Method for estimating parameters of in-vivo organ tissue biomechanics

Abstract

The application relates to a method for estimating the biomechanical parameters of in-vivo organ tissues, which comprises the following steps: in-vivo organ tissue geometry modeling is performed to obtain a tetrahedral mesh structure of the in-vivo organ tissues; according to the obtained tetrahedral mesh structure of the in-vivo organ tissues, in-vivo organ tissue biomechanical model modeling is performed; according to the in-vivo organ tissue biomechanical model, in-vivo organ tissue boundary condition estimation is performed; and the strong tracking Kalman filter is used to estimate the biomechanical parameters of the in-vivo organ tissues under the current boundary condition estimation result. The application can estimate the biomechanical parameters of in-vivo organ tissues of human bodies under complex boundary conditions, and the estimated biomechanical parameters are more accurate.

Description

Technical Field

[0001] This invention relates to a method for estimating biomechanical parameters of organs and tissues in vivo. Background Technology

[0002] Biomechanical models of human organs are of great significance in virtual surgical simulation and soft tissue motion calculation. However, human organs not only have complex internal structures, but are also in a complex internal environment surrounded by multiple organs, which makes the estimation of biomechanical models of internal organs subject to considerable uncertainty.

[0003] With the development of modern medicine and computer technology, intraoperative navigation technology has become one of the important fields in the medical field. Among them, the accurate simulation of the deformation of internal organs is one of the key technologies for the success of intraoperative navigation technology. The simulation of organ deformation relies on personalized biomechanical models, including the complex boundary conditions of organs and personalized elastic biomechanical parameters. Whether the biomechanical model is accurately constructed is related to the accuracy of intraoperative organ deformation tracking.

[0004] Currently, many methods for biomechanical modeling have been proposed both domestically and internationally. In terms of biomechanical parameter estimation, existing techniques such as ultrasound elastography and nuclear magnetic resonance elastography can be directly used to measure the relative elastic distribution of human organs. However, the accuracy of these techniques cannot be guaranteed at present, and they are mainly used for qualitative analysis of human tissues in clinical practice, such as assessing the degree of liver fibrosis. The inverse finite element method (IFM) has been a major research direction in computational biomechanics for human tissue modeling in recent years. These methods measure the deformation of an object under certain stress and then perform inverse solving based on the stress-strain relationship to obtain material parameters. Hajhashemkhani et al., in order to estimate the material mechanical parameters when some boundary conditions are known, used the Gauss-Newton algorithm based on collected partial displacement information and corresponding prediction information to complete the inverse finite element analysis of the target. However, the boundary conditions considered in this method are still relatively simple. In recent years, some scholars have proposed combining Bayesian inference to reduce estimation errors caused by uncertainties. Peterlik et al. used a reduced-order unscented Kalman filter (ROUKF) to estimate the biomechanical parameters of the target to improve the robustness of the simulation process. Nikolaev et al. applied ROUKF to the estimation of biomechanical parameters under abrupt boundary conditions, thus proving that ROUKF also has a good adaptability to changes in boundary conditions. However, these methods require an accurate system model; otherwise, the uncertainty of the system model itself will cause the results of these methods to deviate or even fail to converge. Summary of the Invention

[0005] In view of this, it is necessary to provide an in vivo biomechanical parameter estimation method for organs and tissues that can reduce the uncertainty error in the biomechanical parameter estimation process through its internal adaptive phase.

[0006] This invention provides a method for estimating biomechanical parameters of in vivo organs and tissues. The method includes the following steps: a. performing geometric modeling of the in vivo organ and tissue to obtain a tetrahedral mesh structure; b. modeling a biomechanical model of the in vivo organ and tissue based on the obtained tetrahedral mesh structure; c. estimating boundary conditions of the in vivo organ and tissue based on the biomechanical model; d. estimating the biomechanical parameters of the in vivo organ and tissue using a strong tracking Kalman filter under the current boundary condition estimation results.

[0007] Specifically, step a includes:

[0008] First, the geometric model of the organ tissue is reconstructed from 4D MRI data to obtain the reconstructed surface of the organ tissue. Then, the reconstructed surface of the organ tissue is meshed to obtain the tetrahedral mesh structure of the organ tissue.

