Estimation of the elastic parameters of human liver biomechanical models by means of medical images and evolutionary computation

Intraoperative identification of patient-specific elastic modulus of the meniscus during arthroscopy

BACKGROUND AND OBJECTIVE

Degenerative meniscus tissue has been associated with a lower elastic modulus and can lead to the development of arthrosis. Safe intraoperative measurement of in vivo elastic modulus of the human meniscus could contribute to a better understanding of meniscus health, and for developing surgical simulators where novice surgeons can learn to distinguish healthy from degenerative meniscus tissue. Such measurement can also support intraoperative decision-making by providing a quantitative measure of the meniscus health condition. The objective of this study is to demonstrate a method for intraoperative identification of meniscus elastic modulus during arthroscopic probing using an adaptive observer method.

METHODS

Ex vivo arthroscopic examinations were performed on five cadaveric knees to estimate the elastic modulus of the anterior, mid-body, and posterior regions of lateral and medial menisci. Real-time intraoperative force-displacement data was obtained and utilized for modulus estimation through an adaptive observer method. For the validation of arthroscopic elastic moduli, an inverse parameter identification approach using optimization, based on biomechanical indentation tests and finite element analyses, was employed. Experimental force-displacement data in various anatomical locations were measured through indentation. An iterative optimization algorithm was employed to optimize elastic moduli and Poisson's ratios by comparing experimental force values at maximum displacement with the corresponding force values from linear elastic region-specific finite element models. Finally, the estimated elastic modulus values obtained from ex vivo arthroscopy were compared against optimized values using a paired t-test.

RESULTS

The elastic moduli obtained from ex vivo arthroscopy and optimization showcased subject specificity in material properties. Additionally, the results emphasized anatomical and regional specificity within the menisci. The anterior region of the medial menisci exhibited the highest elastic modulus among the anatomical locations studied (9.97±3.20MPa from arthroscopy and 5.05±1.97MPa from finite element-based inverse parameter identification). The paired t-test results indicated no statistically significant difference between the elastic moduli obtained from arthroscopy and inverse parameter identification, suggesting the feasibility of stiffness estimation using arthroscopic examination.

CONCLUSIONS

This study has demonstrated the feasibility of intraoperative identification of patient-specific elastic modulus for meniscus tissue during arthroscopy.

In vivo mechanical characterization of arterial wall using an inverse analysis procedure: application on an animal model of intracranial aneurysm

Intracranial aneurysm is a pathology related to the deterioration of the arterial wall. This work is an essential part of a large-scale project aimed at providing clinicians with a non-invasive patient-specific decision support tool to facilitate the rupture risk assessment. It will lean on the link between the aneurysm shape clinically observed and a database derived from the in vivo mechanical characterization of aneurysms. To supply this database, a deformation device prototype of the arterial wall was developed. Its use coupled with medical imaging (spectral photon-counting computed tomography providing a spatial resolution down to 250 μm) is used to determine the in vivo mechanical properties of the wall based on the inverse analysis of the quantification of the wall deformation observed experimentally. This study presents the in vivo application of this original procedure to an animal model of aneurysm. The mechanical properties of the aneurysm wall identified were consistent with the literature, and the errors between the numerical and experimental results were less than 10%. Based on these parameters, this study allows the assessment of the aneurysm stress state for a known solicitation and points towards the definition of a rupture criterion.

A generative model of hyperelastic strain energy density functions for multiple tissue brain deformation

PURPOSE

Estimation of brain deformation is crucial during neurosurgery. Whilst mechanical characterisation captures stress-strain relationships of tissue, biomechanical models are limited by experimental conditions. This results in variability reported in the literature. The aim of this work was to demonstrate a generative model of strain energy density functions can estimate the elastic properties of tissue using observed brain deformation.

METHODS

For the generative model a Gaussian Process regression learns elastic potentials from 73 manuscripts. We evaluate the use of neo-Hookean, Mooney-Rivlin and 1-term Ogden meta-models to guarantee stability. Single and multiple tissue experiments validate the ability of our generative model to estimate tissue properties on a synthetic brain model and in eight temporal lobe resection cases where deformation is observed between pre- and post-operative images.

RESULTS

Estimated parameters on a synthetic model are close to the known reference with a root-mean-square error (RMSE) of 0.1 mm and 0.2 mm between surface nodes for single and multiple tissue experiments. In clinical cases, we were able to recover brain deformation from pre- to post-operative images reducing RMSE of differences from 1.37 to 1.08 mm on the ventricle surface and from 5.89 to 4.84 mm on the resection cavity surface.

CONCLUSION

Our generative model can capture uncertainties related to mechanical characterisation of tissue. When fitting samples from elastography and linear studies, all meta-models performed similarly. The Ogden meta-model performed the best on hyperelastic studies. We were able to predict elastic parameters in a reference model on a synthetic phantom. However, deformation observed in clinical cases is only partly explained using our generative model.

