CN114646913A - Non-invasive measurement method for microstructure of biological tissue - Google Patents
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Abstract
A method for non-invasive measurement of a microstructure of a biological tissue, comprising: I. performing magnetic resonance diffusion weighted imaging on the biological tissue; II. Measuring the actual image signal intensity of each voxel point in each magnetic resonance image; III, substituting the actual image signal intensity of the integral pixel points into a formula to solve; IV, judging that the voxel point is in a single-chamber structure, a double-chamber structure or a three-chamber structure according to the solving result; v, judging the tissue type in the voxel point; and VI, repeating the step III to the step V to analyze other voxel points until all the voxel points are analyzed. The method is capable of measuring the microstructure of biological tissue.
Description
Technical Field
The invention relates to a method for measuring a microstructure of a biological tissue, in particular to a non-invasive method for measuring the microstructure of the biological tissue through magnetic resonance imaging.
Background
Magnetic Resonance Imaging (MRI) has been widely used for imaging biological tissues due to its characteristics of no ionization damage, high soft tissue resolution, and sensitivity to chemical components.
Conventionally, there is a method of obtaining a volume ratio of cells, a volume ratio of blood vessels, a volume ratio of extracellular spaces, a diffusion coefficient of cells, a diffusion coefficient of blood vessels, and a diffusion coefficient of extracellular spaces at each voxel point of a biological tissue from an actual image signal intensity at each voxel point in a magnetic resonance image. In the solving process, each voxel point is assumed to be composed of cells, blood vessels and extracellular gaps, which are not in line with the actual structure of biological tissues, and the problem that some voxel points cannot be solved exists.
Disclosure of Invention
It is an object of the present invention to provide a method for non-invasive measurement of the microstructure of a biological tissue, which is capable of measuring the microstructure of a biological tissue.
The invention provides a noninvasive measuring method of a microstructure of a biological tissue, which comprises the following steps:
I. performing magnetic resonance diffusion weighted imaging on the biological tissue to obtain weights b respectively corresponding to different weightsiWherein i is 1,2, 3.. N, n.gtoreq.6;
II. Measuring the actual image signal intensity S (b) of each voxel point in each magnetic resonance imagei)；
III, taking any voxel point in the magnetic resonance image, and calculating the actual image signal intensity S (b) of the voxel pointi) Substituting the following equations 1 to 3 to solve D, V in the equations21、V22、D21、D22、V31、V32、V33、D31、D32And D33，
Single chamber model:
the double-chamber model:
three-chamber model:
wherein: s (b)0) The signal intensity of the voxel point when no diffusion sensitive gradient pulse is applied, D is the diffusion coefficient of the single-chamber structure, V21Volume ratio of the first chamber in a dual chamber configuration, V22Volume ratio of the second chamber in a double chamber configuration, D21Diffusion coefficient of the first chamber in a two-chamber configuration, D22Diffusion coefficient of the second chamber, V, in a dual chamber configuration31Volume ratio of the first chamber, V, in a three-chamber configuration32Volume ratio of the second chamber in a three-chamber structure, V33Volume ratio of the third chamber of three-chamber structure, D31Diffusion coefficient of the first chamber in a three-chamber structure, D32Diffusion coefficient of the second chamber in a three-chamber structure, D33The diffusion coefficient of the third chamber in a three-chamber structure;
IV, judging that the voxel point is in a single-chamber structure, a double-chamber structure or a three-chamber structure according to the result obtained in the step III;
v, if the voxel point is judged to be in the single-chamber structure in the step IV, judging the tissue type of the single-chamber structure according to the D; the tissue types include cells, blood vessels, and extracellular spaces; the volume ratio and diffusion coefficient of the tissue type not included in the single-chamber structure were set to 0. If the voxel point is determined to be a dual-chamber structure in step IV, then according to D21And D22Judging the tissue type of a first chamber and a second chamber of the double-chamber structure; the tissue types include cells, blood vessels, and extracellular spaces; the volume ratio and diffusion coefficient of the tissue type not included in the dual chamber structure were set to 0. If the voxel point is judged to be of a three-chamber structure in the step IV, according to the D31、D32And D33Judging the tissue types of a first chamber, a second chamber and a third chamber of the three-chamber structure; the tissue types include cells, blood vessels, and extracellular spaces.
VI, repeating the step III to the step V to analyze other voxel points until all the voxel points are analyzed.
