Focal Comparison of Experimental and Finite Element Derived Strain Fields in a 3D IVUS-based Computational Model of Vascular Tissue Under Loading

Abstract

Arterial tissues are subjected to mechanical loads that influence biological mechanisms in health and disease. Motivated by these observations, computational models to predict the vascular mechanical environment are increasingly being developed and applied. However, few computational vascular biomechanics studies are evaluated for accuracy. This study aimed to compare the transmural strain fields in healthy vascular tissue under physiologic loading between 3D intravascular ultrasound (IVUS)-based finite element (FE) models and image-based experimental measurements. IVUS image data were captured along a ~15 mm segment in porcine carotid arteries (n=3) in the reference configuration (~10 mmHg) and at five axial positions under varied pressure loads. FE models were constructed from the full-length segment IVUS data, and model-predicted strains were determined using reported soft and stiff material properties for porcine tissue. Experimental strains were determined at each axial slice across the applied loads using a deformable image registration technique (Hyperelastic Warping). Both FE-predicted and experimental deformations exhibited non-linear behavior under loading, as observed in the material response curves. Following Warping parameter selection, results demonstrated that FE-predicted transmural strains with soft and stiff material properties bounded the experimentally-derived data at systolic pressures; however, sample variability was observed. At systolic pressure, Warping-derived and FE-predicted transmural strains showed good agreement, as RMSE values were <0.09 and differences <0.08. In conclusion, this study presents an experimental framework to assess accuracy in IVUS-based FE models, and results indicate that the computational framework can predict realistic deformations of arterial tissue; however, the accuracy strongly depends on tissue-specific material properties.

1. Introduction

The vascular biomechanical environment plays a significant role in various healthy and diseased vascular processes (Humphrey, 2008; Humphrey and Schwartz, 2021). Indeed, the initiation and progression of atherosclerosis, amongst other vascular diseases, has been linked to alterations in the arterial mechanical environment (Candreva et al., 2024; Ku et al., 1985; Pedrigi et al., 2015). Motivated by these observations, computational approaches to quantify the in vivo arterial mechanical environment have been explored to advance patient management and medical device efficacy in areas where analytical solutions are not applicable. For example, predicting hepatic flow distribution across different surgical techniques using computational fluid dynamics has demonstrated potential for enhancing Fontan surgical planning (Trusty et al., 2019). Furthermore, finite element (FE) modeling of the interaction between vascular tissue and implanted devices can aid device performance predictions and identify failure (Morrison et al., 2017; Timmins et al., 2011). As personalized medicine gains traction in the clinic, patient-specific computational models may prove increasingly useful in advancing disease prognosis and treatment. Therefore, demonstrating that model predictions accurately represent the underlying physics is critical to enhancing confidence in these computational frameworks before clinical use.

In the context of atherosclerosis, image-based biomechanical simulations have shown that fluid wall shear stress (WSS) and deformation-induced plaque stress (PS) play a role in disease development and progression (Brown et al., 2016; Pedrigi et al., 2014), and more recently, stabilization (Schake et al., 2023). For example, higher PS was observed in lesions from patients presenting with acute coronary syndromes (Teng et al., 2014), and plaque rupture has been correlated with higher mechanical stress (Costopoulos et al., 2017). Notably, these studies and others employed 2D models and lacked an assessment of the accuracy of the model-predicted transmural mechanical environment. That is to say, a comparison of model-predicted stresses or strains to experimentally-derived values was not performed. While model accuracy has been explored in three-dimensional (3D), image-based patient-specific coronary artery models (Carpenter et al., 2021; Gholipour et al., 2020), efforts have lacked focal comparisons with experimental data acquired under well-controlled conditions. This paucity of model accuracy assessment likely owes to its difficulty, as it requires the development of a robust experimental setup and techniques that enable quantification of transmural strain magnitudes.