Identification of tumor nodule in soft tissue: An inverse finite-element framework based on mechanical characterization

Identification and characterization of nodules in soft tissue, including their size, shape, and location, provide a basis for tumor identification. This study proposes an inverse finite-element (FE) based computational framework, for characterizing the size of examined tissue sample and detecting the presence of embedded tumor nodules using instrumented palpation, without a priori anatomical knowledge. The inverse analysis was applied to a model system, the human prostate, and was based on the reaction forces which can be obtained by trans-rectal mechanical probing and those from an equivalent FE model, which was optimized iteratively, by minimizing an error function between the two cases, toward the target solution. The tumor nodule can be identified through its influence on the stress state of the prostate. The effectiveness of the proposed method was further verified using a realistic prostate model reconstructed from magnetic resonance (MR) images. The results show the proposed framework to be capable of characterizing the key geometrical indices of the prostate and identifying the presence of cancerous nodules. Therefore, it has potential, when combined with instrumented palpation, for primary diagnosis of prostate cancer, and, potentially, solid tumors in other types of soft tissue.

Effect of Residual and Transformation Choice on Computational Aspects of Biomechanical Parameter Estimation of Soft Tissues

Several nonlinear and anisotropic constitutive models have been proposed to describe the biomechanical properties of soft tissues, and reliably estimating the unknown parameters in these models using experimental data is an important step towards developing predictive capabilities. However, the effect of parameter estimation technique on the resulting biomechanical parameters remains under-analyzed. Standard off-the-shelf techniques can produce unreliable results where the parameters are not uniquely identified and can vary with the initial guess. In this study, a thorough analysis of parameter estimation techniques on the resulting properties for four multi-parameter invariant-based constitutive models is presented. It was found that linear transformations have no effect on parameter estimation for the presented cases, and nonlinear transforms are necessary for any improvement. A distinct focus is put on the issue of non-convergence, and we propose simple modifications that not only improve the speed of convergence but also avoid convergence to a wrong solution. The proposed modifications are straightforward to implement and can avoid severe problems in the biomechanical analysis. The results also show that including the fiber angle as an unknown in the parameter estimation makes it extremely challenging, where almost all of the formulations and models fail to converge to the true solution. Therefore, until this issue is resolved, a non-mechanical—such as optical—technique for determining the fiber angle is required in conjunction with the planar biaxial test for a robust biomechanical analysis.

A model order reduction approach to create patient-specific mechanical models of human liver in computational medicine applications

BACKGROUND AND OBJECTIVE

This paper focuses on computer simulation aspects of Digital Twin models in the medical framework. In particular, it addresses the need of fast and accurate simulators for the mechanical response at tissue and organ scale and the capability of integrating patient-specific anatomy from medical images to pinpoint the individual variations from standard anatomical models.

METHODS

We propose an automated procedure to create mechanical models of the human liver with patient-specific geometry and real time capabilities. The method hinges on the use of Statistical Shape Analysis to extract the relevant anatomical features from a database of medical images and Model Order Reduction to compute an explicit parametric solution for the mechanical response as a function of such features. The Sparse Subspace Learning, coupled with a Finite Element solver, was chosen to create low-rank solutions using a non-intrusive sparse sampling of the feature space.

RESULTS

In the application presented in the paper, the statistical shape model was trained on a database of 385 three dimensional liver shapes, extracted from medical images, in order to create a parametrized representation of the liver anatomy. This parametrization and an additional parameter describing the breathing motion in linear elasticity were then used as input in the reduced order model. Results show a consistent agreement with the high fidelity Finite Element models built from liver images that were excluded from the training dataset. However, we evidence in the discussion the difficulty of having compact shape parametrizations arising from the extreme variability of the shapes found in the dataset and we propose potential strategies to tackle this issue.

CONCLUSIONS

A method to represent patient-specific real-time liver deformations during breathing is proposed in linear elasticity. Since the proposed method does not require any adaptation to the direct Finite Element solver used in the training phase, the procedure can be easily extended to more complex non-linear constitutive behaviors - such as hyperelasticity - and more general load cases. Therefore it can be integrated with little intrusiveness to generic simulation software including more sophisticated and realistic models.

New small-intestine modeling method for surface-based computational human phantoms

When converting voxel phantoms to a surface format, the small intestine (SI), which is usually not accurately represented in a voxel phantom due to its complex and irregular shape on one hand and the limited voxel resolutions on the other, cannot be directly converted to a high-quality surface model. Currently, stylized pipe models are used instead, but they are strongly influenced by developer's subjectivity, resulting in unacceptable geometric and dosimetric inconsistencies. In this paper, we propose a new method for the construction of SI models based on the Monte Carlo approach. In the present study, the proposed method was tested by constructing the SI model for the polygon-mesh version of the ICRP reference male phantom currently under development. We believe that the new SI model is anatomically more realistic than the stylized SI models. Furthermore, our simulation results show that the new SI model, for both external and internal photon exposures, leads to dose values that are more similar to those of the original ICRP male voxel phantom than does the previously constructed stylized SI model.