The non-invasive measurement method for the microstructure of the biological tissue measures the microstructure of the biological tissue by judging whether each voxel point of the biological tissue belongs to a single-chamber structure, a double-chamber structure or a three-chamber structure and determining the tissue type of each voxel point based on the judgment result.
In another exemplary embodiment of the method for non-invasive measurement of a microstructure of a biological tissue, the step IV of determining that the voxel point is in a single-chamber structure, a double-chamber structure, or a triple-chamber structure according to the result obtained in the step III specifically includes:
if it is not
And is
Then the voxel point is a single-chamber structure.
If it is not
And is
The voxel point is then a dual chamber structure. Otherwise, the voxel point is in a three-chamber structure. The judging method is simple.
In another exemplary embodiment of the method for non-invasive measurement of a microstructure of a biological tissue, step VI is followed by: and VII, reconstructing a magnetic resonance image according to any one or more of the volume ratio of the cells, the volume ratio of the blood vessels, the volume ratio of the extracellular space, the diffusion coefficient of the cells, the diffusion coefficient of the blood vessels and the diffusion coefficient of the extracellular space of each voxel point. So as to reflect the structure of the biological tissue more intuitively.
In yet another exemplary embodiment of the method for non-invasive measurement of a microstructure of a biological tissue, the solving method in step III is solved using constrained non-linear optimization; wherein,
the optimization formula of equation 1 is:
s.t.D≥0
the optimization formula of equation 2 is:
the optimization formula of equation 3 is:
. Thereby more accurately measuring the microstructure of the biological tissue.
In yet another exemplary embodiment of the method for non-invasive measurement of biological tissue microstructures, the constrained non-linear optimization solution employs a lagrange multiplier method.
In another exemplary embodiment of the method for non-invasive measurement of a microstructure of a biological tissue, step VI is followed by: and VIII, calculating the cellulose trend distribution of the cells, the blood vessels and the extracellular spaces according to the diffusion coefficient of the cells, the diffusion coefficient of the blood vessels and the diffusion coefficient of the extracellular spaces of each voxel point. So as to reflect the diffusion property of the biological tissue more intuitively.
In a further exemplary embodiment of the method for non-invasive measurement of the microstructure of a biological tissue, the estimation is performed using a statistical method or a method based on a principal diffusion direction tracking.
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The following drawings are only schematic illustrations and explanations of the present invention, and do not limit the scope of the present invention.
Fig. 1 and 2 are magnetic resonance images of brain tissue.
FIG. 3 is a distribution diagram of the orientation of the cell fiber bundles in the basal ganglia region.
FIG. 4 is a diagram showing the distribution of the fiber bundle orientation of cells on both sides of a callus.
FIG. 5 is a graph showing the orientation of the fiber bundles of tumor and healthy lateral cells.
Fig. 6 is a magnetic resonance image of brain tissue.
Fig. 7 is a schematic representation after reconstruction.
Detailed Description
In order to more clearly understand the technical features, objects, and effects of the present invention, embodiments of the present invention will now be described with reference to the accompanying drawings.
"exemplary" means "serving as an example, instance, or illustration" herein, and any illustration, embodiment, or steps described as "exemplary" herein should not be construed as a preferred or advantageous alternative.
In this document, "first", "second", etc. do not mean their importance or order, etc., but merely mean that they are distinguished from each other so as to facilitate the description of the document.
Although the object of the embodiments of the method for non-invasive measurement of a microstructure of a biological tissue is brain tissue, the method is not limited to brain tissue, and may be applied to other biological tissues.
According to the recent studies of the inventors, it was found that the distribution of the extracellular space of brain in the brain tissue is heterogeneous, and in a part of the brain region (for example, the inner capsule region), the dense fiber bundle structure makes the volume ratio of the extracellular space in the region 0, and only the cell structure and the vascular structure exist in the ventricular region. In the actual structure of biological tissue, the tissue structure may be one, two or three of cells, blood vessels and extracellular spaces for a voxel.
In order to measure the microstructure of a biological tissue, the present invention provides a method for non-invasive measurement of the microstructure of a brain tissue, which, in one illustrative embodiment, comprises the following steps.