As such, this study utilized a novel biaxial mechanical loading system coupled to a clinical IVUS console and compared transmural strains derived from a 3D intravascular ultrasound (IVUS)-based FE modeling framework with experimental measurements in healthy arterial tissue under physiologic loading. Model-predicted strains were extracted from pressurized FE models constructed from IVUS image data, and experimental strains were derived across load states using image border data and a deformable image registration technique. The hypothesis was that FE-predicted strains would agree with experimental data, indicating that the modeling framework can accurately predict the artery-specific mechanical environment.

2. Methods

2.1. Sample Preparation and Equipment Setup

Frozen porcine common carotid artery samples (n=3) from animals 6–9 months of age were acquired (Animal Technologies, Tyler, TX). Specimens were thawed and residual connective tissue was removed. A 35 mm section was excised from each sample and mounted via barb fittings to a custom biaxial testing machine. The system enabled mechanical testing and simultaneous IVUS imaging via the insertion of an IVUS catheter into the lumen (Fig. 1). The computer-controlled biaxial testing setup consisted of a data acquisition device (National Instruments, Austin, TX), linear actuators and motion controller (Newport Corp., Irvine, CA), a syringe pump (World Precision Instruments, Sarasota, FL), and a pressure transducer (Harvard Apparatus, Holliston, MA). A custom LabVIEW (2021) program enabled control of the axial stretch ratio and static pressure via modulation of saline injection/withdrawal. The tissue was placed in a phosphate-buffered saline (PBS) bath and was aligned with a plastic reference object that measured 15 mm long and was affixed to the bath housing. This object enabled spatial registration of the acquired images (Fig. 1, Fig. 2A). The tissue sample was interrogated with an Eagle Eye Platinum catheter (20 MHz; Philips, San Diego, CA) that interfaced with a Philips Core Mobile console for IVUS image acquisition. The catheter wire was coupled to a linear stage, which allowed control of catheter position within the vessel.

Fig. 1.

Equipment setup for simultaneous biaxial testing and IVUS image acquisition. Image data were acquired in the middle 15 mm of the vessel at 5 axial positions under lumen pressures of 10 (reference configuration) and 120 mmHg (loaded configuration).

Fig. 2.

Image acquisition pipeline to compute experimental and model-predicted strain fields. (A) Intravascular ultrasound image acquisition to collect the reference geometry of the vessel (10 mmHg) and the loaded geometry (120 mmHg) at selected axial locations. (B) Lumen and external elastic laminae (EEM) borders were extracted from co-registered images, and a mask was applied to the reference and loaded images. The vessel was placed in a soft, compressible perivascular (PV) region to aid the finite element (FE)-based deformable image registration. (C) The 3D FE model geometry was reconstructed from the lumen and EEM border data, and an adventitial layer with a constant thickness was added. The vessel was placed in a block of PV tissue to enable the application of boundary conditions during lumen pressurization.

2.2. Image Acquisition and Processing

Tissue samples were preconditioned via 10 cycles of lumen pressure (0–180 mmHg) and axial stretch (1.0–1.8), then loaded to a pressure of 10 mmHg (to prevent vessel collapse). IVUS images of the reference geometry were acquired in the middle 15 mm at an axial stretch ratio of ~1.5 (Han and Ku, 2001). Image acquisition began at the first appearance of the reference object at the distal end of the vessel to enable verification of the total length of the acquired image stack. Image data were acquired every 0.5 mm via controlled catheter pullback. At five axial locations, images were also acquired at a lumen pressure of 40, 80, and 120 mmHg, enabling the collection of the reference and loaded vessel geometry at identical spatial locations (Fig. 2A). The field-of-view for the collected IVUS images was 12 mm in-plane (500×500 pixels), allowing visualization of the artery and reference object.

Reference and loaded images were co-registered using the reference object (average rotation between successive images was <1°). Lumen and external elastic membrane (EEM) borders were manually extracted using a custom MATLAB (R2023B) script. Reference and loaded images were masked using the extracted boundaries to isolate the media, preventing non-physiologic deformations caused by registration of image data outside this layer (Fig. 2B). Circumferential strains ($E_{\theta }$) at the lumen and EEM boundaries were derived from the lengths of the extracted borders in the reference and loaded images.

