A method for making a head and neck model in compliance with human tissue elasticity modulus

By using nuclear magnetic resonance imaging and silicone ratio technology, the problems of three-dimensional reconstruction and material matching of head and neck models were solved, resulting in head and neck models that conform to real tissue parameters and are suitable for experiments and teaching.

CN116228970BActive Publication Date: 2026-06-19CAPITAL UNIVERSITY OF MEDICAL SCIENCES

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
CAPITAL UNIVERSITY OF MEDICAL SCIENCES
Filing Date
2023-02-03
Publication Date
2026-06-19

AI Technical Summary

Technical Problem

Existing technologies struggle to construct complete head and neck models that conform to the Young's modulus of real tissues, particularly in the reconstruction of three-dimensional digital anatomical structures of soft and bony tissues. Furthermore, there is a lack of adjustable model-making materials to adapt to the mechanical parameters of different tissues.

Method used

Multi-directional image reconstruction technology based on nuclear magnetic resonance imaging was used, combined with the level set method to extract tissue boundaries, and a three-dimensional model was constructed using NURBS surface. A solid model that conforms to the elastic modulus of real tissue was then made by using a specific ratio of silicone.

Benefits of technology

It achieves accurate reconstruction of the anatomical structure of the head and neck model and matching of real tissue parameters, which is suitable for various experiments and teaching, reduces the distortion of tissue anatomy, and can reflect the mechanical properties of the head and neck.

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Abstract

This invention relates to a method for fabricating a head and neck model that conforms to the elastic modulus of human tissue. The method includes: reconstructing multi-directional cross-sectional images of the head and neck tissues based on three-dimensional MRI images of the head and neck, according to tissue structural characteristics; segmenting the tissue boundaries of the multi-directional cross-sectional images and extracting tissue boundary points using a level set method and manual methods; constructing a three-dimensional digital anatomical model; fabricating silicone molds for bony structures and various tissues; preparing a silicone solution according to a certain proportion based on the actual elastic modulus of the tissues and pouring it into molds; and assembling the silicone models of each tissue and the fixing frame according to the actual anatomical structure and practical usage requirements. The model constructed by this method can accurately represent the anatomical structure and topological relationships of the tissues and has the elastic modulus of real tissues. It can be used for in vitro models of upper airway breathing experiments, head and neck surgical simulations, and the fabrication of anatomical teaching aids.
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Description

Technical Field

[0001] This invention relates to the field of in vitro model making of human head and neck, and to a method for making head and neck models based on the elastic modulus of human tissue. Background Technology

[0002] Human anatomical models have diverse applications, including various in vitro experiments and teaching. Compared to animal experiments and simulation systems, physical models offer advantages such as lower risk, higher repeatability, and lower cost. However, constructing a complete, accurate head and neck model that conforms to the Young's modulus of real tissues remains a significant challenge.

[0003] First, constructing a realistic head and neck model requires establishing a complete three-dimensional geometric model of human tissue. However, the head and neck contain complex soft and bony tissues, and currently there is no effective method to construct a relatively complete three-dimensional digital anatomical model of the head and neck. Common methods based on unidirectional MRI image reconstruction struggle to reflect the complete contours of tissues, especially for tissues and organs with complex anatomical structures such as the tongue muscles and soft palate. This method is insufficient for constructing accurate tissue structures. Furthermore, the surfaces of three-dimensional structures constructed using image voxels require smoothing, which can distort the anatomical structure of the tissues. Second, the elastic moduli of different tissues in the head and neck vary greatly, by as much as seven to eight orders of magnitude. Currently, most head and neck models are made of plastic or resin materials, which have uniform elastic moduli that differ significantly from the parameters of real tissues, and there is a lack of relatively complete head and neck tissue models. Several factors limit the production of physical models. On the one hand, due to limitations in effective three-dimensional reconstruction methods, existing head and neck tissue models cannot accurately separate different tissues individually. On the other hand, there is a lack of adjustable model-making materials to adapt to the different mechanical parameters of head and neck tissues.