Step I: using a plurality of different weights biPerforming magnetic resonance diffusion weighted imaging on the measurement interest region of the brain tissue to obtain weights b respectively corresponding to different weightsiThe brain tissue magnetic resonance image of (1), 2, 3.. N, N ≧ 6. In an exemplary embodiment, the weight biFor vectors with directions, a plurality of different weights b can be obtained by changing the modulus valueiThat is, this step obtains at least six magnetic resonance images of the region of interest for measurement of the same brain tissue, and the weight b of each magnetic resonance imageiAre in the same direction and have different modulus values. In an exemplary embodiment, the weight biIn the direction of (1) is, for example, laboratory [1, 0 ]]Direction or laboratory [0.446, 0.895, 0]Of course, in the exemplary embodiment, other orientations are possible as desired. In the exemplary embodiment, the weight b may also be changediObtains a plurality of different weights biThat is, this step obtains at least six magnetic resonance images of the region of interest for measurement of the same brain tissue, and the weight b of each magnetic resonance imageiE.g. when N is 6, the weight b is differentiAre respectively [1, 0 ]]，[0.446，0.895，0]，[0.447，0.275，0.851]，[0.448，-0.723，-0.525]，[0.447，-0.724，0.526]，[-0.449，-0.277，0.850]。
Step II: measuring the actual image signal intensity S (b) of each voxel point in each magnetic resonance image obtained in step Ii) And the actual image signal intensity S (b)i) Reflected in the magnetic resonance image as the grey scale of the voxel points in the image.
Step III: in the magnetic resonance image, any one pixel point is selected, and the actual image signal intensity S (b) of the pixel point is calculatedi) Substituting into the following equation 1 to publicEquation 3, and solve D, V in the equation21、V22、D21、D22、V31、V32、V33、D31、D32And D33。
Single chamber model:
the double-chamber model:
three-chamber model:
wherein, S (b)0) The signal intensity of the voxel point when no diffusion sensitive gradient pulse is applied, D is the diffusion coefficient of the single-chamber structure, V21Volume ratio of the first chamber in a dual chamber configuration, V22Volume ratio of the second chamber in a double chamber configuration, D21Diffusion coefficient of the first chamber in a two-chamber configuration, D22Diffusion coefficient of the second chamber, V, in a dual chamber configuration31Volume ratio of the first chamber in a three-chamber structure, V32Volume ratio of the second chamber in a three-chamber structure, V33Volume ratio of the third chamber of three-chamber structure, D31Diffusion coefficient of the first chamber in a three-chamber structure, D32Diffusion coefficient of the second chamber in a three-chamber structure, D33The diffusion coefficient of the third chamber in a three-chamber structure. The volume ratio refers to the percentage of each chamber to the total volume of the voxel point, and the diffusion coefficient refers to the movement velocity of water molecules in each chamber.
In the above solving process, when the number of unknowns is less than the number of effective equations, an overdetermined equation is needed to solve the optimal solution. For example, if more than one of the voxel points is associated with different weights biActual image signal strength ofS(bi) Substituting formula 1 to obtain more than one effective equation number; if more than four of the integral element points are corresponding to different weights biActual image signal intensity S (b)i) Substituting into formula 2, more than four effective equations can be obtained; if more than six of the integral element points are corresponding to different weights biActual image signal intensity S (b)i) Substituting equation 3 results in more than six valid equations. In this case, an overdetermined equation is required to find the optimal solution. It will be appreciated that the greater the number of equations that are available, the greater the accuracy of the solution.
In the present exemplary embodiment, the solution described above employs a constrained non-linear optimization solution, wherein,
the optimization formula of equation 1 is:
s.t.D of 0
The optimization formula of equation 2 is:
the optimization formula of equation 3 is:
in this step, the voxel point is assumed to be a single-compartment structure (i.e., including one of cells, blood vessels, and extracellular spaces), a double-compartment structure (i.e., including two of cells, blood vessels, and extracellular spaces), and a triple-compartment structure (i.e., including cells, blood vessels, and extracellular spaces), respectively, to be calculated. In the present exemplary embodiment, the constrained nonlinear optimization solution employs the lagrangian multiplier method. Without limitation, in other exemplary embodiments, other constrained nonlinear optimization solutions may be used, such as conjugate gradient, steepest descent, and multidimensional newton's method.
Step IV: and judging that the voxel point is in a single-chamber structure, a double-chamber structure or a three-chamber structure according to the result of the solution in the step III. In the present exemplary embodiment, specifically:
if it is not
And is
Then the voxel point is a single-chamber structure.
