International Journal for Numerical Methods in Biomedical Engineering

Identification and treatment of pregnancies at risk for preterm birth is a central challenge in obstetric research. Many of the known causes of preterm birth originate from mechanical failure in reproductive tissues. To better understand the biomechanical environment of the gravid uterus and its potential contribution to preterm birth, this computational study presents a parametric method for modeling maternal reproductive anatomy during the early second trimester. A finite element modeling approach was built using existing sonographic measurements from early second-trimester maternal anatomy and material properties from published mechanical tests. We applied the same physiologically relevant intrauterine pressure to all models and quantified the resulting tissue stretch. The sensitivity of the stretch in the proximal cervix was explored by varying material properties and sonographic maternal anatomy dimensions. Cervical material properties, particularly the fiber stiffness modulus and ground substance Youngs modulus, were found to have the greatest effect on proximal cervix stretch compared to other material properties and sonographic dimensions. Among the sonographic dimension measurements, those defining the region surrounding the proximal cervix had the greatest effect on proximal cervix stretch, including the curvature of the posterior uterine wall and the thickness of the lower uterine segment. The computational modeling approach presented here enables future patient-specific studies of gravid reproductive tissues to elucidate differences between individuals who do and do not deliver preterm. Additionally, this study is foundational for building digital twins to support future virtual clinical studies on diagnostic and therapeutic device design to prevent preterm birth.

The control of uterine activity during pregnancy is a complex process that involves regulating myometrial excitability across multiple scales. While numerous studies have investigated various regulatory mechanisms and established the contributions of ion channels and gap junctions, how these mechanisms interact to produce observed changes in uterine activity remains poorly understood. Pivotal to these efforts are computational models that effectively capture gestational changes in excitability across scales. In this study, we propose a multiscale computational modeling framework that can reproduce measured activity at the cellular and tissue scales at a given gestational stage. At the cellular level, we identify key ion currents underlying the observed electrophysiological properties based on a literature review of their regulation and a sensitivity analysis of the Tong 2011 uterine smooth muscle cell activation model. The conductances of these ion currents are then fit to reproduce characteristic resting membrane potentials and burst properties using Bayesian optimization. To extend to the tissue level, we employ an anisotropic monodomain model, parameterized by the resistivity of late pregnancy uterine muscle, to investigate electrical propagation in a two-dimensional section of uterine tissue. We then apply the multiscale model to study myometrial activation in late pregnancy and elucidate the contributions of ion channel and gap junction regulation in transitioning the uterus from a quiescent state to labor. Our resulting model successfully reproduces measured electrophysiological properties at the cellular level and characteristic single-spike and burst-propagation patterns at the tissue level across the three late-pregnant time points analyzed (days 16/17, 18/19, and 20/21) in a murine model. Furthermore, our results suggest that the regulation of the conductances of the voltage-dependent potassium current (IK1), L-type calcium current (ICaL), and sodium current (INa) is most important in determining preterm uterine excitability. The framework established here will promote the development of more gestationally relevant models to better understand labor progression and the factors involved in dysfunctional labor.

