A Framework for Local Mechanical Characterization of Atherosclerotic Plaques: Combination of Ultrasound Displacement Imaging and Inverse Finite Element Analysis

Characterisation of human penile tissue properties using experimental testing combined with multi-target inverse finite element modelling

This paper presents an inverse finite element (FE) approach aimed at estimating multi-layered human penile tissues. The inverse FE approach integrates experimental force-displacement and boundary deformation data of penile tissues with a developed FE model and uses new experimental data on human penile tissue. The experimental study encompasses whole organ plate-compression tests and individual layer tensile and compression tests, providing comprehensive insights into the tissue's mechanical behaviour. The biomechanical characterisation of penile tissue is of crucial significance for understanding its mechanical behaviour under various physiological and pathological conditions. The FE model is constructed using the realistic geometry of the penile segment and appropriate constitutive models for each tissue layer to leverage the accuracy and consistency of the model. Through systematic variation of tissue parameters in the inverse FE algorithm, simulations achieve the best match with both force-displacement and deformed boundary results obtained from the whole organ plate-compression tests. Test results from individual tissue layers are also utilised to assess the estimated parameters. The proposed inverse FE approach allows for the estimation of penile tissue parameters with high precision and reliability, shedding light on the mechanical properties of this complex biological organ. This work has applications not only in urology but also for researchers in various disciplines of biomechanics. As a result, our study contributes to advancing the understanding of human penile tissue mechanics whilst the methodology could also be applied to a range of other soft biological tissues. STATEMENT OF SIGNIFICANCE: This research uses a multi-target inverse finite element (FE) approach for estimating the material parameters of human penile tissues. By integrating experimental data and a realistic FE model, this study achieves high-precision constitutive model parameter estimation, offering key insights into penile tissue mechanics under various loading conditions. The significance of this work lies in the use of this inverse FE approach for fresh-frozen human penile tissues, to identify the mechanical properties and constitutive models for both segregated tunica albuginea and corpus cavernosum as well as intact penile tissue segments. The study's scientific impact lies in its advancement of the understanding of human urological tissue mechanics, impacting researchers and clinicians alike.

Experimental testing combined with inverse-FE for mechanical characterisation of penile tissues

Erectile dysfunction (ED) predominantly affects men in their 40-70s and can lead to poor quality of life. One option for ED treatment is surgical implantation of an inflatable penile prosthesis (IPP). However, they can be associated with negative outcomes including infection, migration or fibrosis. To improve outcomes, the interaction between the IPP device and surrounding tissues needs further investigation and this could be achieved using pre-clinical testbeds, but they need to be informed by extensive tissue testing. In this study, an experimental approach is adopted to characterise the mechanics of horse penile tissue and establish a testing protocol for penile tissue. The whole penis segments were tested in plate compression tests to obtain whole penis behaviour which is necessary for validation of a pre-clinical testbed, whilst tensile and compression tests were performed on individual penile tissues, namely corpus cavernosa and tunica albuginea. The second part of the paper deals with the development of a computational model employing an inverse finite element approach to estimate the material parameters of each tissue layer. These material parameters are in good agreement with the experimental results obtained from the individual tissue layers and whole organ tissue tests. This paper presents the first study proposing realistic nonlinear elastic material parameters for penile tissues and offers a validated testbed for IPPs. STATEMENT OF SIGNIFICANCE: Erectile Dysfunction (ED) affects over half the male population aged 40-70 potentially leading to poor quality of life. Patients not responding to conventional treatments of ED, are advised to use penile prostheses which can create an erection using implanted inflatable cylinders. A significant drawback of such prostheses, however, is the substantial tissue damage they can induce during their usage. Preclinical testbeds, including computational and bench-top models, could offer an efficient means of improving device designs to mitigate this damage but such testbeds require extensive knowledge of penile tissue properties. In this study, the authors determine penile tissue mechanics and apply an inverse FE approach to characterise the penile material properties required to validate preclinical models of the penis.