If it is not
And is
The voxel point is then a dual chamber structure. Otherwise, the voxel point is in a three-chamber structure. Where e is an empirical parameter that varies with the nuclear magnetic equipment and the tissue being scanned, e.g., brain tissue scanned based on a GE nuclear magnetic resonance machine, e can take 0.1. The determination of e is based on anatomical results. The actual distribution of cells, blood vessels and extracellular spaces in the biological tissue is determined according to the anatomy, the steps I to IV are carried out aiming at the same biological tissue, and the empirical value epsilon is determined by selecting proper epsilon to ensure that the judgment result is consistent with the anatomical result. In other exemplary embodiments, e can also be obtained using machine learning methods from a large amount of labeled data. But is not limited thereto. In an exemplary embodiment, the above determination may be made based on a method such as machine learning instead.
Step V: if the voxel point is judged to be in the single-chamber structure in the step IV, judging the tissue type of the single-chamber structure according to D; the volume ratio and diffusion coefficient of the tissue type not included in the single chamber structure were set to 0. If the voxel point is determined to be a dual-chamber structure in step IV, then according to D21And D22Determining a tissue type of a first chamber and a second chamber of the dual chamber structure; the volume ratio and diffusion coefficient of the tissue type not included in the dual chamber structure were set to 0. If the voxel point is judged to be of a three-chamber structure in the step IV, according to the D31、D32And D33The tissue types of the first chamber, the second chamber and the third chamber of the three-chamber structure are judged. The tissue types mentioned above include cells, blood vessels and extracellular spaces. In the present illustrative embodiment, D, D is used to determine the anatomical outcome, for example, based on the anatomical results21、D22、Dg1、D32And D33The value of (b) determines the tissue type. Specifically, the actual distribution of cells, blood vessels and extracellular spaces in the biological tissue is determined according to the anatomy, and the above steps I to IV are performed for the same biological tissue, and the D values of voxel points determined as the single-chambered structure of cells, the single-chambered structure of blood vessels and the single-chambered structure of extracellular spaces in the anatomical result are used as the basis for respectively judging the corresponding tissue types.
Step VI: and repeating the step III to the step V to analyze other voxel points until all the voxel point analysis is completed.
Step VII: reconstructing a magnetic resonance image from one or more of the volume ratio of the cells, the volume ratio of the blood vessels, the volume ratio of the extracellular space, the diffusion coefficient of the cells, the diffusion coefficient of the blood vessels, and the diffusion coefficient of the extracellular space at each voxel point. By displaying the reconstructed image, the structure of the biological tissue is favorably and intuitively reflected.
Step VIII: the cellulose trend distribution of the cells, the blood vessels and the extracellular spaces is calculated by the diffusion coefficient of the cells, the diffusion coefficient of the blood vessels and the diffusion coefficient of the extracellular spaces of each voxel point. The estimation is performed by statistical methods or by a main diffusion direction tracking method, for example, by the recursive method described in chinese patent with CN 201510082396.3. However, in other exemplary embodiments, other methods may be used to estimate.
The following are experimental results obtained by the method for non-invasive measurement of a microstructure of a biological tissue according to the present exemplary embodiment. Wherein the values of N are all 6, and the values of the epsilon are all 0.1. Magnetic resonance equipment manufactured by GE company, weight biAre respectively [1, 0 ]]，[0.446，0.895，0]，[0.447，0.275，0.851]，[0.448，-0.723，-0.525]，[0.447，-0.724，0.526]，[-0.449，-0.277，0.850]。
Fig. 1 is a magnetic resonance image of brain tissue, in which the rectangular area is the center of the hemi-oval to be analyzed. Table 1 shows the volume ratios and diffusion coefficients of the cells, blood vessels and extracellular spaces in the center of the hemioval obtained by the above-mentioned non-invasive measurement method of the microstructure of the biological tissue. Wherein, VvasIs the volume ratio of the blood vessel, VecsIs the volume ratio of the extracellular space, VcellIs the volume ratio of the cells, DvasIs the diffusion coefficient of the blood vessel, DecsIs the diffusion coefficient of the extracellular space, DcellIs the diffusion coefficient of the cell.