[0009] Specifically, step b includes:

[0010] The boundary conditions of a body organ or tissue are equivalently represented as a set of equivalent external forces λ applied to the surface of the body organ or tissue due to collisions and contacts with anatomical tissues surrounding it. Common elastic parameters, Young's modulus and Poisson's ratio, are then used as parameters representing the elastic material properties of the body organ or tissue. The equilibrium equation for the body organ or tissue is:

[0011] f(q t )+f+J T λ = 0,

[0012] Where, f(q) t ) represents the external force, f represents the internal force, and λ and J are the Jacobian matrices of the boundary equivalent external force and external force constraint to be solved, respectively.

[0013] Specifically, step c includes:

[0014] First, non-rigid registration is performed on in vivo organ and tissue models under different deformation states to obtain the correspondence between surface points of in vivo organ and tissue geometric models under two deformation states.

[0015] Then, the free deformation of the organ or tissue in the body under unbounded conditions is calculated. At this point, the displacement information of the organ or tissue in the body is calculated at the corresponding points:

[0016] δ=dot(q s -q t nc ),

[0017] q s and q t These represent the displacements of corresponding points on the surface of organs and tissues under unbounded and bounded conditions, respectively, n. c It is a unit vector pointing to the deformation of various points in an organ or tissue in the body;

[0018] Finally, the boundary condition λ is estimated by solving the constraint problem:

[0019] Wλ+δ=0,

[0020] Where W = JCJ T The delassus operator is a common operator, and C represents the compliance matrix of the elastic properties of organs and tissues in vivo; finally, the estimated boundary conditions λ are obtained by solving the problem based on the Gauss-Seidel algorithm.

[0021] Specifically, step d includes:

[0022] Using a strong tracking Kalman filter, the biomechanical parameters of in vivo organs and tissues are estimated in three stages under the current boundary condition estimation results; the three stages include: prediction stage, adaptation stage, and update stage.

[0023] Specifically, the prediction phase includes:

[0024] The state vector containing biomechanical parameters and initial shape information of organs and tissues in vivo is represented using a Gaussian distribution. Predict the state of the current frame after organ and tissue deformation based on the initial state. and the corresponding covariance matrix

[0025]

[0026]

[0027] in, In the initial state Gaussian distribution group The i-th (i = 1, 2, ..., 2N+1) Sigma group, and Let represent the mean weight and covariance weight, respectively, and Qk represent Gaussian noise.

[0028] Specifically, the adaptive phase includes: in order to minimize the impact of uncertainty errors in the system model, the adaptive phase incorporates observational information Y of the historical deformation of in vivo organs and tissues. k For covariance matrix The model is continuously updated until its uncertainty error (i.e., Mahalanobis distance) is less than a certain threshold. The update formula is:

[0029]

[0030] in, It is the innovation vector of the observation data, M and R represents the historical window size and its corresponding weight, respectively. k The table shows Gaussian white noise in the observation data.

[0031] Specifically, the update phase includes: combining the observed surface displacement information of the organ tissue portion in the current frame with the calculated Kalman gain K. k The predicted in vivo organ and tissue status results were modified as follows:

[0032]

[0033]

[0034] in It is the covariance matrix of the observed data.

[0035] The beneficial effects of this application include:

[0036] First, the boundary conditions handled in this application are more complex. By using equivalent external forces to represent the boundary conditions, the influence of the surrounding anatomical tissues on the in vivo organ tissues is reflected more completely, while the problem to be dealt with is not made too complicated. It more comprehensively reflects the constraints on the surface of the in vivo organ tissues. At the same time, this application is more generalizable to other scenarios.

[0037] Secondly, the strong tracking Kalman filter used in this application can better handle the uncertainty error in the biomechanical parameter estimation process. The adaptive stage of the strong tracking Kalman filter reduces the uncertainty error in the system to within the specified threshold by combining historical information, making the estimated biomechanical parameters more accurate. Attached Figure Description

[0038] Figure 1 This is a flowchart of the in vivo organ and tissue biomechanical parameter estimation method of the present invention. Detailed Implementation

[0039] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0040] See Figure 1 The diagram shown is a flowchart of a preferred embodiment of the biomechanical parameter estimation method for organs and tissues in vivo according to the present invention.