BackgroundQuantitative dynamic contrast-enhanced myocardial perfusion cardiovascular magnetic resonance (CMR) enables estimation of myocardial blood flow (MBF) and myocardial perfusion reserve (MPR). These measurements require an arterial input function (AIF), which is typically derived from the left ventricular blood pool. However, the contrast agent bolus undergoes dispersion during transport through the coronary vasculature before reaching the myocardial microcirculation. This may introduce systematic and spatially heterogeneous errors in MBF and MPR estimates. PurposeThis work provides an extended segmental analysis of bolus-dispersion-induced errors in quantitative myocardial perfusion MRI using previously established computational fluid dynamics (CFD) simulations in realistic porcine coronary artery models. The focus of the present analysis is the assignment of coronary outlets to myocardial segments and the resulting segmental variability of MBF and MPR errors. MethodsRealistic three-dimensional models of the left and right coronary arteries were extracted from an ex-vivo porcine imaging cryomicrotome dataset. The models extended down to the pre-arteriolar level and included 364 outlets for the left coronary artery and 104 outlets for the right coronary artery, with an average outlet diameter of 383 {+/-} 85 {micro}m. Blood flow was simulated under rest and stress conditions using OpenFOAM. Contrast agent transport was then modeled by solving the advection-diffusion equation using a gamma-variate bolus as input. Outlet concentration-time curves were analyzed using an indicator-dilution model to estimate MBF and MPR errors. Outlets were assigned to standardized myocardial segments, and segmental averages were evaluated with respect to coronary supply territory and travel distance from the model inlet. ResultsThe simulations demonstrated marked segmental heterogeneity of volume blood flow and bolus-dispersion-induced MBF and MPR errors. Errors increased with travel distance from the coronary artery inlet and were more pronounced in regions supplied by the right coronary artery, consistent with lower flow velocities and stronger bolus dispersion. The resulting systematic errors led to underestimation of MBF and overestimation of MPR, with segmental deviations reaching up to approximately 60%. ConclusionBolus dispersion in the coronary vasculature may lead to substantial segmental and location-dependent errors in quantitative myocardial perfusion MRI. This extended analysis indicates that dispersion-related bias is not spatially uniform, but depends on coronary supply territory, travel distance, and flow conditions. These effects should be considered when interpreting regional MBF and MPR estimates, particularly as automated quantitative myocardial perfusion CMR becomes more widely used.

PurposeComputational models of the uterus during pregnancy enable analysis of electro-chemo-mechanical pathways to predict labor timing and guide treatment planning. We aim to develop a robust image-based modeling pipeline to investigate uterine passive mechanics during late pregnancy. MethodsA parametric model of the uterus and cervix was created using a patients MRI measurements at 38 weeks of gestation. Inspired by advances in cardiac mechanics models, we created Laplace-Dirichlet solutions to inform tissue domains, fiber structure within the uterus and cervix, and spatially varying Robin boundary conditions. Prior imaging and mechanical testing data were used to fit material parameters. Boundary condition parameters were tuned to match the displacements of a previously established approach that employed contact with surrounding tissue. The tissue mechanical response to a physiologic load was assessed across varying material properties and fiber architectures. ResultsDiscrepancies in nodal displacements between the current approach and the contact-based model were limited to 3.4 {+/-} 1.8 mm, yielding nearly 90 % computational savings. Uterine tensile strains were more sensitive to ground substance elastic modulus (E) compared to fiber properties. Reduced E and fiber stiffness increased cervical strains and compression. Fiber dispersion and architecture modulated the opening of the cervical internal ostium but had a reduced impact on compression. ConclusionWe developed a novel workflow for modeling passive uterine mechanics, informed by patient-specific measurements and in vitro mechanical tests. The robust workflow may prove useful for studying labor progression and conducting longitudinal studies to enhance our understanding of normal and pathological pregnancies.

The osteocyte network in bone is believed to play an important role for how bone tissues sense and respond to mechanical stimulation. Yet, bone adaptation to mechanical loads is often conceptualised as a simple response to mechanical stimuli, such as Wolffs law, which is based on mechanical variables only and takes no account of the cellular basis of mechanosensation. Wolffs law presumes the existence of a reference mechanical stimulus, the mechanical setpoint, above which bone is consolidated, and under which bone is removed. In this paper, we develop a theory of bone tissue sensing and adaptation based on osteocytes to provide new understanding of the role played by osteocyte signals in mechanical adaptation. In this theory, the mechanical setpoint of Frosts mechanostat is explicitly embodied as osteocyte properties involved in mechanotransduction. The mechanical setpoint is allowed to adapt due to the replacement of osteocytes during remodelling, making the setpoint space and time dependent. We propose a mathematical model to implement this new theory of bone adapation and present numerical simulations of this model to explore how mechanobiological response curves (effective Wolffs laws) are modulated by setpoint adaptation during remodelling. By accounting for varying osteocyte populations within bone tissue, we explore bone adaptation under osteocyte disruptions, which is particularly relevant to age-related bone loss. Our model suggests that biological disruptions of remodelling balance cannot always be compensated by mechanical feedback, and that setpoint adaptation during remodelling may have significant observable consequences, such as hysteresis in bone response signatures that resemble lazy zones.

