup.2 is the reduced chi-squared value with all parameters optimized, and F is the F distribution function, K is the number of the estimated model parameters, N is the number of measurements in the DCE-MRI signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0029] FIG. 1 shows the calculation flow chart of the general shutter speed model analysis method of dynamic contrast-enhanced magnetic resonance image provided by the present invention.

[0030] FIG. 2 shows the calculation flow chart of the full shutter speed model (SSM.sub.full).

[0031] FIG. 3 shows the flow chart of simplified vascular shutter speed model (SSM.sub.vas).

[0032] FIG. 4 shows the calculation flow chart of the error analysis of SSM.sub.full and SSM.sub.vas.

[0033] FIG. 5 is a schematic diagram of the shutter speed model.

[0034] FIG. 6 shows the MRI data of glioma subjects.

[0035] FIG. 7 shows the typical DCE-MRI time-series curve (open circles) and model fitting performance.

[0036] FIG. 8 shows the fitting residuals of different models in FIG. 7;

[0037] FIG. 9 shows the error analysis results;

[0038] FIG. 10 shows the SSM parametric maps of the images in FIG. 6.

SPECIFIC DESCRIPTION OF THE EMBODIMENTS

[0039] The present invention is further described in detail below in conjunction with the accompanying figures and embodiments (e.g., head imaging).

[0040] 1. As shown in FIG. 1, dynamic contrast-enhanced MRI and T1 images are imported at first.

[0041] 2. As shown in FIG. 1, according to the imported image, time-series signal of vascular contrast agent concentration AIF of the biological individual is obtained.

[0042] 3. As shown in FIG. 1, pixels with longitudinal relaxation time T1 larger than 3500 ms in the image are filtered out, because most of them are cerebrospinal fluid, there pixels are not analyzed. As shown in FIG. 6, the data from the T1<3500 ms pixels are analyzed in this embodiment. It is generally believed that the pixels with T1 greater than 3500 ms are mainly cerebrospinal fluid in 3T MRI brain imaging.

[0043] 4. As shown in FIG. 1, the nonlinear least square sum fitting of SSM.sub.full and SSM.sub.vas is performed on each DCE-MRI time-series signals pixel, and the DCE-MRI signal fitting results of SSM.sub.full and SSM.sub.vas of each pixel are obtained respectively.

[0044] As shown in FIG. 5, SSM.sub.full is a comprehensive three-point two exchange model, and three-point (physical space) includes water molecules in blood vessels, extravascular-extracellular space and intercellular space. Two exchange refers to water molecule exchange between blood and extravascular-extracellular space and water molecule exchange between intercellular space and extravascular-extracellular space. In the present invention, it is considered that the direct exchange of water molecules between blood and cells can be ignored in SSM.sub.full. SSM.sub.vas is a simplified three-point two-exchange model. It is considered that the effect of water exchange between intercellular space and extravascular-extracellular space and extravascular-extracellular water molar fraction to DCE-MRI signal can be ignored.

[0045] (4-1) As shown in FIG. 2, the SSM.sub.full model is used to fit the DCE-MRI time-series signals of each pixel respectively, and the specific process of obtaining the DCE-MRI signal fitting results of SSM.sub.full of each pixel point is as follows:

[0046] (4-1-1) in the SSM.sub.full, DCE-MRI time-series signal, T1 image and AIF (namely [CA.sub.p]) signal is imported at first.

[0047] (4-1-2) SSM.sub.full sets the initial values and ranges of the five fitting parameters, p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo. In this embodiment, the initial values of the five parameters are 0.02, 0.2, 0.01 min.sup.−1, 3 s.sup.−1, 3 s.sup.−1, and the fitting ranges are 0.001˜0.3, 0.01˜0.65, 10.sup.−5˜1 min.sup.−1, 0˜20 s.sup.−1, 0˜20 s.sup.−1, respectively.

[0048] (4-1-3) Substitute the five parameters p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo.