[0041] Step S1 involves performing in vivo organ tissue geometry modeling to obtain the tetrahedral mesh structure of the in vivo organ tissue. Specifically:

[0042] In this embodiment, the in vivo organ tissue geometric model is first reconstructed from 4D MRI data to obtain the in vivo organ tissue reconstruction surface, and then the in vivo organ tissue reconstruction surface is meshed to obtain the tetrahedral mesh structure of the in vivo organ tissue.

[0043] Step S2: Based on the obtained tetrahedral mesh structure of the in vivo organ tissue, a biomechanical model of the in vivo organ tissue is created. Specifically:

[0044] First, the boundary conditions of the organ / tissue are equivalently represented as a set of equivalent external forces λ applied to the surface of the organ / tissue due to collisions and contacts with surrounding anatomical tissues. Then, the commonly used elastic parameters Young's modulus and Poisson's ratio are used as parameters representing the elastic material properties of the organ / tissue. The equilibrium equation for the organ / tissue is:

[0045] f(q t )+f+J T λ = 0,

[0046] Where, f(q) t ) represents the external force, f represents the internal force, and λ and J are the Jacobian matrices of the boundary equivalent external force and external force constraint to be solved, respectively.

[0047] Step S3: Based on the in vivo organ and tissue biomechanical model, estimate the boundary conditions of the in vivo organ and tissue. Specifically:

[0048] First, non-rigid registration is performed on in vivo organ and tissue models under different deformation states to obtain the correspondence between surface points of the in vivo organ and tissue geometric models under two deformation states.

[0049] Then, the free deformation of the organ or tissue in the body under unbounded conditions is calculated. At this point, the displacement information of the organ or tissue in the body is calculated at the corresponding points:

[0050] δ=dot(q s -q t n c ),

[0051] q s and q t These represent the displacements of corresponding points on the surface of organs and tissues under unbounded and bounded conditions, respectively, n. c It is a unit vector that refers to the deformation of various points in an organ or tissue.

[0052] Finally, the boundary condition λ is estimated by solving the constraint problem:

[0053] Wλ+δ=0,

[0054] Where W = JCJ T Here, C is a common delassus operator, and C represents the compliance matrix of the elastic properties of organs and tissues in vivo. The estimated boundary conditions λ are finally obtained by solving using the Gauss-Seidel algorithm.

[0055] Step S4: Using a strong tracking Kalman filter, the biomechanical parameters of in vivo organs and tissues are estimated based on the current boundary condition estimation results. Specifically:

[0056] The estimation of biomechanical parameters of in vivo organs and tissues using a strong tracking Kalman filter under the current boundary condition estimation results is mainly divided into three stages:

[0057] The first stage is the prediction phase: a Gaussian distribution is used to represent the state vector containing biomechanical parameters and initial shape information of organs and tissues in vivo. Predict the state of the current frame after organ and tissue deformation based on the initial state. and the corresponding covariance matrix

[0058]

[0059]

[0060] in, In the initial state Gaussian distribution group The i-th (i = 1, 2, ..., 2N+1) Sigma group. and Q represents the mean weight and covariance weight, respectively. k This represents Gaussian noise.

[0061] Then comes the adaptive phase: In order to minimize the impact of uncertainties and errors in the system model, the adaptive phase incorporates observational information Y of the historical deformation of organs and tissues in vivo. k For covariance matrix The model is continuously updated until its uncertainty error (i.e., Mahalanobis distance) is less than a certain threshold. The update formula is:

[0062]

[0063] in, It is the innovation vector of the observation data, M and R represents the historical window size and its corresponding weight, respectively. k The table shows Gaussian white noise in the observation data.

[0064] Finally, the update phase: combining the observed displacement information of the organ tissue surface in the current frame, and using the calculated Kalman gain K... k The predicted in vivo organ and tissue status results were modified as follows:

[0065]

[0066]

[0067] in It is the covariance matrix of the observed data.

[0068] This application considers the influence of complex boundary conditions on in vivo organ tissue deformation and employs an improved strong tracking Kalman filter to reduce the uncertainty error in the biomechanical parameter estimation process through its internal adaptive stage.