TABLE 1 volume ratio and diffusion coefficient of cells, vessels and extracellular space in the center of the hemioval of brain tissue
| Types of | Maximum value | Minimum value | Median number | Standard deviation of | Number of pixels |
| Vvas(％) | 18 | 0.67 | 7.3 | 0.091 | 56 |
| Vecs(％) | 40 | 0.75 | 12 | 0.74 | 56 |
| Vcell(％) | 94 | 56 | 79 | 0.73 | 56 |
| Dvas(*10-6mm2/s) | 2.2 | 0.28 | 0.49 | 0.23 | 56 |
| Decs(*10-6mm2/s) | 0.71 | 0.32 | 0.52 | 0.0084 | 56 |
| Dcell(*10-6mm2/s) | 0.004 | 0.0016 | 0.0023 | 0.00000026 | 56 |
。
Fig. 2 is a magnetic resonance image of brain tissue in which a rectangular region is a callus region to be analyzed. Table 1 shows the volume ratios and diffusion coefficients of the cells, blood vessels and extracellular spaces of the callus region obtained by the above-mentioned noninvasive measurement method of the microstructure of the biological tissue.
TABLE 2 volume ratio and diffusion coefficient of cells, vessels and extracellular spaces of the callus region of brain tissue
| Type (B) | Maximum value of | Minimum value of | Median number | Standard deviation of | Number of pixels |
| Vvas(％) | 20 | 3.5 | 11 | 0.2 | 39 |
| Vecs(％) | 38 | 3.7 | 16 | 0.68 | 39 |
| Vcell(％) | 89 | 53 | 70 | 0.87 | 39 |
| Dvas(*10-6mm2/s) | 2.6 | 0.25 | 0.37 | 0.55 | 39 |
| Decs(*10-6mm2/s) | 1.3 | 0.21 | 0.43 | 0.035 | 39 |
| Dcell(*10-6mm2/s) | 0.0041 | 0.0012 | 0.0019 | 0.00000047 | 39 |
。
Fig. 3 to 5 are fiber bundle orientation distribution diagrams obtained by the above-mentioned non-invasive measurement method of the microstructure of the biological tissue. In which, FIG. 3 shows the orientation distribution of the cell fiber bundle in the basal ganglia region, including the transection site, the coronal orientation, the sagittal orientation, and the enlarged view. FIG. 4 shows the distribution of the fiber bundles of the cells on both sides of the corpus callosum, including the crossing site, the coronal site, the sagittal site and the enlarged image. FIG. 5 shows the distribution of the fiber bundles of the tumor and healthy lateral cells, including the transection site, the coronal site, the sagittal site, and the enlarged image.
The noninvasive measurement method of a biological tissue microstructure according to the present exemplary embodiment obtains the volume ratios of cells, blood vessels, and extracellular spaces of normal human brain tissue as follows:
frontal cortex: the volume fraction of cells is about 90%;
center of hemioval: the volume ratio of cells is about 80-85%, the volume ratio of extracellular space to blood vessel is about 1: 1;
basal nodal region: the volume ratio of extracellular space is about 15%, which is consistent with 15-20% reported in the literature.
Figure 6 shows a magnetic resonance image of brain tissue of a patient. As can be seen in FIG. 6, malignant edema in the right hemisphere (i.e., left side of the drawing) of the patient's brain. Fig. 7 is a schematic view corresponding to fig. 6 of reconstruction by the above-described non-invasive measurement method of the microstructure of the biological tissue. In the upper three images in fig. 7, the diffusion coefficient of the cell, the diffusion coefficient of the blood vessel, and the diffusion coefficient of the extracellular space are shown from left to right, respectively; in the lower three images, the volume ratio of cells, the volume ratio of blood vessels, and the volume ratio of extracellular spaces are shown from left to right.
The noninvasive measuring method for the biological tissue microstructure judges whether each voxel point of the biological tissue belongs to a single-chamber structure, a double-chamber structure or a three-chamber structure, and determines the tissue type of each voxel point based on the judgment result, so that the noninvasive measuring method is more accordant with the actual structural characteristics of the biological tissue, and the biological tissue microstructure is measured.
It should be understood that although the present description has been described in terms of various embodiments, not every embodiment includes only a single embodiment, and such description is for clarity purposes only, and those skilled in the art will recognize that the embodiments described herein may be combined as suitable to form other embodiments, as will be appreciated by those skilled in the art.
The above-listed detailed description is only a specific description of possible embodiments of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications such as combinations, divisions, or repetitions of features, which do not depart from the technical spirit of the present invention, should be included in the scope of the present invention.