[0049] (4-1-4) Calculate the contrast agent concentration in interstitial space according to the following formula,

[CA.sub.o](T)=K.sup.transv.sub.o.sup.−1∫.sub.0.sup.T[CA.sub.p](t)exp(−K.sup.transv.sub.o.sup.−1(T−t))dt

[0050] where v.sub.o is the volume fraction of interstitial space and is linearly proportional to p.sub.o (v.sub.o=p.sub.of.sub.w), [CA.sub.p] is the concentration of CA in plasma, T is the measurement time, t is the time to proceed.

[0051] (4-1-5) R.sub.1b and R.sub.1o are obtained from the contrast agent concentration [CA], assuming that they were linearly related to the contrast agent concentration, that is, R.sub.1=R.sub.1,0+r.sub.1[CA], R.sub.1 is R.sub.1b or R.sub.1o, and r.sub.1 is the relaxation rate of contrast agent.

[0052] (4-1-6) k.sub.oi and k.sub.ob are obtained by proportional relation, because in equilibrium or steady state (homeostasis), the two water exchange processes satisfy the principle of microscopic reversibility, that is, k.sub.io/k.sub.oi=p.sub.o/p.sub.i, k.sub.bo/k.sub.ob=p.sub.o/p.sub.b, where p.sub.i=1−p.sub.b−p.sub.o.

[0053] (4-1-7) it can be obtained that the exchange matrix is X, and X is shown in the following formula,

[00005]$X=\left(\begin{array}{ccc}-\left(R_{1b}+k_{bo}\right)& k_{ob}& 0\\ k_{bo}& -\left(R_{1o}+k_{ob}+k_{oi}\right)& k_{io}\\ 0& k_{oi}& -\left(R_{1i}+k_{io}\right)\end{array}\right)$

[0054] (4-1-8) The Bloch equation considering the longitudinal .sup.1H2O relaxation and water molecule exchange can be expressed as dM/dt=XM+C, where the longitudinal magnetization vector and relaxation rate vector are M=(M.sub.b, M.sub.o, M.sub.i) and C=(M.sub.b0R.sub.1b, M.sub.o0R.sub.1o, M.sub.i0R.sub.1i, respectively. The subscript “0” represents the equilibrium state.

[0055] (4-1-9) For DCE-MRI based on Gradient Recalled Echo (GRE) type, the time-series signal strength S can be obtained by substituting parameters, and the formula is as follows:

S=1.sub.1×3M=1.sub.1×3[I−e.sup.TR.Math.X cos(α)].sup.−1(I−e.sup.TR.Math.X)M.sub.0 sin(α)

[0056] TR and α are the reputation time and flip angle of GRE sequence, respectively

[0057] (4-1-10) Compare the fitted time-series signal strength S obtained by substituting the parameters with the scanned DCE-MRI time-series signal.

[0058] (4-1-11) Judge whether the fitting results meet the fitting error requirements of nonlinear least square sum algorithm.

[0059] (4-1-12) If step (4-1-11) does not meet the requirements, adjust the substitution values of five parameters p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo according to the parameter fitting range and nonlinear least square algorithm iteration, and start from step (4-1-3) again until the requirements of step (4-1-11) are met.

[0060] (4-1-13) If step (4-1-11) is satisfied, the p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo of SSM.sub.full fitting can be obtained, and then p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo parameter distributions, signal fitting results and fitting error of all pixels fitted by SSM.sub.full can be obtained.

[0061] (4-2) As shown in FIG. 3, the SSM.sub.vas is used to fit the DCE-MRI time-series signals of each pixel respectively for nonlinear least square sum fitting. The specific process of obtaining the fitting results of DCE-MRI signals of SSM.sub.vas of each pixel is as follows:

[0062] (4-2-1) Firstly, DCE-MRI time-series signal, T1 signal and AIF (i.e. [CA.sub.p]) signal were imported into SSM.sub.vas.