Characterizing atherosclerotic tissues: in silico analysis of mechanical properties using intravascular ultrasound and inverse finite element methods

Atherosclerosis is a prevalent cause of acute coronary syndromes that consists of lipid deposition inside the artery wall, creating an atherosclerotic plaque. Early detection may prevent the risk of plaque rupture. Nowadays, intravascular ultrasound (IVUS) is the most common medical imaging technology for atherosclerotic plaque detection. It provides an image of the section of the coronary wall and, in combination with new techniques, can estimate the displacement or strain fields. From these magnitudes and by inverse analysis, it is possible to estimate the mechanical properties of the plaque tissues and their stress distribution. In this paper, we presented a methodology based on two approaches to characterize the mechanical properties of atherosclerotic tissues. The first approach estimated the linear behavior under particular pressure. In contrast, the second technique yielded the non-linear hyperelastic material curves for the fibrotic tissues across the complete physiological pressure range. To establish and validate this method, the theoretical framework employed in silico models to simulate atherosclerotic plaques and their IVUS data. We analyzed different materials and real geometries with finite element (FE) models. After the segmentation of the fibrotic, calcification, and lipid tissues, an inverse FE analysis was performed to estimate the mechanical response of the tissues. Both approaches employed an optimization process to obtain the mechanical properties by minimizing the error between the radial strains obtained from the simulated IVUS and those achieved in each iteration. The second methodology was successfully applied to five distinct real geometries and four different fibrotic tissues, getting median R 2 of 0.97 and 0.92, respectively, when comparing the real and estimated behavior curves. In addition, the last technique reduced errors in the estimated plaque strain field by more than 20% during the optimization process, compared to the former approach. The findings enabled the estimation of the stress field over the hyperelastic plaque tissues, providing valuable insights into its risk of rupture.

Inverse material parameter estimation of patient-specific finite element models at the carotid bifurcation: The impact of excluding the zero-pressure configuration and residual stress

The carotid bifurcation experiences a complex loading environment due to its anatomical structure. Previous in-vivo material parameter estimation methods often use simplified model geometries, isotropic hyperelastic constitutive equations or neglect key aspects of the vessel, such as the zero-pressure configuration or residual stress, all of which have independently been shown to alter the stress environment of the vessel wall. Characterizing the location of high stress in the vessel wall has often been proposed as a potential indicator of structural weakness. However, excluding the afore-mentioned zero-pressure configuration, residual stress and patient-specific material parameters can lead to an incorrect estimation of the true stress values observed, meaning that stress alone as a risk indicator of rupture is insufficient. In this study, we investigate how the estimated material parameters and overall stress distributions in geometries of carotid bifurcations, extracted from in-vivo MR images, alter with the inclusion of the zero-pressure configuration and residual stress. This approach consists of the following steps: (1) geometry segmentation and hexahedral meshing from in-vivo magnetic resonance images (MRI) at two known phases; (2) computation of the zero-pressure configuration and the associated residual stresses; (3) minimization of an objective function built on the difference between the stress states of an "almost true" stress field at two known phases and a "deformed" stress field by altering the input material parameters to determine patient-specific material properties; and (4) comparison of the stress distributions throughout these carotid bifurcations for all cases with estimated material parameters. This numerical approach provides insights into the need for estimation of both the zero-pressure configuration and residual stress for accurate material property estimation and stress analysis for the carotid bifurcation, establishing the reliability of stress as a rupture risk metric.

Multicomponent material property characterization of atherosclerotic human carotid arteries through a Bayesian Optimization based inverse finite element approach

OBJECTIVE

Plaque rupture in atherosclerotic carotid arteries is a main cause of ischemic stroke and it is correlated with high plaque stresses. Hence, analyzing stress patterns is essential for plaque specific rupture risk assessment. However, the critical information of the multicomponent material properties of atherosclerotic carotid arteries is still lacking greatly. This work aims to characterize component-wise material properties of atherosclerotic human carotid arteries under (almost) physiological loading conditions.

METHODS

An inverse finite element modeling (iFEM) framework was developed to characterize fibrous intima and vessel wall material properties of 13 cross sections from five carotids. The novel pipeline comprised ex-vivo inflation testing, pre-clinical high frequency ultrasound for deriving plaque deformations, pre-clinical high-magnetic field magnetic resonance imaging, finite element modeling, and a sample efficient machine learning based Bayesian Optimization.

RESULTS

The nonlinear Yeoh constants for the fibrous intima and wall layers were successfully obtained. The optimization scheme of the iFEM reached the global minimum with a mean error of 3.8% in 133 iterations on average. The uniqueness of the results were confirmed with the inverted Gaussian Process (GP) model trained during the iFEM protocol.

CONCLUSION

The developed iFEM approach combined with the inverted GP model successfully predicted component-wise material properties of intact atherosclerotic human carotids ex-vivo under physiological-like loading conditions.