2.3. Determining Experimentally-derived Transmural Strain Fields

A deformable image registration technique termed Hyperelastic Warping was utilized to determine strain fields directly from acquired IVUS images (Veress et al., 2005, 2002). Warping is a validated FE-based approach that computes displacement maps in soft biological tissues without discrete fiducials across finite deformations. Textural information in the image data is used to compute a deformation map by aligning a reference (template) image with a loaded (target) image (Fig. 2B). An image-based energy density ($U$) is defined using pointwise differences between the reference and loaded intensities to generate pseudo-body forces that warp the FE mesh into the deformed geometry,

$$U\left(\mathit{X},\mathit{\phi }\right)=\frac{\lambda }{2}{\left(T\left(\mathit{X},\mathit{\phi }\right)-S\left(\mathit{X},\mathit{\phi }\right)\right)}^2,$$ (1)

where $T$ is the reference (template) image intensity, $S$ is the loaded (target) image intensity, and $\lambda$ is a penalty parameter that scales body forces derived from the image intensity differences to drive deformations. The registration process minimizes the total energy of the system ($E$), which is defined as,

$$E\left(\mathit{\phi }\right)={\int }_{B}W\left(\mathit{X},\mathit{C}\left(\mathit{\phi }\left(\mathit{X}\right)\right)\right)dV+{\int }_{B}U\left(\mathit{X},\mathit{\phi }\left(\mathit{X}\right)\right)dV,$$ (2)

where $W$ and $U$ are the respective strain and image-based energy densities, $\mathit{C}$ is the right Cauchy-Green deformation tensor, $\mathit{\phi }$ is the deformation map, and $\mathit{X}$ is the nodal position. Given that the Warping algorithm is a continuum mechanics-based formulation, the uniqueness of the resulting displacement field is ensured. Accordingly, material properties are assigned to all regions of the mesh and serve to regularize the ill-posed problem of image registration across large deformations. The medial layer for the Warping analysis was constructed from the extracted boundaries and was embedded in a soft perivascular (PV) region (Fig. 2B) to enable the application of boundary conditions. The mesh density was selected according to a convergence test (Appendix A, Supplemental Fig. 1A). Image blurring was used to aid global and local registrations and was selected such that the final width was equal to the average medial thickness for each specimen (sample 1 = 0.72 ± 0.04, sample 2 = 0.60 ± 0.05, sample 3 = 0.48 ± 0.05). Initial blurring was held 2× higher than the final value to enable alignment of large features during quasi-time 0 to 0.5, then linearly reduced to the final value at time 1.0 to enable focal registration (Fig. 3). As the Warping process is sensitive to choice of penalty factor ($\lambda$; Eq. 1), a range of penalty factors (1 – 30 mN) were considered for each slice to identify the optimal value that achieved suitable boundary alignment at the lowest maximum Warping energy ($U$, Eq. 1). Incompressible and compressible neo-Hookean formulations were used to describe the material response of the artery ($G=13.65\mathrm{k}\mathrm{P}\mathrm{a}$) and PV ($E=10\mathrm{k}\mathrm{P}\mathrm{a},v=0.3$) regions, respectively. The artery stiffness was derived from the isotropic stiffness parameter from previous porcine carotid uniaxial tensile testing (García et al., 2011), while the PV parameters were selected to minimize the impact on vessel distension. Out-of-plane deformations were prohibited, and the outer PV edges were fixed in all directions. Warping analyses were created and run in FEBio Studio and FEBio using the Hyperelastic Warping plugin (Maas et al., 2017, 2012). First principal Green-Lagrange strains ($E_1$) in the media region were extracted from the analyses.

Fig. 3.

Blurring, Warping energy, and 1^st principal strains ($E_1$) throughout the image registration procedure. Blurring was held constant from quasi-time 0 to 0.5, then linearly reduced to half the initial value at 1.0.