[0063] (4-2-2) Fix p.sub.o=0.2 and k.sub.io=1000 s.sup.−1 in SSM.sub.vas, and set the initial values and fitting ranges of three parameters p.sub.b, K.sup.trans and k.sub.bo. In this embodiment, the initial values of the three parameters and the fitting range and steps (4-1-2) are the same.

[0064] (4-2-3) Substitute the five parameters p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo.

[0065] (4-2-4) repeat steps (4-1-3) to (4-1-9)

[0066] (4-2-5) The parameters are substituted into the fitted signal strength S and compare S with the scanned DCE-MRI time-series signal.

[0067] (4-2-6) Judge whether the fitting results meet the fitting error requirements of nonlinear least square sum algorithm.

[0068] (4-2-7) if step (4-2-6) is not satisfied, adjust the substitution values of p.sub.b, K.sup.trans and k.sub.bo according to the parameters fitting range and nonlinear least squares sum algorithm iteration, and start from step (4-2-3) again until the requirements of step (4-2-6) are met. If step (4-2-6) is satisfied, the p.sub.b, K.sup.trans and k.sub.bo of SSM.sub.vas fitting can be obtained, and then the p.sub.b, K.sup.trans and k.sub.bo parameter distributions of all pixels fitted by SSM.sub.vas, as well as signal fitting results and fitting errors, can be obtained.

[0069] 5. As shown in FIG. 1, after the SSM.sub.full and SSM.sub.vas fitting are completed, the corrected Akaike Information Criterion is used to score the two submodels of each pixel, and the optimal model is selected by scoring.

[0070] 6. As shown in FIG. 4, DCE-MRI signal fitting results of SSM.sub.full and SSM.sub.vas of each pixel are scored and compared by using the corrected Akaike Information Criterion of SSM.sub.full and SSM.sub.vas of each pixel, and the optimal model is selected from SSM.sub.full and SSM.sub.vas according to the corrected Akaike Information Criterion score of SSM.sub.full and SSM.sub.vas of each pixel.

[0071] (6-1) In the error analysis after fitting, the fitting results of SSM.sub.full and SSM.sub.vas are imported firstly.

[0072] (6-2) The corrected Akaike Information Criterion scores of SSM.sub.full and SSM.sub.vas are calculated respectively. Among them, the calculation formula of corrected Akaike Information Criterion score is as follows:

[00006]$\mathrm{AI}{C}_c=-2\log ℒ+2K\frac{N}{N-K-1}$

[0073] where K is the number of independent parameters of the fitting model and equal to 4 and 6 for SSM.sub.vas and SSM.sub.full, respectively, N is the number of measurement points in DCE-MRI data, and log L is the maximum logarithmic likelihood probability.

[0074] (6-3) Calculate the corrected Akaike Information Criterion score difference between the two models, ΔAIC.sub.c=AIC.sub.c(SSM.sub.full)−AIC.sub.c (SSM.sub.vas).

[0075] (6-4) Judge whether AAIC.sub.c is no more than −10.

[0076] (6-5) when the conditions in step (6-4) are satisfied, it means that the pixel is more suitable for SSM.sub.full. The fitting parameter results p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo obtained by SSM.sub.full are assigned to the final p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo. When the conditions in step (6-4) are not met, it means that the pixel is more suitable for SSM.sub.vas. The fitting parameter results p.sub.b, K.sup.trans, k.sub.bo obtained by SSM.sub.vas are assigned to the final p.sub.b, K.sup.trans, k.sub.bo. In the process of SSM.sub.vas, p.sub.o and k.sub.io are not fitting parameters and fixed, so they have no fitting values and are set as invalid values (NaN).