[0004] Currently, there are still many problems in constructing relatively complete in vitro models of the human head and neck, and a complete scheme for the production of in vitro models of the head and neck needs to be developed. Summary of the Invention

[0005] The purpose of this invention is to provide a method for fabricating a head and neck model that conforms to the elastic modulus of human tissue.

[0006] The method for fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention includes:

[0007] Step 1: Based on three-dimensional magnetic resonance imaging of the head and neck, reconstruct multi-directional oblique cross-sectional images of the tissue according to its structural characteristics;

[0008] Step 2: Extract tissue boundaries by using the level set method or manually segmenting multi-directional tissue boundaries;

[0009] Step 3: Construct a complete three-dimensional digital anatomical model of the head and neck;

[0010] Step 4: Create a skeletal structure model, fixation frame, and silicone mold;

[0011] Step 5: Prepare the silica gel solution and use the silica gel mold from Step 4 to create silica gel models of each tissue.

[0012] Step 6: Assemble the silicone models of each tissue;

[0013] According to the method for fabricating a head and neck model conforming to the elastic modulus of human tissue of the present invention, step 1 includes:

[0014] Step 101: Acquire three-dimensional sagittal images of the subject's head and neck, and reconstruct coronal and axial images with consistent inter-slice spacing and pixel size.

[0015] Step 102: Manually generate an auxiliary curve along the tissue contour line in the midsagittal plane, and reconstruct the image along the direction perpendicular to the auxiliary curve to obtain the oblique cross-sectional image of the tissue. The pixel value G at point P on the straight line L where the oblique cross-sectional image intersects the sagittal image is... p Expressed as follows:

[0016]

[0017] Where G represents the gray level of a pixel, S i S represents the area of ​​a pixel reconstructed along the direction of the auxiliary curve. P Let P be the pixel area of ​​the intersecting straight lines L;

[0018] Step 103: Reconstruct the image along the normal direction of the auxiliary curve to obtain the curved cross-section image, and then expand the curved cross-section image into a plane. The curved cross-section image is obtained by interpolation of the sagittal plane image. The curved cross-section image intersects with each sagittal plane image by a curve. The parametric expression of the curve is expressed as:

[0019]

[0020] Where j∈(0,1),

[0021] Pixel value G at point T on intersecting curve R T Similar to oblique section images, it is expressed by the following formula:

[0022]

[0023] Where G represents the gray level of a pixel, S i S represents the area of ​​a pixel reconstructed along the direction of the auxiliary curve. T Let T be the pixel area at point T on the intersecting curve R.

[0024] According to the method for fabricating a head and neck model conforming to the elastic modulus of human tissue of the present invention, step 2 includes:

[0025] Step 201: Use MATLAB to segment the boundaries of each tissue in the planar cross-sectional image and extract the spatial 3D coordinates of the boundary points. The cross-sectional image includes planar cross-sectional images and curved cross-sectional images.

[0026] Step 202: Use NX-UG modeling software to generate NURBS surfaces of various human tissues from the boundary points.

[0027] According to the method for fabricating a head and neck model conforming to the elastic modulus of human tissue of the present invention, step 3 includes:

[0028] Step 301: Based on the actual anatomical structure, assemble the various tissues and organs, and perform Boolean operations on each tissue to generate the common surface between adjacent tissues;

[0029] Step 302: Adjust the model according to actual usage needs. The following operations can be performed on the model: enlarge or reduce the model proportionally, remove irrelevant tissue, set data measurement points and fixation supports, etc.

[0030] According to the method for fabricating a head and neck model conforming to the elastic modulus of human tissue of the present invention, step 4 includes:

[0031] Step 401: Use 3D printing photosensitive resin to create bony structures such as the hyoid bone, hard palate, and mandible;

[0032] Step 402: Use 3D printing materials such as photosensitive resin or acrylic to create a device for displaying or fixing the model;

[0033] Step 403: Shell the other tissue 3D models and leave injection holes and ventilation holes, and use photosensitive resin 3D printing to make silicone molds.