2.4. Predicting Strain Fields via Finite Element Modeling

For each tissue sample, a 3D geometry was reconstructed from the IVUS boundary data (Fig. 2C; Geomagic Wrap, 3D Systems, Rock Hill, SC). An adventitial layer was added with a constant thickness of 0.33 mm, which was identified from measurements of histology data from the tissue samples. This layer was added due to the difficulty in defining the adventitial boundary because of reflection artifact at the vessel-PBS interface. The reconstructed vessel was embedded in a block of PV tissue (neo-Hookean, $E=10\mathrm{k}\mathrm{P}\mathrm{a},v=0.3$) with a minimum thickness of 10 mm (Berggren et al., 2024) to aid application of boundary conditions. Both arterial layers and the PV region were meshed with quadratic tetrahedral elements using TetGen via GIBBON (M Moerman, 2018; Maas et al., 2016, 2011; Si, 2015). Nodes were shared at the outer adventitia/PV interface. A convergence test confirmed the mesh density was sufficient, with an absolute change in median strain < 0.0025 across a two-fold increase in mesh density (Appendix A, Supplemental Fig. 1B). Exterior PV surfaces were fixed in all global directions and axial displacement at the artery end faces was restricted. A 110 mmHg pressure load was applied to the lumen surface (recall, the geometry was acquired at 10 mmHg). Material properties for the arterial layers were described by a microstructurally motivated strain energy function (SEF) with two symmetrical fiber families (Holzapfel et al., 2005). Material parameters previously reported from the uniaxial tensile testing of intact porcine carotids defined the artery wall, which was assumed a homogeneous tissue (García et al., 2011). To capture the range of tissue sample variability, two FE models using distinct sets of material properties were employed. The material parameters corresponded to the reported softest and stiffest proximal samples under loading in the circumferential direction (Supplemental Table 1)¹. The implicit FE analyses were created and performed in FEBio Studio and FEBio (Maas et al., 2017, 2012). Following solution convergence, cross-sections were extracted at the axial positions associated with the acquired images (and Warping analyses) using gptoolbox (Jacobson, 2021). Lumen and EEM boundaries were extracted from the deformed geometry to compute $E_{\theta }$ for each boundary at pressures of 40, 80, and 120 mmHg, while $E_1$ values at 120 mmHg were interpolated at the aforementioned slice planes.

2.5. Statistical Analysis

Experimental and FE-derived principal ($E_1$) and circumferential ($E_{\theta }$) strains from the medial layer were compared at corresponding axial locations and pressure loads, as well as localized circumferential and radial positions. Box plots were used to compare median, quartile, and whisker values between the experimental and FE-predicted $E_1$ data at 120 mmHg. Statistical comparisons were performed using a one-way ANOVA. Bland-Altman analysis and calculation of the root mean square error (RMSE) were performed to quantify transmural differences between the strain values. Data are reported as mean ± standard deviation, unless stated otherwise.

3. Results

3.1. FE and Experimental Characterization of Material Response to Loading

Although image data were acquired at 15 axial positions for Warping analysis, 2 axial positions were excluded from analysis (sample 1, axial positions 1 and 2) due to the proximity of the IVUS catheter to the vessel wall, producing regions of low intensity that prevented image registration. Thus, a total of 13 slices across 3 samples were analyzed.

Across the loading range, non-linear mechanical behavior was observed in pressure-$E_{\theta }$ curves derived from both the FE models and direct measurements of the IVUS image data. The experimental strains exhibited non-linear stiffening at the lumen and EEM, with a stiffer response observed at the EEM. Larger strains were observed in the experimental data compared to the two FE models at corresponding pressure loads, and the smallest strains were observed in the stiffest FE model. Loading curves averaged across five axial locations in sample 2 are shown in Figure 4, with similar trends observed in the other two samples. Of note, the FE models corroborated experimental data by showing a stiffer response at the EEM as compared to the lumen. Interestingly, the stiffest FE model and the experimental data exhibited monotonic strain-stiffening behaviors, whereas the softest FE model displayed a non-monotonic behavior, displaying an early softening followed by stiffening at higher pressures (>150 mmHg, Fig. 4).

Fig. 4.