[0077] FIGS. 6-8 show an example of step 6. Among them, (A) in FIG. 6 shows axial, 1.5 mm slice thickness DCE-MR images before CA injection, 1.5 minutes after CA injection and 9 minutes after CA injection (from left to right), in which the left and right arrows point to the recurrent tumor and radiation necrosis area, respectively. Enlarged images of the area surrounded by box (A, middle) are shown in FIG. 6B, including T1 image with skull removed, DCE-MRI image at 1.5 min after CA injection, and AIC difference distribution map with ΔAIC.sub.c=AIC.sub.c(SSM.sub.full I)−AIC.sub.c(SSM.sub.vas). According to the AIC.sub.c analysis, most of the pixels located in the tumor region showed obvious SSM.sub.full preference (the AIC.sub.c score of SSM.sub.full model is much lower than that of SSM.sub.vas, ΔAIC.sub.c<−10), while nearly normal tissues preferred SSM.sub.vas model.

[0078] FIG. 7 shows the typical DCE-MRI time-series curve (open circles) and model fitting performance. Four pixels are selected, and A-C and D are from tumor and normal tissue, respectively. The positions of the representative pixels are shown with asterisks in FIG. 6B (middle). Different gray-scale curves show the fitting results of SSM.sub.vas, SSM.sub.full and classical model—extended Tofts (eTofts) model. ΔAIC.sub.c in each panel is marked as the difference of AIC.sub.c between the corresponding model and the SSM.sub.vas. FIG. 8 shows the fitting residuals of different models in FIG. 7.

[0079] FIG. 7 and FIG. 8 show that SSM.sub.vas can't fit DCE-MRI time-series curve well in tumor region, while SSM.sub.full can fit DCE-MRI time-series curves better without obvious abnormal fitting residual points. In normal tissues, SSM.sub.vas and SSM.sub.full can both fit the DCE-MRI time-series curve of the selected pixels well, but the AIC.sub.c score of SSM.sub.full is higher than that of SSM.sub.vas, which suggests that the SSM.sub.full with more fitting parameters over fits the signal, and SSM.sub.vas is enough to fit the curve.

[0080] 7. As shown in FIG. 4, the error analysis of k.sub.io and k.sub.bo in step 6 is carried out, and only pixel results with 95% confidence interval localized in [0 s.sup.−1 20 s.sup.−1] or the lower limit of 95% confidence interval bigger than 5 s.sup.−1 are retained to generate the final distribution maps of k.sub.io, k.sub.bo, along with the distribution maps of K.sup.trans, p.sub.b, p.sub.o.

[0081] (7-1) When the optimal model is SSM.sub.full, the specific process of k.sub.bo (or k.sub.io) error analysis is as follows:

[0082] (7-1-1) Determine the 95% confidence interval of k.sub.bo (or k.sub.io) by fixed k.sub.bo (or k.sub.io) value, fitting all the remaining parameters of SSM.sub.full by the nonlinear least square algorithm, and then changing the value of k.sub.bo (or k.sub.io) in the interval of [0 s.sup.−1 20 s.sup.−1] in small steps, and repeat the fitting processes until:

[00007]${\chi }^2\ge {\chi }_0^2\left[1+\frac{K}{N-K}F\left(K,N-K,0.95\right)\right]$

[0083] Among them, χ.sup.2 is the reduced chi-squared value from the fitting with the k.sub.bo or k.sub.io fixed at a certain value, χ.sub.0.sup.2 is the reduced chi-squared value with all parameters optimized, F is the F distribution function, K is the number of independent parameters in the fitting model, and N is the number of measurement points in the DCE-MRI data.

[0084] (7-1-2) If the 95% confidence interval of k.sub.bo or k.sub.io is in the interval of [0 s.sup.−1 20 s.sup.−1] or the lower limit of 95% confidence interval is bigger than 5 s.sup.−1, the fitted k.sub.bo or k.sub.io are retained. When this requirement cannot be met, k.sub.bo or k.sub.io=NaN.

