Conference Agenda

Introduction:
Biomechanical computational models should be largely patient-specific to provide deeper insight into the pathophysiology of abdominal aortic aneurysms (AAA) and to be relevant for future clinical diagnostics. The identification of individual material properties is crucial but remains challenging in vivo. Time-resolved 3D ultrasound combined with speckle tracking (4D-US) is a non-invasive imaging technique that provides full-field information of heterogeneous aortic wall strain distributions [1]. These strains are cyclic with respect to diastole. We present a novel 4D-US strain imaging approach for identifying parameters of a nonlinear, anisotropic material equation using only in vivo-accessible data, a further development of a previously presented method [2]. For this new method, we performed both in vitro and in vivo validations.

Material and Methods:
For in vitro validation, an intact porcine aorta was tested in an inflation-extension device. The vessel was immersed in 0.9% NaCl solution at 37°C and subjected to cyclic physiological pressure and length changes at 0.84 Hz. Forces, pressures, and deformations were recorded using two CMOS cameras and 4D-US imaging in parallel. A finite element analysis (FEA) model was generated from 4D-US images, with boundary conditions replicating the experimental setup. Parameters for the anisotropic Holzapfel-Gasser-Ogden (HGO) material equation were identified by (1) fitting to stress-stretch curves derived from mechanical data and (2) using the in vivo 4D-US strain imaging approach.

For in vivo validation, 4D-US data of two AAA patients (AAA1, AAA2) were acquired using a commercial 3D echocardiography system with a transthoracic probe. Diastolic and systolic blood pressures were recorded. During open AAA repair of the same patients, six wall specimen (three longitudinal, three circumferential) were harvested and tested in uniaxial tensile experiments, with deformations recorded optically. First, stress-stretch curves were calculated from mechanical data, and HGO parameters were identified by fitting the model to this mechanical data. Secondly, a patient-specific FEA model was created from in vivo 4D-US images, incorporating vessel wall and intraluminal thrombus. Physiological boundary conditions were applied, including measured diastolic and systolic pressures. HGO material parameters were identified using the in vivo 4D-US strain imaging approach.

Both in vitro and in vivo validations used an evolutionary self-adaptive Differential Evolution (JADE) algorithm for parameter optimization. The algorithm iteratively computed the material-dependent load-free geometry and then diastolic/systolic geometries using measured blood pressures, from which cyclic strains were derived. HGO parameters were identified by minimizing the error between measured (4D-US) and calculated (FEA) cyclic strains.

Results:
Comparison of stress-stretch curves calculated using the identified parameter sets of optical and 4D-US methods show coefficients of determination in the range R²=0.952−0.990. Performance was improved by a factor of seven compared to previous implementation.

For in vivo validation, AAA1 showed mean absolute percentage errors (MAPE) of 0.76%-0.07% when comparing stress-stretch curves calculated using the identified parameter sets of optical and 4D-US methods. AAA2 exhibited MAPE values between 0.51% and 17.83%. When averaging tensile test results from the four specimens, the stress-stretch curve aligned well with the 4D-US-derived global material behavior.

Conclusion:
We successfully validated a 4D-US strain imaging approach both in vitro and in vivo for identifying patient-specific parameters of an anisotropic material equation using only in vivo-accessible data. The method demonstrated high accuracy and feasibility for clinical application in AAA biomechanics.

Literature:
[1] Karatolios K, Wittek A et al., Ann. Thorac. Surg, 2013
[2] Wittek A et al. JMBBM 2016; 58: 122-138

Background: Abdominal aortic aneurysm (AAA) is a degenerative vascular disease characterized by significant changes in the geometry and microstructure of the aortic wall. AAA particularly affects elderly men, with a prevalence ranging from 1.3% to 8.9% in men over 60. Rupture of the aneurysm wall is associated with a high mortality rate of up to 80 %, so that adequate identification of patients at risk is crucial for their survival. Clinically, rupture risk is assessed using the maximum diameter criterion, which guides surgical decision-making. While statistically validated, this criterion lacks precision as it fails to account for patient-specific variations in aortic wall strength and local stress concentrations. The need for more patient-specific biomarkers is therefore widely acknowledged. It is hypothesized that Wall Motion Indices (WMI), derived from 4D ultrasound (4D-US)-based local strain measurements, can provide a more accurate assessment of patient-specific rupture risk by capturing aortic wall kinematics.

Methods: Preoperative data from 9 AAA patients were collected, including 4D-US strain imaging, CT angiography, maximum diameter, and blood pressure. Patients underwent open surgical repair, during which tissue samples were harvested for mechanical testing. WMI, describing the distribution of the aortic wall’s strain field, were computed from 4D-US strain data. The analysis focused specifically on wall regions corresponding to the locations from which tissue samples were obtained during surgery. These indices were correlated with a normalized experimental rupture potential (NERP), calculated as the ratio between in vivo wall tension (derived from Finite Element Analysis based on CT-A and mean arterial pressure) and the experimental failure tension (yield and maximum tension) determined via uniaxial tensile tests on the harvested tissue.

Results: Several WMI demonstrated significant correlations with NERP (r>0.75, p<0.05), particularly indices describing heterogeneous strain distributions within the aneurysmal wall. These WMI also correlated significantly with the experimental failure tension determined from uniaxial testing of the tissue samples (r<-0.67, p<0.05). Conversely, no significant correlation was found between maximum diameter and NERP, highlighting the limitation of size alone in predicting the individual mechanical failure risk.

Conclusion: This study indicates that 4D-US-derived WMI can provide patient-specific information correlated to rupture potential of AAA independent of the maximum diameter. The strong correlation between heterogeneous strain patterns and tension-based rupture potential highlights the potential of WMI to refine clinical decision-making. As a non-invasive modality, 4D-US derived WMI could potentially improve patient selection for elective repair, identifying individuals truly at high risk irrespective of diameter alone, thus personalizing AAA management. Further validation in larger patient cohorts is necessary to confirm these findings.

We propose a novel model for a vascularized poroelastic composite representing the myocardium which incorporates both mechanical deformations and electrical conductivity. Our structure comprises a poroelastic extracellular matrix with embedded vasculature and elastic inclusions (representing the myocytes) and we consider the electrical conductance between these two solid compartments. There is a distinct length scale separation between the scale where we can visibly see the connected fluid compartment (vessels) separated from the poroelastic matrix and the elastic myocyte and the overall size of the heart muscle.

We therefore apply the asymptotic homogenisation technique to derive the new model. The effective governing equations that we obtain describe the behaviour of the myocardium in terms of the zero-th order stresses, current densities, relative fluid-solid velocities, pressures, electric potentials and elastic displacements. It effectively accounts for the fluid filling in the pores of the poroelastic matrix, flow in the vessels, the transport of fluid between the vessels and the matrix, and the elastic deformation and electrical conductance between the poroelastic matrix and the myocyte.

This work paves the way towards a myocardium model that incorporates multiscale deformations and electrical conductivity whilst also considering the effects of the vascularisation and indeed the impact on mechanotransduction.