Experimental and model-predicted circumferential strains ($E_{\theta }$) at the lumen and EEM borders across the entire pressure range for all five axial positions in Sample 2. Note that experimental data were only evaluated up to 140 mmHg, while FE models were evaluated up to higher pressures. Experimental strains were greater than both FE models at low pressure but aligned well at physiologic pressures. All data sets showed a softer response at the lumen compared to the EEM.

3.2. Identification of Image-Specific Penalty Factors for Warping Analysis

Across the considered range of penalty factors (1–30 mN), maximum Warping energy decreased; however, registration demonstrated mixed alignment with boundaries from the IVUS images acquired at 120 mmHg. For example, low penalty factors yielded under distension (Fig. 5A). In contrast, high values showed non-physical deformations exhibited by non-circumferential $E_1$ vectors (Fig. 5A). A subset of penalties that produced well-matched warped and loaded vessel boundaries was identified, and the penalty factor with the lowest maximum Warping energy was selected for the final registration. An example is shown for axial position 4 in sample 2 (Fig. 5B) and all other slices followed a similar trend. Table 1 lists the selected penalty factors and the associated maximum Warping energy across all samples.

Fig. 5.

Penalty selection scheme to facilitate physical deformations during image registration. (A) Incorrect penalty selection produced under- (top row) or over-warping (bottom row), leading to non-physiologic deformations and an under- or over-estimation of strains. (B) Warping energy as a function of penalty factors at an example slice (sample 2, axial position 4). The optimized penalty factor had the lowest maximum Warping energy amongst the range of penalties that produced adequate boundary agreement between the Warping-deformed model and the loaded vessel geometry.

Table 1.

Maximum Warping energy and the selected penalties across all slices.

	Maximum Warping energy [μJ]				Penalty parameter [mN]
Axial position	Sample 1	Sample 2	Sample 3		Sample 1	Sample 2	Sample 3
1	-	.052	0.104		-	11.3	7.9
2	-	0.058	0.104		-	15.0	4.3
3	0.016	0.045	0.080		13.0	17.0	5.4
4	0.023	0.043	0.074		13.0	9.0	3.9
5	0.012	0.054	0.086		17.0	12.0	4.6

Note: axial positions 1 and 2 in sample 1 were excluded from analysis due to difficulties in image registration that arose from the proximity of the IVUS catheter to the vessel wall.

3.3. Slice to Slice Strain Comparisons at Corresponding Axial Positions at Systole

Experimentally-derived (Warping) and FE model-predicted $E_1$ strain fields at 120 mmHg exhibited deformations typical of arteries under physiologic loading, with larger strains at the intima surface that decreased transmurally. Circumferential heterogeneities in strain fields existed across the experimentally-derived and model-predicted data, with greater heterogeneities appearing in the experimental data. A representative slice from each sample is presented in Figure 6, with all slices shown in Supplemental Figure 2. Strains from FE models with the softest and stiffest material properties largely bounded the Warping-derived strains. Samples 1 and 3 Warping data agreed better with the FE model that employed stiff material properties, whereas model results with soft material properties yielded better agreement in sample 2. At axial position 3 (center slice) in sample 1, for example, the median strain from the Warping analysis was 0.17 (IQR: 0.14 – 0.21), while FE predicted strains were 0.36 (0.30 – 0.47) and 0.11 (0.09 – 0.14) for the soft and stiff material properties, respectively (Fig. 7A). Similarly, the experimental median strain for sample 3 at axial position 2 was 0.24 (0.20 – 0.29), while model-predicted strains were 0.42 (0.36 – 0.55) and 0.12 (0.10 – 0.16) (Fig. 7C). Warping-derived strains were not significantly different than FE model predictions ($p>0.05$), and similar trends existed across all other axial positions in samples 1 and 3. In sample 2 at axial position 4, the median experimental strain was 0.28 (0.23 – 0.35), whereas the FE predicted strains were 0.33 (0.27 – 0.45) and 0.10 (0.08 – 0.14) for the soft and stiff material properties, respectively (Fig. 7B; $p>0.05$ between Warping-derived and FE-predicted).