PurposeFunctional tricuspid regurgitation (FTR) is driven by right ventricular (RV) remodeling, annular dilation, and papillary muscle dislocation. Free wall approximation (FWA) has been proposed to treat FTR by addressing RV dilation, but its effects on tricuspid valve (TV) biomechanics remain unclear. We present a real-time 3D echocardiographic (rt3DE)-based finite element framework to quantify TV biomechanics under FTR, and preliminarily apply it to assess FWA effects. MethodsSubject-specific models were developed from rt3DE data of three dilated porcine hearts in an ex-vivo mock-loop. TV geometries at end-diastole and peak systole (PS) were complemented by parametric chordae tendineae and hyperelastic tissue properties. TV closure was simulated under a standard pressure load and image-based annular motion. After tuning chordae length to replicate the PS ground truth in FTR, FWA was simulated as 30% and 60% approximations along three anatomical directions (anterior-posterior, A-P; anterior-septal, A-S; anterior-septal wall, A-SW). ResultsIn FTR simulations, median geometric errors ranged from 1.16 to 1.26 mm; median stress ranged from 56.4 to 74.7 kPa. FWA simulations predicted regurgitant orifice area (ROA) reductions by 53-99%, albeit overestimating the residual ROA vs. in vitro ground truth when starting from particularly extreme FTR conditions; concomitantly, a median stress reduction by 8-43% vs. FTR conditions was predicted. ConclusionPreliminary data suggest that our rt3DE-based framework can reliably quantify FTR-related TV biomechanics and that post-FWA biomechanics depends on initial FTR conditions. A larger cohort is required to verify the method and obtain statistically significant results.

Constitutive models of myocardial mechanics form a cornerstone of personalized cardiac simulations and cardiac digital twins. Researchers traditionally prescribe these models a priori and calibrate them from ex vivo tissue experiments, even though tissue excision alters loading conditions, removes residual stresses, and eliminates important physiological interactions. Multimodal cardiac MRI now provides subject-specific ventricular geometry, deformation, and myocardial microstructure, yet current inverse approaches still rely on predefined constitutive laws. Here we present the first framework to discover constitutive models of passive myocardial mechanics directly from in vivo cardiac imaging data by embedding a constitutive artificial neural network within a nonlinear finite element model of ventricular filling. Using multimodal cardiac MRI that combines ventricular geometry, deformation, and microstructure from a representative healthy individual, the framework identifies sparse, mechanically admissible strain-energy functions without prescribing their form a priori. The best-performing model contains only two fiber- and two sheet-invariant terms, achieves a mean displacement error of 1.62 mm, and reduces the error of the widely used Guccione and Holzapfel models by 34.14% and 26.01%. The discovered models indicate that fiber- and sheet-related anisotropic mechanisms dominate the passive mechanical response during physiological ventricular filling. More broadly, this work establishes a non-invasive strategy for subject-specific constitutive discovery from cardiac imaging data and lays the foundation for personalized cardiac simulations and cardiac digital twins.

Control of fluids is a hallmark of microfluidic systems and fundamental for the successful application of microfluidic devices. Trigger valves use geometric features to autonomously control the release of fluids in microfluidic devices. Our previous work has adapted geometries used in closed trigger valve systems to enable use in open systems, allowing for open microfluidic devices with up to three trigger valves. Here, we focus on the parallel co-flows produced by sequential release of trigger valves and present a model that predicts their layer widths as a function of the geometric characteristics of the different side channels of each trigger valve. We show layered co-flows with widths as low as 50 microns. Additionally, we expand the use of trigger valves in open microfluidic devices by incorporating 1) varied step heights, 2) devices with up to seven trigger valves, and 3) use of varied fluids and plastics. To validate the implementation and use of these trigger valves in open systems, we have developed a theoretical framework to compare predicted outcomes (i.e., fluid travel distance, velocity, and layering width) with our experimental values. This theoretical work offers applications in various fields, including hydrogel patterning for 3D cell culture, organ-on-a-chip models, at-home sample preparation, and autonomous microfluidic systems for biosensing.