[0034] According to the method for fabricating a head and neck model conforming to the elastic modulus of human tissue of the present invention, step 5 includes:

[0035] Step 501: Spray petroleum jelly or release agent evenly on the inner surface of the mold, assemble the mold and fix it in place;

[0036] Step 502: According to the elastic modulus of the tissue to be produced, mix silicone, silicone curing agent and silicone oil in a certain proportion, and add an appropriate amount of oil pigment to distinguish different tissues. After stirring evenly, use a vacuum pump to remove air bubbles.

[0037] Step 503: Pour the silicone solution into the corresponding mold, wait for the model to fully solidify, remove the model and adjust it as needed.

[0038] According to the method for fabricating a head and neck model conforming to the elastic modulus of human tissue of the present invention, silicone, silicone curing agent, and silicone oil are mixed in the following proportions based on the elastic modulus of the fabricated tissue:

[0039]

[0040] Where T is the tissue elastic modulus value, the unit is kPa, M1 is the mass of silicone, M2 is the mass of silicone oil, M3 is the mass of curing agent, and K ranges from 0.015 to 0.02.

[0041] The beneficial effects of this invention are as follows:

[0042] Currently, constructing a relatively complete in vitro model of the human head and neck presents technical challenges. These challenges stem not only from the lack of a comprehensive and effective 3D reconstruction scheme for head and neck tissues, but also from the fact that no in vitro head and neck model has yet been able to accurately reflect the mechanical properties of the tissues. For the head and neck region, with its numerous complex anatomical structures, a complete method for 3D reconstruction and model fabrication is needed to accurately reflect the anatomical structure and tissue parameters of the head and neck. The method described in this application is based on magnetic resonance imaging (MRI) to construct a complete and accurate head and neck model, and uses silicone to fabricate a solid model that conforms to the elastic modulus of real tissues. The constructed model can be used for various in vitro head and neck model experiments, surgical teaching, and simulated tissue resection and suturing; it can also be used for virtual simulation and numerical simulation of upper airway airflow changes and particulate matter deposition.

[0043] This invention provides a method for creating a head and neck model that conforms to the elastic modulus of human tissue. It proposes to reconstruct multi-directional images based on the structural features of the tissue. Compared with single-directional MRI images, such as coronal, sagittal, and axial images, multi-directional images can accurately display the boundary information of the tissue contour in different directions, and can effectively solve the problem of accurate reconstruction of tissues and organs with complex anatomical structures.

[0044] This invention relates to a method for fabricating a head and neck model that conforms to the elastic modulus of human tissue. It proposes constructing a tissue NURBS surface using boundary curves to form the corresponding three-dimensional structure of the tissue. This method eliminates the need for tissue smoothing, thereby reducing distortion of the tissue's anatomical structure caused by reconstruction.

[0045] This invention relates to a method for fabricating a head and neck model that conforms to the elastic modulus of human tissue. It proposes to fabricate a three-dimensional solid model using an adjustable silicone ratio scheme. The tissue model fabricated in this way has an elastic modulus that matches the parameters of real tissue, thus reflecting the mechanical properties of the corresponding tissue. Attached Figure Description

[0046] Figure 1This is a flowchart illustrating the method for fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention.

[0047] Figure 2 This is a schematic diagram of a cross-sectional image of the tongue muscle tissue in the method for fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention.

[0048] Figure 3 The formula for generating oblique section images of the method for making a head and neck model that conforms to the elastic modulus of human tissue according to the present invention is shown.

[0049] Figure 4 This is a schematic image of the curved cross-section of the tongue muscle tissue in the method for fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention.

[0050] Figure 5 The present invention provides a formula for generating a curved section image of a head and neck model conforming to the elastic modulus of human tissue.

[0051] Figure 6 This invention displays a complete three-dimensional digital model of the head and neck conforming to the elastic modulus of human tissue;

[0052] Figure 7 A tongue muscle tissue mold illustrating the method for fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention;

[0053] Figure 8 This demonstrates the relationship between the elastic modulus and silicone oil content in a head and neck model fabrication method that conforms to the elastic modulus of human tissue.

[0054] Figure 9 This is a schematic diagram of a complete head and neck model for the method of fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention.

[0055] Figure 10 This is a schematic diagram of a cross-sectional image of the skull for the method of fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention.

[0056] Figure 11 This is a schematic diagram of a mandibular oblique section image of the method for fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention.