Fig. 6.

Slice-to-slice comparison of experimental (Warping analysis) and model-predicted strains ($E_1$, FE model) at 120 mmHg that utilized the soft or stiff material properties. Data were extracted at corresponding axial positions within the vessel for both analyses. All slices are shown in Supplemental Fig. 2.

Fig. 7.

Distribution of experimental (Warping) and FE-predicted strains at 120 mmHg, utilizing the soft or stiff material properties, at specific axial positions. Box plots show median, quartile, and whisker (1.5 times the interquartile range away from the quartiles) values, as well as data outside the whisker range (circles). * indicates p < 0.05 for comparisons between soft and stiff FE models: all other comparisons were not significantly different.

3.4. Transmural Strain Comparisons Between Warping and FE Models at Systole

A focal analysis of Warping-derived and FE-predicted transmural strains revealed similar trends as observed in the slice-to-slice analysis, with soft and stiff model-predicted strains bounding the Warping-derived data. For example, average Warping strains across all slices in sample 1 at the inner and outer boundaries were 0.27 ± 0.05 and 0.14 ± 0.03, respectively. At the same positions in the FE models with soft and stiff material properties, predicted strains were 0.54 ± 0.02/0.28 ± 0.02 (inner/outer) and 0.16 ± 0.01/0.08 ± 0.01, respectively (Fig. 8). Boundary strains for Samples 2 and 3 demonstrated similar patterns across all slices (Sample 2 | Warping: 0.48 ± 0.09/0.24 ± 0.04, soft FE model: 0.50 ± 0.02/0.25 ± 0.02, stiff FE model: 0.16 ± 0.01/0.08 ± 0.01; Sample 3 | Warping: 0.32 ± 0.04/0.19 ± 0.03, soft FE model: 0.59 ± 0.02/0.35 ± 0.02, stiff FE model: 0.17 ± 0.01/0.10 ± 0.01.). Like the slice-to-slice comparison, sample 1 and 3 strains agreed better with the stiff model (RMSE: 0.08 ± 0.04 and 0.12 ± 0.04), while sample 2 better aligned with the soft model (RMSE: 0.08 ± 0.07). Lastly, Bland-Altman analysis demonstrated biases of 0.076, 0.12, and −0.018 between Warping- and FE-derived data for samples 1 (stiff model), 3 (stiff), and 2 (soft), respectively (Fig. 9).

Fig. 8.

Comparison between experimentally-derived and model-predicted strains under a 120 mmHg load at normalized transmural positions across a range of material properties. Note only 4 of 8 circumferential locations are shown.

Fig. 9.

Bland-Altman analysis between transmural experimental and model-predicted strains across all axial positions within each sample at 120 mmHg. The closest-matched FE analysis for each sample was selected for the comparison.

4. Discussion

Utilizing an image-based experimental approach to quantify the deformations in soft biologic tissue, this study compared 3D strain fields derived from experimental and FE analyses in healthy arterial tissue under physiologic loading. Recognizing and incorporating variability in arterial material properties, FE model strain predictions bounded experimental data across spatial evaluation tiers (e.g., slice-to-slice, transmural levels) at systolic pressure. These results indicate that the computational framework presented herein can accurately predict the physiologic deformations of arterial tissue and capture the underlying physics across multiple specimens. Moreover, this work outlines an ex vivo approach to comprehensively evaluate FE model accuracy in vascular mechanics.

Despite the availability of techniques to quantify experimental vascular mechanics, few have been applied to assess accuracy in computational models. Primary applications of measuring arterial transmural deformations have focused on ultrasound-based elastography. Strains can be determined in vivo by applying cross-correlation techniques to IVUS data acquired across multiple load states at the same spatial location (Baldewsing et al., 2005; de Korte et al., 2000; Schaar et al., 2004). Although elastography can aid in evaluating model predictions, its central application has focused on determining plaque material properties and vulnerable plaque detection (Baldewsing et al., 2005; Schaar et al., 2004). Importantly, elastography is limited to capturing only radial deformations, which are smaller in magnitude than those in the circumferential direction for an artery under pressure loading. The technique employed in the present study, Hyperelastic Warping, enables detailed and continuous in-plane calculations of both radial and circumferential strain, enabling a more rigorous approach to quantify deformations. While a direct comparison between elastography and Hyperelastic Warping has not been performed, each relies on textural information, highlighting the importance of imaging technologies. Thus, continued advancements in medical imaging, particularly those modalities that afford transmural data, have broad applications in vascular mechanics that have a direct clinical impact.