The development of digital twins in medicine, i.e., virtual replicas of human organs, offers a promising path toward precision medicine by enabling interpretable, mechanistic, and actionable insights. In the brain, cerebrovascular twins support individualized modeling of hemodynamics and bio-transport, with broad applications. A major bottleneck, however, is the lack of robust methods to transform in vivo cerebrovascular images into simulation-ready cerebrovascular meshes or graphs. Here, we present CerebroVascular Imaging to Graph reconstruction (CVIG), a robust and multiscale framework for reconstructing whole brain cerebrovascular graphs from in vivo cerebrovascular images. CVIG integrates vessel vectorization, with tolerance to discontinuity in vessel structures, using a topology-guided assembly of vessel trees to generate cerebrovascular graphs from medical images. We demonstrate the ability of CVIG to generate vascular graphs with improved vascular coverage and topological correctness, the capability essential for high fidelity brain biophysical simulations. This work establishes a vascular graph framework for individualized modeling and analysis, providing a key foundation for digital twins of the human brain.

Acute subdural hematoma (ASDH) is a prevalent injury with high mortality and morbidity, often resulting from bridging vein (BV) disruption secondary to cortical relative motion. As a thin membrane enveloping the brain surface and anchoring BVs, the pia mater is hypothesized to play a critical mechanical role in cortical response and hence ASDH pathogenesis. Finite element (FE) head models are valuable tools to predict ASDH occurrence during impacts. However, the pia mater is often represented as an elastic material in existing FE head models, despite experimental evidence reporting its nonlinear mechanical behavior. In this study, both linear (Young's modulus of 11.5 MPa) and nonlinear (the stress-strain curve derived from pial tension tests) material models of the pia mater were implemented in one FE head model. The models were subjected to three experimental impact loadings, one of which was known to cause ASDH and two of which were not. Results demonstrated that, across all simulated impacts, the model with nonlinear pia mater properties predicted larger cortical displacements and BV responses than the linear model. For the impact with known ASDH occurrence, the predicted BV strain was 0.17 for the nonlinear model and 0.094 for the linear model, with only the former approaching the reported rupture strain range of the BV-superior sagittal sinus complex (0.29 {+/-} 0.13). These findings verified the mechanical importance of the pia mater in cortical responses and hence the prediction of ASDH, suggesting that conventional linear pia modeling might over-constrain cortical motion, leading to underestimation of BV strain and ASDH risk. The current study supported the adoption of experimentally derived nonlinear pia mater properties in FE head models to improve the reliability of ASDH prediction.

Type 2 diabetes is characterized by progressive aggregation of islet amyloid polypeptide (IAPP) within the islets of Langerhans, a process strongly implicated in beta-cell dysfunction and loss. Although oligomeric IAPP intermediates are widely considered the principal cytotoxic species, the relative contributions of the many biological and kinetic processes governing their formation, clearance, and conversion into fibrils remain poorly quantified. Here, a mathematical model of IAPP aggregation is developed that incorporates the physiology of beta-cell secretion and the microanatomy of the islet, including capillary-mediated clearance, enzymatic degradation, and the kinetics of oligomer and fibril formation within a well-mixed control volume. Building on the hypothesis that oligomers are the major cytotoxic species, the concept of accumulated cytotoxicity is introduced, defined as the time integral of the oligomer concentration, and a systematic sensitivity analysis of this quantity with respect to all model parameters is performed. The results reveal a striking hierarchy: only two parameters, the basal rate of IAPP monomer secretion and the rate constant for spontaneous oligomer dissociation, exert a first-order influence on long-term accumulated cytotoxicity, with dimensionless sensitivities approaching +1 and -1, respectively, while the effect of all other parameters remains subordinate and decays at long times. The model further shows that capillary clearance, owing to the physical exclusion of oligomers from fenestrated capillaries, selectively reduces fibril accumulation and amyloid deposition without affecting oligomer-mediated cytotoxicity, indicating that amyloid area fraction, the standard histological metric of disease severity, may not be a reliable surrogate for cytotoxic burden. The model predicts that approximately 48% of the islet area is replaced by amyloid after 30 years, broadly consistent with histological observations of advanced disease. These findings identify monomer secretion and oligomer dissociation as the most promising therapeutic targets to limit cytotoxic damage in type 2 diabetes and provide a quantitative framework for evaluating candidate intervention strategies.