[0069] Although the present invention has been described with reference to the present preferred embodiments, those skilled in the art should understand that the above preferred embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for estimating biomechanical parameters of organs and tissues in vivo, characterized in that, The method includes the following steps: a. Perform in vivo organ and tissue geometric modeling to obtain the tetrahedral mesh structure of the in vivo organ and tissue; b. Based on the obtained tetrahedral mesh structure of in vivo organ tissues, perform biomechanical modeling of in vivo organ tissues; c. Based on the aforementioned in vivo organ and tissue biomechanical model, estimate the boundary conditions of the in vivo organ and tissue; d. Using a strong tracking Kalman filter, estimate the biomechanical parameters of in vivo organs and tissues under the current boundary condition estimation results; where: Step a specifically includes: First, the in vivo organ tissue geometric model is reconstructed from 4D MRI data to obtain the in vivo organ tissue reconstruction surface. Then, the in vivo organ tissue reconstruction surface is meshed to obtain the tetrahedral mesh structure of the in vivo organ tissue. Step b specifically includes: The boundary conditions of a body organ or tissue are equivalently represented as a set of equivalent external forces λ applied to the surface of the body organ or tissue due to collisions and contacts with anatomical tissues surrounding it. Common elastic parameters, Young's modulus and Poisson's ratio, are then used as parameters representing the elastic material properties of the body organ or tissue. The equilibrium equation for the body organ or tissue is: f(q t )+f+J T λ=0, Where, f(q) t ) represents external force, f represents internal force, and λ and J are the Jacobian matrices of the boundary equivalent external force and external force constraint to be solved, respectively. Step c specifically includes: First, non-rigid registration is performed on in vivo organ and tissue models under different deformation states to obtain the correspondence between surface points of in vivo organ and tissue geometric models under two deformation states. Then, the free deformation of the organ or tissue in the body under unbounded conditions is calculated. At this point, the displacement information of the organ or tissue in the body is calculated at the corresponding points: δ=dot(q s -q t ,n c ), q s and q t These represent the displacements of corresponding points on the surface of organs and tissues under unbounded and bounded conditions, respectively, n. c It is a unit vector pointing to the deformation of various points in an organ or tissue in the body; Finally, the equivalent external force λ at the boundary is estimated by solving the constraint problem: Wλ+δ=0, Where W = JCJ T The delassus operator is a common operator, and C represents the compliance matrix of the elastic properties of organs and tissues in vivo. Finally, the estimated boundary equivalent external force λ is obtained by solving the problem based on the Gauss-Seidel algorithm.

2. The method for estimating biomechanical parameters of organs and tissues in vivo as described in claim 1, characterized in that, Step d specifically includes: Using a strong tracking Kalman filter, the biomechanical parameters of in vivo organs and tissues are estimated in three stages under the current boundary condition estimation results; the three stages include: prediction stage, adaptation stage, and update stage.

3. The method for estimating biomechanical parameters of organs and tissues in vivo as described in claim 2, characterized in that, The prediction phase includes: The state vector containing biomechanical parameters and initial shape information of organs and tissues in vivo is represented using a Gaussian distribution. Predict the state of the current frame after organ and tissue deformation based on the initial state. and the corresponding covariance matrix in, In the initial state Gaussian distribution group The i-th (i = 1, 2, ..., 2N+1) Sigma group, and Q represents the mean weight and covariance weight, respectively. k This represents Gaussian noise.

4. The method for estimating biomechanical parameters of organs and tissues in vivo as described in claim 3, characterized in that, The adaptive phase includes: in order to minimize the impact of uncertainties and errors in the system model, the adaptive phase incorporates observational information Y of the historical deformation of in vivo organs and tissues. k For covariance matrix The model is continuously updated until its uncertainty error (i.e., Mahalanobis distance) is less than a certain threshold. The update formula is: in, It is the innovation vector of the observation data, M and R represents the historical window size and its corresponding weight, respectively. k This represents Gaussian white noise in the observation data.

5. The method for estimating biomechanical parameters of organs and tissues in vivo as described in claim 4, characterized in that, The update phase includes: combining the observed surface displacement information of the organ tissue portion in the current frame with the calculated Kalman gain K. k The predicted in vivo organ and tissue status results were modified as follows: in It is the covariance matrix of the observed data.

Images