While FE approaches to predict the 3D arterial mechanical environment have been broadly applied across artery types, few studies have evaluated their accuracy. Anderson and colleagues (2007) offer a useful description of assessing accuracy (i.e., validation), defined as “the process of determining the predictive capability of computational models by comparison to experimental data”. To this end, model outputs are often compared with experimental data reported in the literature, which has practical benefits. However, this approach can pose significant limitations. Specifically, “…difficulties can often arise when using data from the literature for model validation, including: (1) reliance on another’s ability to gather quality experimental data, (2) difficulty in extrapolating experimental uncertainty error and (3) gross differences in the test specimen, loading and boundary conditions.” (Anderson et al., 2007). Vascular mechanics FE studies have largely avoided this issue, yet assessing model accuracy has often been either qualitative or relied on global quantitative metric(s) that may mask differences between experimental and model predictions. In a computed tomography (CT)-based patient-specific coronary artery model, accuracy was assessed through a quantitative comparison of model-predicted and image-derived vessel centerlines (Wu et al., 2018). Another set of CT-based coronary models compared distal displacements or the model-predicted deformed intima surface against angiographic-derived data (Carpenter et al., 2021; Gholipour et al., 2020). While these studies are examples of assessing model accuracy against experimental data collected in the same study, comparisons were limited to global measures of motion. A more rigorous approach demonstrated agreement in model predictions of lumen geometries in 3D virtual histology IVUS-derived FE models of femoral arteries (Noble et al., 2020). Notably, this study acquired vessel-specific material properties and demonstrated minor differences (<2%) in experimental and FE results when using median versus vessel-specific material parameters. Important to the rigor of assessing accuracy, however, is that this study only compared lumen deformations. Herein, we integrate a novel IVUS-based experimental approach to assess FE model agreement across localized regions within the wall to promote rigor and credibility in the FE model before its application (or translation). Moreover, the increased spatial comparisons ensure that the predicted focal mechanics, which may be correlated with biological or clinical data, have a measure of confidence. Promoting the credibility, confidence, and safety of computational model predictions is central to their adoption and translation.

We recognize the variability of tissue material properties and its consequence when interpreting comparative results. Indeed, this directly addresses the comments made by Anderson et al. on relying on another’s ability to gather quality experimental data and the associated difficulties (Anderson et al., 2007). The material parameter data used herein showed a standard deviation >20% for the isotropic term, for example, of the SEF across 14 carotid artery samples (García et al., 2011). In addition, differences in material properties were observed when evaluating samples in the proximal and distal regions of the vessel. Although we did not quantify material properties, variability in our samples was evident when comparing the experimentally derived strain fields (Figs. 6–8). Had average material properties been incorporated into the FE models, the impact of the comparative results could have been lessened. Future investigations incorporating simultaneous image acquisition and material testing could be performed as the experimental platform is refined and extended. While we selected a more basic approach to handle variability, analyzing a soft and stiff model for each sample and incorporating modern uncertainty quantification (UQ) tools would promote rigor when evaluating model accuracy (Berggren et al., 2024). Additionally, the question of the required level of accuracy arises, one which is difficult to interpret at the onset of model development if the framework has yet to be applied to its specific use case. Regardless, the accuracy and impact of model output variation should be considered when applying biomechanical simulations to clinical problems.