Diffuse gliomas are deadly because the individual tumor cells invade - they travel far from the imageable mass, so it is impossible to remove the tumor completely. On the cellular level, glioma cells seem to be in either a "go" state (in which they do not divide) or a "grow" state (in which they do not migrate). We investigate what this tiny choice has to say about the large-scale speed of the invasion front and whether the implication is sufficiently strong to rule out the classical description of the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) type, in which a single phenotype migrates and proliferates. We derive a two-phenotype reaction-diffusion model with density-dependent switching, and we prove the cooperative (quasi-monotone) structure and the associated comparison principle and study travelling-wave solutions of the model. A leading-edge linearization gives minimal front speed as minimizer of an explicit dispersion relation, and direct simulation verifies the predicted speed. In the experimentally relevant fast switching limit, we find a closed-form expression for the speed, that is, we obtain an effective Fisher-KPP equation with rescaled diffusivity and growth rate, with the fractions of the phenotypes. The "go-or-grow" (GoG) front can move at a maximum speed of half the Fisher speed for the same single-cell motility $D$ and proliferation rate $r$, which occurs only when the cells divide their time equally between the two phenotypes. This bound is directly testable: measurement of the front speed, plus independent determination of $D$ and $r$, discriminates the two hypotheses, and in the GoG case, yields recovery of the phenotype balance. We then extend the result to anisotropic (DTI-informed) invasion along white-matter tracts and discuss implications for understanding clinical measurements of growth rate.

The suspension culture of pluripotent stem (PS) cells in stirred bioreactors poses a delicate balance between maintaining homogeneous cell dispersion and avoiding excessive shear stress that can compromise cell viability and pluripotency. In this study, we used computational fluid dynamics (CFD) coupled with a discrete particle method (DPM) to simulate iPS cell behavior in a 5 mL delta-impeller stirred tank. Our analysis revealed that upward flow at the tank bottom and downward flow at the top are critical for maintaining a stable suspension. To optimize the stirring protocol, we applied Bayesian optimization to identify a time-dependent stirring schedule that begins with a high-speed phase for resuspension, followed by a low-speed phase for sustained suspension with minimal hydrodynamic stress. The optimized schedule demonstrated improved suspension ratio and reduced slip velocity, indicating lower mechanical stress on cells. These findings provide engineering insights into scalable bioreactor operation, contributing to the design of robust iPS cell manufacturing systems.

Angiogenesis drives the formation and remodeling of capillary networks throughout tissue repair, regulating the vascular environment that supports healing and tissue remodeling. Experimental characterization of these processes is commonly performed using CD31-stained histological tissue sections to quantify capillary surface density and morphology throughout healing. However, these measurements provide only two-dimensional characterization of an underlying three-dimensional (3D) vascular network, limiting direct estimation of volumetric capillary density and vascular architecture. To address this limitation, an experimentally informed framework was developed to generate representative 3D capillary networks, enabling estimation of volumetric capillary density from histologically quantified vascular measurements. CD31-stained histological sections obtained from a longitudinal porcine lumpectomy study were analyzed to quantify the percentage of CD31-positive area (%CD31+) and capillary morphology within healthy tissue and healing surgical cavities. Histologically quantified morphology distributions and literature-informed vascular branching characteristics were incorporated into a capillary network generation framework to construct representative 3D vascular networks. Capillary branches were iteratively generated within representative tissue volumes until virtual histological sections reproduced experimental %CD31+ measurements, enabling estimation of volumetric capillary density. Generated capillary networks demonstrated good agreement with experimentally characterized 3D vascular architecture, while simulated histological sections accurately reproduced experimentally quantified capillary counts and vascularization measurements. Application of the framework to the porcine lumpectomy dataset captured temporal changes in vascular remodeling throughout healing, revealing progressive increases in volumetric capillary density and vascular maturation. Collectively, this framework provides an experimentally informed methodology for relating histological vascular measurements to volumetric capillary density estimates, supporting future computational studies of angiogenesis and tissue repair.