SIGNIFICANCE

We developed a novel iFEM framework for the nonlinear, component-wise material characterization of atherosclerotic arteries and utilized it to obtain human atherosclerotic carotid material properties. The developed iFEM framework has great potential to be advanced for patient-specific in-vivo application.

An inverse method for mechanical characterization of heterogeneous diseased arteries using intravascular imaging

The increasing prevalence of finite element (FE) simulations in the study of atherosclerosis has spawned numerous inverse FE methods for the mechanical characterization of diseased tissue in vivo. Current approaches are however limited to either homogenized or simplified material representations. This paper presents a novel method to account for tissue heterogeneity and material nonlinearity in the recovery of constitutive behavior using imaging data acquired at differing intravascular pressures by incorporating interfaces between various intra-plaque tissue types into the objective function definition. Method verification was performed in silico by recovering assigned material parameters from a pair of vessel geometries: one derived from coronary optical coherence tomography (OCT); one generated from in silico-based simulation. In repeated tests, the method consistently recovered 4 linear elastic (0.1 ± 0.1% error) and 8 nonlinear hyperelastic (3.3 ± 3.0% error) material parameters. Method robustness was also highlighted in noise sensitivity analysis, where linear elastic parameters were recovered with average errors of 1.3 ± 1.6% and 8.3 ± 10.5%, at 5% and 20% noise, respectively. Reproducibility was substantiated through the recovery of 9 material parameters in two more models, with mean errors of 3.0 ± 4.7%. The results highlight the potential of this new approach, enabling high-fidelity material parameter recovery for use in complex cardiovascular computational studies.

Finite element analysis in clinical patients with atherosclerosis

Endovascular plaque composition is strongly related to stent strut stress and is responsible for strut fatigue, stent failure, and possible in-stent restenosis. To evaluate the effect of plaque on artery wall resistance to expansion we performed in silico analysis of atherosclerotic vessels. We generated finite element models from in vivo intravascular ultrasound virtual histology images to determine local artery surface stiffness and determined which plaque structures have the greatest influence. We validated the predictive capacity of our modeling approach by testing an atherosclerotic peripheral artery ex vivo with pressure-inflation testing at physiological pressures ranging from 10 to 200 mmHg. For this purpose, the in silico deformation of the arterial wall was compared to that observed ex vivo. We found that calcification had a positive effect on surface stiffness with fibrous plaque and necrotic core having negative effects. Additionally, larger plaque structures demonstrated significantly higher average surface stiffness and calcification located nearer the lumen was also shown to increase surface stiffness. Therefore, more developed plaques will have greater resistance to expansion and higher stent strut stress, with calcification located near the lumen further increasing stress in localized areas. Thus, it may be expected that such plaque structures may increase the likelihood of localized stent strut fracture.

Multicomponent Mechanical Characterization of Atherosclerotic Human Coronary Arteries: An Experimental and Computational Hybrid Approach

Atherosclerotic plaque rupture in coronary arteries, an important trigger of myocardial infarction, is shown to correlate with high levels of pressure-induced mechanical stresses in plaques. Finite element (FE) analyses are commonly used for plaque stress assessment. However, the required information of heterogenous material properties of atherosclerotic coronaries remains to be scarce. In this work, we characterized the component-wise mechanical properties of atherosclerotic human coronary arteries. To achieve this, we performed ex vivo inflation tests on post-mortem human coronary arteries and developed an inverse FE modeling (iFEM) pipeline, which combined high-frequency ultrasound deformation measurements, a high-field magnetic resonance-based artery composition characterization, and a machine learning-based Bayesian optimization (BO) with uniqueness assessment. By using the developed pipeline, 10 cross-sections from five atherosclerotic human coronary arteries were analyzed, and the Yeoh material model constants of the fibrous intima and arterial wall components were determined. This work outlines the developed pipeline and provides the knowledge of non-linear, multicomponent mechanical properties of atherosclerotic human coronary arteries.

Heartbeat-Induced Corneal Axial Displacement and Strain Measured by High Frequency Ultrasound Elastography in Human Volunteers

Purpose

The purpose of this study was to establish in vivo data acquisition and processing protocols for repeatable measurements of heartbeat-induced corneal displacements and strains in human eyes, using a high-frequency ultrasound elastography method, termed ocular pulse elastography (OPE).