A validation experiment is designed to capture the central physics of the problem of interest, incorporating all relevant physical features and boundary conditions (Anderson et al., 2007). Failure to do so can lead to discrepancies between experimental measures and model predictions, and errors may compound if not properly accounted for. In the presented validation study, the geometry and boundary conditions were carefully controlled between the experiments and FE models within the limitations of the equipment. For example, the Warping and 3D FE model geometries each were constructed from acquired image data (Fig. 2), and the lumen pressure in the cannulated vessel was monitored via a computer-controlled system, ensuring agreement with the applied load in the FE model. However, and as noted above, inconsistencies between the physical system and FE model existed in the material properties. Moreover, the prescribed material properties were derived from uniaxial loading, which is insufficient to fully capture the multi-dimensional material response to loading. This limitation was apparent when observing the structural stiffness of the tissue derived from the experimental and FE models, as the softest FE model exhibited a strain-softening response at pressures ≤ ~125 mmhg (Fig. 4). Although a comprehensive examination of potential sources for error was beyond the scope of this study, it is likely that variations in material properties were the leading cause of differences between experimental measures and model predictions. Furthermore, these data highlight the need to derive material properties from physiologic loading conditions to better predict the vascular mechanical environment.

We acknowledge the presence of limitations in this study. First, the lack of vessel-specific material properties in the FE models introduces uncertainty in predictions that impact experimental and FE comparisons. However, comprehensive mechanical testing (Ferruzzi et al., 2013) and IVUS acquisition is time-intensive and requires distinct experimental setups and computational methods. Second, the comparison of deformations in the adventitia was excluded in this study due to the difficulty in defining the adventitial boundary. Although the adventitial layer was ignored in the Warping models due to boundary identification issues, it was included in the 3D FE models to account for its impact on distension of the medial layer. Third, axial stretch was not included in the 3D FE models, while IVUS data were acquired on a stretched vessel. While image data could have been acquired on an unloaded vessel and the 3D FE models constructed from those data, difficulties in axial co-registration between experimental and model slices could have produced errors that obscured comparison efforts. The similar magnitudes and trends observed in strain data (Figs. 6–8) suggest that the exclusion of axial stretch had no major impact on results. Lastly, while diastolic prestrain was not included, the developed experimental platform enables the evaluation of techniques to estimate this prestress using observed deformations.

In conclusion, this study presents a combined experimental and modeling platform to quantitatively compare image-based model predictions of vascular tissue under physiologic loading. Examining healthy porcine tissue, we demonstrate that our modeling framework can predict physiologic strains observed experimentally across multiple specimens, including localized strains through the arterial wall. Moreover, these efforts demonstrate the importance of recognizing heterogeneity in material response across samples when evaluating the accuracy of modeling approaches. Ultimately, this study lays the foundation to validate computational models that predict the vascular mechanical environment in healthy and diseased soft biologic tissues.

Supplementary Material

Supp Figure 1

Supplemental Fig. 1. Mesh convergence results. (A) Warping strains across mesh densities with varying numbers of radial and circumferential elements. (B) FE model strains at the center axial position for mesh convergence testing.

Supp Figure 2

Supplemental Fig. 2. Experimental and computational strain data at 120 mmHg for all axial positions across the three samples.

Supp Table 1

Supplemental Table 1. Strain energy function (SEF) material parameters for the 3D FE models. $\varphi$ is reported with respect to the circumferential direction.

Appendix A Supplementary Data

Mesh convergence for the Hyperelastic Warping models was tested by increasing the number of elements by a factor of 2 in the radial and circumferential directions of the artery and PV regions. Box plots of the medial strain data at the central slice were then compared and convergence was achieved when absolute changes in median strain values were < 0.0004 (changes in 25^th/75^th percentiles: 0.0006/0.0018, low/high whiskers: 0.0042/0.0089) (Supplemental Fig. 1A). FE model mesh convergence was tested in a similar manner by increasing the total number of elements by a factor of 2. Convergence was achieved at the 2x mesh when absolute changes in the median strain data were < 0.0025 (25^th/75^th percentiles: 0.0047/0.0070, low/high whiskers: 0.0001/0.0059) (Supplemental Fig. 1B).