[0057] Figure label:

[0058] 1: Skin; 2: Hard palate; 3: Soft palate; 4: Mandible; 5: Tongue muscle; 6: Sublingual fat; 7: Hyoid bone; 8: Hyoid-epiglottic ligament; 9: Epiglottis; 10: Thyroepiglottic ligament; 11: Thyroid cartilage; 12: Cricoid cartilage; 13: Soft tissue; 14: Irrigation port; 15: Ventilation port; 16: Tongue muscle mold A; 17: Tongue muscle mold B. Detailed Implementation

[0059] The method for fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention involves reconstructing multi-directional cross-sectional images based on magnetic resonance imaging (MRI) and various tissue anatomical structures, extracting tissue boundary information, and constructing a tissue model; then, a silicone model conforming to the elastic modulus of real tissue is fabricated according to a specific ratio. The fabricated model has accurate anatomical structure and conforms to real tissue parameters.

[0060] The following description, with reference to the accompanying drawings, illustrates the method for fabricating a head and neck model conforming to the elastic modulus of human tissue according to the present invention. A detailed explanation of the model fabrication method is provided using the construction of a three-dimensional model and a solid model of tongue muscle tissue as an example. The flowchart is shown below. Figure 1 As shown, the specific steps include:

[0061] Step 1: Reconstruct multi-directional MRI images based on tissue structure characteristics. Taking tongue muscle tissue as an example, this specifically includes:

[0062] Step 101: Acquire three-dimensional sagittal sequence images of the subject's head and neck, and reconstruct coronal and axial images with consistent image layer spacing and pixel size.

[0063] Step 102: Manually generate an auxiliary curve along the tissue contour line in the midsagittal plane, and reconstruct the image along the direction perpendicular to the auxiliary curve to obtain a slant image of the tissue's oblique section, as shown below. Figure 2 As shown, (a) is a fan-shaped distribution of oblique cross sections, where the white lines are the projections of each oblique cross section image onto the sagittal plane; (b) is the spatial position of the reconstructed cross-sectional image relative to the midsagittal image, and the projection of this image onto the midsagittal plane image is (a). Figure 2 The dashed line in figure (c) shows the reconstructed oblique section image. Figure 3 As shown, the oblique cross-sectional planar image of the tongue muscle is obtained by interpolation from the sagittal plane image. The oblique cross-sectional planar image intersects with each sagittal plane image by a straight line, and the pixel value G at point P on the straight line L is... p Expressed as follows:

[0064]

[0065] Where G represents the gray level of a pixel, S i S represents the area of ​​a pixel reconstructed along the direction of the auxiliary curve. P Let P be the pixel area of ​​the intersecting straight lines L;

[0066] Step 103: Reconstruct the image along the normal direction of the auxiliary curve to obtain the surface cross-section image, and expand the surface cross-section image into a plane, such as... Figure 4As shown, (a) is the spatial position of the curved cross-sectional image relative to the mid-sagittal image, and (b) is the planar image unfolded from the curved cross-sectional image. The curved cross-sectional image is obtained by interpolation from the sagittal image. The curved cross-sectional image intersects with each sagittal image by a curve, and the parametric expression of the curve is expressed as:

[0067]

[0068] Where j∈(0,1),

[0069] like Figure 5 As shown, the pixel value G at point T on the intersecting curve R T Expressed as follows:

[0070]

[0071] Where G represents the gray level of a pixel, S i S represents the area of ​​a pixel reconstructed along the direction of the auxiliary curve. T Let T be the pixel area at point T on the intersecting curve R.

[0072] Step 2: Segment tissue boundaries based on reconstructed images, extract boundary points, and generate tissue contours based on boundary points in each direction. Taking tongue muscle tissue as an example, this specifically includes:

[0073] Step 201: Use MATLAB to segment the tongue muscle boundary in the planar cross-sectional image, and store the extracted boundary points in a separate text file in the form of spatial 3D coordinates. The planar cross-sectional image includes coronal, sagittal, and axial images, as well as the aforementioned oblique and curved cross-sectional images;

[0074] Step 202: Use NX-UG modeling software to fit smooth curves to the boundary points of the tongue muscle tissue in each direction;

[0075] Step 203: Import the smooth curves fitted above into the same project file in NX-UG software, and construct the NURBS surface of the tongue muscle tissue based on the curves in each direction.