[0085] The (A) in FIG. 9 performed the error analysis on k.sub.io for the tumor pixels A-C in FIG. 7 (when the cellular water efflux rate constant k.sub.io is set to the fixed value of the transformation, the reduced chi-squared curve of the data of pixels A-C in FIG. 7). The dashed vertical lines represent the 95% confidence level. Pixel A displays a well-defined error range. And Pixel B displays a wider but still determined error range. In Pixel C, the significant lower error bound can be determined. All three cases are acceptable error range.

[0086] (7-2) When the optimal model is SSM.sub.vas, the specific process of k.sub.bo error analysis is as follows:

[0087] (7-2-1) Determine the 95% confidence interval of k.sub.bo by fixed k.sub.bo value, fitting all the remaining parameters of SSM.sub.vas by the nonlinear least square algorithm, and then changing the value of k.sub.bo in the interval of [0 s.sup.−1 20 s.sup.−1] in small steps, and repeat the fitting processes until:

[00008]${\chi }^2\ge {\chi }_0^2\left[1+\frac{K}{N-K}F\left(K,N-K,0.95\right)\right]$

[0088] Among them, χ.sup.2 is the reduced chi-squared value from the fitting with the k.sub.bo fixed at a certain value, χ.sub.0.sup.2 is the reduced chi-squared value with all parameters optimized, F is the F distribution function, K is the number of independent parameters in the fitting model, and N is the number of measurement points in the DCE-MRI data.

[0089] (7-2-2) If the 95% confidence interval of k.sub.bo is in the interval of [0 s.sup.−1 20 s.sup.−1] or the lower limit of 95% confidence interval is bigger than 5 s.sup.−1, the fitted k.sub.bo are retained. When this requirement cannot be met, k.sub.bo=NaN.

[0090] The (B) in FIG. 9 performed the error analysis on k.sub.bo for the typic normal gray matter (GM) pixel, normal white matter (WM) pixel, and Pixel C located in tumor in FIG. 8 (when the vascular water efflux rate constant k.sub.bo is set to the fixed value of the transformation, the reduced chi-squared curve of the data of the three pixels). The dashed vertical lines represent the 95% confidence level. GM pixel and Pixel C displays a well-defined error range (well-determined upper error boundary and the lower error boundary is 0 s.sup.−1). In WM pixel, only the lower error bound can be determined. All three cases are acceptable error range.

[0091] Through the above steps 1-7, p.sub.b, p.sub.o, K.sup.trans, k.sub.io, k.sub.bo distribution maps can be generated.

[0092] In the present invention, the analysis results of this method are shown in FIG. 10, which are parametric maps corresponding to the enlarged area in FIG. 6, including K.sup.trans, p.sub.b, k.sub.bo, k.sub.io, p.sub.o and k.sub.pe*(=2.2 K.sup.trans/p.sub.b). This method only analyzes pixels with T1<3500 ms. In these parametric maps, only the pixels with ΔAIC.sub.c no more than −10 are analyzed by SSM.sub.full, and the following parameters are generated: K.sup.trans, p.sub.b, k.sub.bo, k.sub.io, p.sub.o and its derivative k.sub.pe*(=2.2 K.sup.trans/p.sub.b). All other pixel data are analyzed by SSM.sub.vas and the following parameter are displayed: K.sup.trans, p.sub.b, k.sub.bo, k.sub.pe*. In the final k.sub.bo (or k.sub.io) map, only the following pixels are included: the upper and lower boundaries of the 95% confidence interval of k.sub.bo (or k.sub.io) of this pixel are between 0-20 s.sup.−1 or the lower boundary is bigger than 5 s.sup.−1.

[0093] Tumor tissues show obvious enhancement of X.sup.trans, p.sub.b and k.sub.pe*, which was in line with expectations. A large number of references show that there are vascular hyperplasia and enhanced vascular permeability in tumors. However, there is an obvious heterogeneity of k.sub.io distribution in tumors, which may represent the distribution of tumor subcells with different metabolic levels and pathology. The tumor shows a rapid decrease of k.sub.bo, which may indicate that the active transmembrane water molecule exchange of vascular is stopped in the tumor.