Kidney cortex shear wave motion simulations based on segmented biopsy histology

Background and Objective: Biopsy stands as the gold standard for kidney transplant assessment, yet its invasive nature restricts frequent use. Shear wave elastography (SWE) is emerging as a promising alternative for kidney transplant monitoring. A parametric study involving 12 biopsy data sets categorized by standard biopsy scores (3 with normal histology, 3 with interstitial inflammation (i), 3 with interstitial fibrosis (ci), and 3 with tubular atrophy (ct)), was conducted to evaluate the interdependence between microstructural variations triggered by chronic allograft rejection and corresponding alterations in SWE measurements. Methods: Heterogeneous shear wave motion simulations from segmented kidney cortex sections were performed employing the staggered-grid finite difference (SGFD) method. The SGFD method allows the mechanical properties to be defined on a pixel -basis for shear wave motion simulation. Segmentation techniques enabled the isolation of four histological constituents: glomeruli, tubules, interstitium, and fluid. Baseline ex vivo Kelvin-Voigt mechanical properties for each constituent were drawn from established literature. The parametric evaluation was then performed by altering the baseline values individually. Shear wave velocity dispersion curves were measured with the generalized Stockwell transform in conjunction with slant frequency-wavenumber analysis (GST-SFK) algorithm. By fitting the curve within the 100-400 Hz range to the Kelvin-Voigt model, the rheological parameters, shear elasticity (mu 1) and viscosity (mu 2), were estimated. A time-to-peak algorithm was used to estimate the group velocity. The resultant in silico models emulated the heterogeneity of kidney cortex within the shear wave speed (SWS) reconstructions. Results: The presence of inflammation showed considerable spatial composition disparities compared to normal cases, featuring a 23 % increase in interstitial area and a 19 % increase in glomerular area. Concomitantly, there was a reduction of 12 % and 47 % in tubular and fluid areas, respectively. Consequently, mechanical changes induced by inflammation predominate in terms of rheological differentiation, evidenced by increased elasticity and viscosity. Mild tubular atrophy showed significant elevation in group velocity and mu 1. Conversely, mild and moderate fibrosis exhibited negligible alterations across all parameters, compatible with relatively limited morphological impact. Conclusions: This proposed model holds promise in enabling patient-specific simulations of the kidney cortex, thus facilitating exploration into how pathologies altering cortical morphology correlates to modifications in SWE-derived rheological measurements. We demonstrated that inflammation caused substantial changes in measured mechanical properties.