[0076] Step 3: Assemble the tongue muscles and various tissues and organs according to the actual anatomical structure to construct a complete three-dimensional digital anatomical model of the head and neck. Modify the tongue muscle tissue model according to actual needs, specifically including:

[0077] Step 301: Based on the actual anatomical structure, assemble the tongue muscles and various tissues and organs, and perform Boolean operations on the tongue muscles and their adjacent tissues to generate common surfaces between adjacent tissues.

[0078] Step 302: Adjust the tongue muscle model according to actual usage needs, proportionally adjust the size of the tongue muscle tissue model, and determine the measurement sites for the tongue muscle tissue. The complete head and neck model constructed is as follows: Figure 6 As shown.

[0079] Step 4: Create a bony structure model, a fixation framework, and molds for each tissue. Taking the construction of the tongue muscle mold as an example, the specific steps include:

[0080] Step 401: Use 3D printing photosensitive resin to fabricate the bony structures of the mandible, hard palate, and mandible;

[0081] Step 402: Use 3D printing materials such as photosensitive resin or acrylic to create a device for displaying or fixing the model;

[0082] Step 403: As Figure 7 As shown, the three-dimensional digital model of the tongue muscle is shelled. An injection hole and a ventilation hole are set at the highest point of the shelled model. The shelled model is divided into two parts, A and B, along the midline plane to facilitate demolding. Grooves and protrusions are set to facilitate precise positioning.

[0083] Step 5: Prepare the silica gel solution and use the silica gel mold from Step 4 to create silica gel models of various tissues. Taking the tongue muscle tissue as an example, the specific steps include:

[0084] Step 501: Spray petroleum jelly or release agent evenly on the inner surface of the tongue muscle mold, assemble the mold, and fix it with tape;

[0085] Step 502: Based on the elastic modulus of the tissue being prepared, mix the silicone, silicone curing agent, and silicone oil in the following proportions:

[0086]

[0087] Where T is the elastic modulus of the tissue, in kPa; M1 is the mass of silicone; M2 is the mass of silicone oil; and M3 is the mass of curing agent. K ranges from 0.015 to 0.02; in this example, K is 0.02. The relationship between T and n is as follows: Figure 8 As shown, an appropriate amount of oily pigment can be added to distinguish different tissues. After stirring the mixed solution evenly, use a vacuum pump to remove all air bubbles.

[0088] Step 503: Slowly pour the silicone solution into the tongue muscle mold through the inlet to prevent air bubbles from forming. After the model has completely solidified, remove the tongue muscle model and adjust it according to the actual anatomical structure.

[0089] Step 6: Assemble the silicone models of each tissue and the fixation frame according to the actual anatomical structure and usage requirements. The complete head and neck solid model is as follows: Figure 9As shown, (a) shows the rear side of the solid model, and (b) shows the front side of the solid model.

[0090] Steps 1-5 are the specific steps for reconstructing the three-dimensional model of the tongue muscle tissue. For the bony structures of the head and neck, such as the skull, maxilla, mandible, hyoid bone, and cricothyroid cartilage, corresponding cross-sectional images are constructed based on the anatomical characteristics of these bony structures. Figure 10 , Figure 11 As shown. Figure 10 In the middle (a) image, the white rays originate at the center of the foramen magnum, and the cross-sectional image of the skull is along the direction of these rays and perpendicular to the axial plane image shown in the image. Figure 10 (b) shows the spatial position of the cross-sectional image of the skull relative to the axial plane image. Figure 11 In the middle (a) image, the black line runs along the medial edge of the mandible and is located on the axial plane image. The cross-sectional image of the mandible passes through the white reference line and is perpendicular to the axial plane image. Figure 11 Figure (b) shows the spatial position of the cross-sectional image of the mandible relative to the axial image.