Claims (7)
1. A method for non-invasive measurement of a microstructure of a biological tissue, comprising:
i, carrying out magnetic resonance diffusion weighted imaging on biological tissues to obtain weights b respectively corresponding to different weightsiWherein i is 1,2,3 … N, N is 6;
II, measuring each of the magnetic fluxesActual image signal intensity S (b) of each voxel point in the dither imagei)；
III, selecting any voxel point in the magnetic resonance image, and calculating the actual image signal intensity S (b) of the voxel pointi) Substituting the following equations 1 to 3 to solve D, V in the equations21、V22、D21、D22、V31、V32、V33、D31、D32And D33The single-chamber model:
the double-chamber model:
three-chamber model:
wherein:
S(b0) The signal intensity at the voxel point when no diffusion sensitive gradient pulse is applied,
d is the diffusion coefficient of the single-cell structure,
V21the volume ratio of the first chamber in the dual chamber structure,
V22the volume ratio of the second chamber in the dual chamber structure,
D21the diffusion coefficient of the first chamber of the dual chamber structure,
D22the diffusion coefficient of the second chamber of the dual chamber structure,
V31the volume ratio of the first chamber in the three-chamber structure,
V32the volume ratio of the second chamber in the three-chamber structure,
V33the third chamber is of a three-chamber structureThe ratio of the products is such that,
D31the diffusion coefficient of the first chamber in a three-chamber structure,
D32the diffusion coefficient of the second chamber in a three-chamber structure,
D33the diffusion coefficient of the third chamber in a three-chamber structure;
IV, judging that the voxel point is in a single-chamber structure, a double-chamber structure or a three-chamber structure according to the result of the solution in the step III;
v, if the voxel point is judged to be in the single-chamber structure in the step IV, judging the tissue type of the single-chamber structure according to D; the tissue types include cells, blood vessels, and extracellular spaces; the volume ratio and diffusion coefficient of the tissue type not contained in the single-chamber structure were set to 0,
if the voxel point is judged to be a double-chamber structure in the step IV, according to D21And D22Determining a tissue type of a first chamber and a second chamber of the dual chamber structure; the tissue types include cells, blood vessels, and extracellular spaces; the volume ratio and diffusion coefficient of the tissue type not contained in the dual chamber structure were set to 0,
if the voxel point is judged to be of a three-chamber structure in the step IV, the voxel point is judged to be of a three-chamber structure according to D31、D32And D33Judging the tissue types of a first chamber, a second chamber and a third chamber of the three-chamber structure; the tissue types include cells, blood vessels, and extracellular spaces;
and VI, repeating the steps III to V to analyze other voxel points until all the voxel points are analyzed.
2. The method for non-invasive measurement of biological tissue microstructure according to claim 1, wherein said step iv of determining whether the voxel point is in a single chamber structure, a double chamber structure or a triple chamber structure according to the result of the solution in step iii is specifically:
if it is not
And is
Then the voxel point is a single-chamber structure;
if it is not
And is
Then the voxel point is a dual chamber structure;
otherwise, the voxel point is in a three-chamber structure.
3. The method for non-invasive measurement of a microstructure of biological tissue according to claim 1, further comprising, after step vi:
and a step VII of reconstructing the magnetic resonance image based on one or more of the volume ratio of the cells, the volume ratio of the blood vessels, the volume ratio of the extracellular space, the diffusion coefficient of the cells, the diffusion coefficient of the blood vessels, and the diffusion coefficient of the extracellular space at each voxel point.
4. The method for non-invasive measurement of a microstructure of a biological tissue according to claim 1, wherein the solving method in the step iii is solved by using a constrained non-linear optimization; wherein,
the optimization formula of equation 1 is:
s.t.D≥0
the optimization formula of equation 2 is:
the optimization formula of equation 3 is:
5. the method for non-invasive measurement of biological tissue microstructures of claim 4, wherein the constrained non-linear optimization solution employs a Lagrangian multiplier method.
6. The method for non-invasive measurement of a microstructure of biological tissue according to claim 1, further comprising, after step vi:
and VIII, calculating the cellulose trend distribution of the cells, the blood vessels and the extracellular spaces according to the diffusion coefficient of the cells, the diffusion coefficient of the blood vessels and the diffusion coefficient of the extracellular spaces of each voxel point.
7. The method for non-invasive measurement of biological tissue microstructure according to claim 6, wherein said estimation is statistical or based on a principal diffusion direction tracking method.
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