Simulation and experiment of soft-tissue deformation in prostate brachytherapy

Soft-tissue deformation is one of the major reasons for the inaccurate positioning of percutaneous needle insertion process. In this article, simulations and experiments of the needle insertion soft-tissue process are both applied to study soft-tissue deformation. A needle deflection model based on the mechanics is used to calculate the needle deflection during the interaction process. The obtained needle deflection data are applied into finite element analysis process as the system input. The uniaxial tensile strength tests, compression tests, and static indentation experiments are used to obtain the soft-tissue parameters and choose the best strain-energy function to model in the simulation. Magnetic resonance imaging is used to reconstruct the prostate, establishing both prostate three-dimensional finite element model and artificial prostate model. The needle–soft tissue interaction simulation results are compared with those of the needle insertion experiment. The displacement data of the mark point in the experiment are comparable to the simulation results. It is concluded that, using this simulation method, the surgeon can predict the deformation of the tissue and the displacement of the target in advance.

Methodology based on genetic heuristics for in-vivo characterizing the patient-specific biomechanical behavior of the breast tissues

This paper presents a novel methodology to in-vivo estimate the elastic constants of a constitutive model proposed to characterize the mechanical behavior of the breast tissues. An iterative search algorithm based on genetic heuristics was constructed to in-vivo estimate these parameters using only medical images, thus avoiding invasive measurements of the mechanical response of the breast tissues. For the first time, a combination of overlap and distance coefficients were used for the evaluation of the similarity between a deformed MRI of the breast and a simulation of that deformation. The methodology was validated using breast software phantoms for virtual clinical trials, compressed to mimic MRI-guided biopsies. The biomechanical model chosen to characterize the breast tissues was an anisotropic neo-Hookean hyperelastic model. Results from this analysis showed that the algorithm is able to find the elastic constants of the constitutive equations of the proposed model with a mean relative error of about 10%. Furthermore, the overlap between the reference deformation and the simulated deformation was of around 95% showing the good performance of the proposed methodology. This methodology can be easily extended to characterize the real biomechanical behavior of the breast tissues, which means a great novelty in the field of the simulation of the breast behavior for applications such as surgical planing, surgical guidance or cancer diagnosis. This reveals the impact and relevance of the presented work.

An inverse method to determine the mechanical properties of the iris in vivo

BACKGROUND

Understanding the mechanical properties of the iris can help to have an insight into the eye diseases with abnormalities of the iris morphology. Material parameters of the iris were simply calculated relying on the ex vivo experiment. However, the mechanical response of the iris in vivo is different from that ex vivo, therefore, a method was put forward to determine the material parameters of the iris using the optimization method in combination with the finite element method based on the in vivo experiment.

MATERIAL AND METHODS

Ocular hypertension was induced by rapid perfusion to the anterior chamber, during perfusion intraocular pressures in the anterior and posterior chamber were record by sensors, images of the anterior segment were captured by the ultrasonic system. The displacement of the characteristic points on the surface of the iris was calculated. A finite element model of the anterior chamber was developed using the ultrasonic image before perfusion, the multi-island genetic algorithm was employed to determine the material parameters of the iris by minimizing the difference between the finite element simulation and the experimental measurements.

RESULTS

Material parameters of the iris in vivo were identified as the iris was taken as a nearly incompressible second-order Ogden solid. Values of the parameters μ1, α1, μ2 and α2 were 0.0861 ± 0.0080 MPa, 54.2546 ± 12.7180, 0.0754 ± 0.0200 MPa, and 48.0716 ± 15.7796 respectively. The stability of the inverse finite element method was verified, the sensitivity of the model parameters was investigated.

CONCLUSION

Material properties of the iris in vivo could be determined using the multi-island genetic algorithm coupled with the finite element method based on the experiment.

Liver segmentation in MRI: A fully automatic method based on stochastic partitions

There are few fully automated methods for liver segmentation in magnetic resonance images (MRI) despite the benefits of this type of acquisition in comparison to other radiology techniques such as computed tomography (CT). Motivated by medical requirements, liver segmentation in MRI has been carried out. For this purpose, we present a new method for liver segmentation based on the watershed transform and stochastic partitions. The classical watershed over-segmentation is reduced using a marker-controlled algorithm. To improve accuracy of selected contours, the gradient of the original image is successfully enhanced by applying a new variant of stochastic watershed. Moreover, a final classifier is performed in order to obtain the final liver mask. Optimal parameters of the method are tuned using a training dataset and then they are applied to the rest of studies (17 datasets). The obtained results (a Jaccard coefficient of 0.91 ± 0.02) in comparison to other methods demonstrate that the new variant of stochastic watershed is a robust tool for automatic segmentation of the liver in MRI.

Direct volume manipulation for visualizing intraoperative liver resection process

This paper introduces a new design and application for direct volume manipulation for visualizing the intraoperative liver resection process. So far, interactive volume deformation and resection have been independently handled due to the difficulty of representing elastic behavior of volumetric objects. Our framework models global shape editing and discontinuous local deformation by merging proxy geometry encoding and displacement mapping. A local-frame-based elastic model is presented to allow stable editing of the liver shape including bending and twisting while preserving the volume. Several tests using clinical CT data have confirmed the developed software and interface can represent the intraoperative state of liver and produce local views of reference vascular structures, which provides a "road map of vessels" that are key features when approaching occluded tumors during surgery.