[0091] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for fabricating a head and neck model conforming to the elastic modulus of human tissue, characterized in that, The method includes the following steps: Step 1: Based on three-dimensional magnetic resonance imaging of the head and neck, according to the structural characteristics of the tissue, reconstruct multi-directional cross-sectional images of the tissue along the tissue contour direction, including planar cross-sectional images and curved cross-sectional images. The planar cross-sectional images include coronal images, sagittal images, axial images, and oblique cross-sectional planar images. Step 2: Extract tissue boundaries by using the level set method or manually segmenting multi-directional tissue boundaries; Step 3: Construct a complete three-dimensional digital anatomical model of the head and neck; Step 4: Create a bony structure model, fixation frame, and silicone mold; Step 5: Prepare the silica gel solution and use the silica gel mold made in Step 4 to create silica gel models of each tissue; Step 6: Assemble the silicone models of each tissue. Step 1 includes: Step 101: Acquire three-dimensional sagittal sequence images of the subject's head and neck, and reconstruct coronal and axial images with consistent image layer spacing and pixel size; Step 102: Generate an auxiliary curve along the tissue contour line in the midsagittal plane of the obtained sagittal sequence image, and reconstruct the image along the direction perpendicular to the auxiliary curve to obtain an oblique cross-sectional planar image of the tissue. The pixel value G at point P on the straight line L where the oblique cross-sectional planar image intersects the sagittal image is... P As shown in the following formula: , Where G represents the gray level of a pixel, S i S represents the area of ​​a pixel reconstructed along the direction of the auxiliary curve. P Let P be the pixel area of ​​the intersecting straight lines L; Step 103: Reconstruct the image along the normal direction of the auxiliary curve to obtain a curved cross-sectional image, and then expand the curved cross-sectional image into a plane. The curved cross-sectional image is obtained by interpolation of the sagittal plane image. The curved cross-sectional image intersects with each sagittal plane image by a curve. The parametric expression of the intersection curve R is: , wherein (0, 1), The pixel value G at point T on the intersecting curve R T It can be expressed by the following formula: Where G represents the gray level of a pixel, and S... i S represents the area of ​​a pixel reconstructed along the direction of the auxiliary curve. T Let T be the pixel area at point T on the intersecting curve R.

2. The method of claim 1, wherein Step 2 includes: Step 201: Use MATLAB to segment the boundaries of each tissue in the planar cross-sectional image and extract the spatial 3D coordinates of the boundary points; Step 202: Using the 3D coordinates of the boundary points, generate NURBS surfaces of various human tissues from the boundary points using NX-UG modeling software.

3. The method of claim 1, wherein: Step 3 includes: Step 301: Based on the actual anatomical structure, assemble the various tissues and organs, and perform Boolean operations on each tissue to generate the common surface between adjacent tissues; Step 302: Adjust the model according to actual usage needs, enlarge or reduce the model proportionally, remove irrelevant tissue, and set data measurement points and fixation supports.

4. The method of claim 1, wherein Step 4 includes: Step 401: Use 3D printing photosensitive resin to create a bony structure model of the head and neck bones; Step 402: Fabricate the fixing bracket using 3D printing; Step 403: Shell the other tissue 3D models and leave injection holes and ventilation holes, and use photosensitive resin 3D printing to make silicone molds.

5. The method of claim 1, wherein: Step 5 includes: Step 501: Spray petroleum jelly or release agent evenly on the inner surface of the prepared silicone mold, assemble the mold and fix it; Step 502: According to the elastic modulus of the tissue being produced, mix silicone, silicone curing agent and silicone oil in proportion, and add oily pigment to distinguish different tissues to obtain silicone solution. Stir evenly and remove air bubbles. Step 503: Pour the silicone solution into the corresponding silicone mold, wait for the model to fully cure, remove the model and adjust it as needed.

6. The method of claim 5, wherein the head and neck model having the human tissue modulus of elasticity is made by: For step 502, based on the elastic modulus of the produced tissue, silicone, silicone curing agent, and silicone oil are mixed in the following proportions: Where T is the elastic modulus of the tissue, and its unit is kPa; M1 is the mass of silicone; M2 is the mass of silicone oil; M3 is the mass of curing agent; and K ranges from 0.015 to 0.02.