Methods

Twenty-four volunteers with no known ocular diseases were recruited for this study. Intraocular pressure (IOP) and ocular pulse amplitude (OPA) were measured using a PASCAL Dynamic Contour Tonometer (DCT). An in vivo OPE protocol was developed to measure heartbeat-induced corneal displacements. Videos of the central 5.7 mm of the cornea were acquired using a 50-MHz ultrasound probe at 128 frames per second. The radiofrequency data of 1000 frames were analyzed using an ultrasound speckle tracking algorithm to calculate corneal displacements and quantify spectral and temporal characteristics. The intrasession and intersession repeatability of OPE- and DCT-measured parameters were also analyzed.

Results

The in vivo OPE protocol and setup were successful in tracking heartbeat-induced corneal motion using high-frequency ultrasound. Corneal axial displacements showed a strong cardiac rhythm, with good intrasession and intersession repeatability, and high interocular symmetry. Corneal strain was calculated in two eyes of two subjects, showing substantially different responses.

Conclusions

We demonstrated the feasibility of high-frequency ultrasound elastography for noninvasive in vivo measurement of the cornea's biomechanical responses to the intrinsic ocular pulse. The high intrasession and intersession repeatability suggested a robust implementation of this technique to the in vivo setting.

Translational Relevance

OPE may offer a useful tool for clinical biomechanical evaluation of the cornea by quantifying its response to the intrinsic pulsation.

Patient specific characterization of artery and plaque material properties in peripheral artery disease

Patient-specific finite element (FE) modeling of atherosclerotic plaque is challenging, as there is limited information available clinically to characterize plaque components. This study proposes that for the limited data available in vivo, material properties of plaque and artery can be identified using inverse FE analysis and either a simple neo-Hookean constitutive model or assuming linear elasticity provides sufficient accuracy to capture the changes in vessel deformation, which is the available clinical metric. To test this, 10 human cadaveric femoral arteries were each pressurized ex vivo at 6 pressure levels, while intravascular ultrasound (IVUS) and virtual histology (VH) imaging were performed during controlled pull-back to determine vessel geometry and plaque structure. The VH images were then utilized to construct FE models with heterogeneous material properties corresponding to the vessel plaque components. The constitutive models were then fit to each plaque component by minimizing the difference between the experimental and the simulated geometry using the inverse FE method. Additionally, we further simplified the analysis by assuming the vessel wall had a homogeneous structure, i.e. lumping artery and plaque as one tissue. We found that for the heterogeneous wall structure, the simulated and experimental vessel geometries compared well when the fitted neo-Hookean parameters or elastic modulus, in the case of linear elasticity, were utilized. Furthermore, taking the median of these fitted parameters then inputting these as plaque component mechanical properties in the finite element simulation yielded differences between simulated and experimental geometries that were on average around 2% greater (1.30-5.55% error range to 2.33-11.71% error range). For the homogeneous wall structure the simulated and experimental wall geometries had an average difference of around 4% although when the difference was calculated using the median fitted value this difference was larger than for the heterogeneous fits. Finally, comparison to uniaxial tension data and to literature constitutive models also gave confidence to the suitability of this simplified approach for patient-specific arterial simulation based on data that may be acquired in the clinic.

Mechanical Deformation of Human Optic Nerve Head and Peripapillary Tissue in Response to Acute IOP Elevation

Purpose

To measure the deformation of the human optic nerve head (ONH) and peripapillary tissue (PPT) in response to acute intraocular pressure (IOP) elevation.

Methods

The ONH and PPT of 14 human donor globes were imaged with high-frequency ultrasonography during inflation testing from 5 to 30 mm Hg. A correlation-based speckle tracking algorithm was used to compute tissue displacements, and the through-thickness, in-plane, and shear strains were calculated by using least-squares strain estimation methods. The ONH and PPT were segmented along the anterior-posterior direction and the nasal-temporal direction. Regional displacements and strains were analyzed and compared.

Results

The ONH displaced more posteriorly than the PPT in response to an acute IOP increase. Scleral canal expansion was minimal but correlated with ONH posterior displacement at all IOP levels. Through-thickness compression was concentrated in the anterior of both the ONH and the PPT. Shear was concentrated in the vicinity of the canal with higher shear in the peripheral ONH than the central ONH and higher shear in the PPT near the scleral canal than that further away from the canal.

Conclusions

High-resolution ultrasound speckle tracking showed a displacement mismatch between the ONH and the PPT, larger compressive strains in the direction of IOP loading in the anterior ONH and PPT, and higher shear strains in the periphery of ONH in response to acute IOP elevation in the human eye. These findings delineate the deformation patterns within and around the ONH and may help understand IOP-associated optic nerve damage.