Reaction diffusion (RD) systems play a fundamental role in numerous biochemical and biophysical processes. Here, we present a novel analytical framework for solving RD equations by applying the Wentzel Kramers Brillouin Jeffreys (WKBJ) formalism to Ca nanodomains generated by individual membrane channels, a widely used paradigm for intracellular Ca signaling. Previous models have primarily focused on stationary Ca nanodomains while neglecting diffusion and saturation of intracellular Ca buffers and sensors. In contrast, we derive analytical solutions without these simplifying assumptions. Our analysis demonstrates that sustained Ca influx generates continuously expanding distributions of free Ca, whereas Ca bound buffers and sensors propagate as traveling waves. These predictions are supported experimentally by measurements of one-dimensional fluorescence profiles produced by single-channel activity and two-dimensional profiles generated by whole cell Ca currents. The analytical framework developed here readily extends Michaelis Menten type kinetics to reaction diffusion systems and may therefore be broadly applicable to biochemical and biophysical processes in which diffusion cannot be neglected.

golgi is an open-source platform that takes a peripheral nerve from image to stimulated fiber population through a single graphical interface, with an equivalent scriptable Python API and command-line interface for batch and high-performance use. It integrates promptable image segmentation, automated multi-region tetrahedral meshing, anisotropic finite-element solution of the extracellular field with an explicit perineurium contact impedance, generation of realistic fiber populations and their three-dimensional trajectories, and biophysical activation thresholds through interchangeable backends-- NEURON (via PyFibers) and a GPU-accelerated surrogate (AxonML). Every study exports as an integrity-hashed bundle whose image-to-recruitment provenance is verifiable byte-for-byte. golgi lowers the barrier to in-silico peripheral nerve stimulation modeling for experimentalists and clinicians, using a fully open finite-element stack with no commercial dependencies.

Cetaceans reduce the net cost of sustained swimming through intermittent locomotion, alternating active fluking with unpowered gliding. The energy balance of this strategy is central to understanding survival rates, population sustainability, and the effects of anthropogenic and environmental pressures. While active-phase energetics have been characterized extensively, the glide phase remains largely unexplored. Here we derive the optimal glide duration (Topt) and the maximum glide duration beyond which energy savings vanish (Tzero) for three odontocetes spanning a 20-fold range in body mass, using high-fidelity CAD models and wall-modeled large eddy simulations. We show analytically that speed retention at Topt and mass-specific peak energy savings are both fully determined by the active-to-passive drag ratio, propulsive efficiency, and swimming speed, independently of body morphometry and drag coefficient, and are therefore invariant across species at any given speed. These passive-phase optima extend the known size-independent active-phase invariants to the glide phase, towards a scale-independent energetic framework for burst-and-glide locomotion in small cetaceans.

Cells adjust their internal circuits in response to changes in their environment. Hence, exposing cells to changing conditions provides a way to probe the intrinsic dynamics of cellular internal circuits. Metabolic networks are examples of such circuits since metabolic fluxes dynamically adjust when environmental conditions are transiently altered. Most existing theoretical frameworks focus on cellular metabolic steady states and do not consider the dynamics of changes in metabolic fluxes. In this work, we applied transfer function analysis from control theory to analyze the changes of NADH oxidative fluxes in the mitochondria and cytoplasm in mouse oocytes in response to dynamical perturbations of oxygen depletion and recovery. We observed an overshoot of NADH oxidative flux in the cytoplasm upon oxygen recovery which is absent in the mitochondrial NADH oxidative flux. Metabolic perturbation experiments and transfer function analysis indicate that this cytoplasmic NADH overshoot results from the coupling of the mitochondrial and cytoplasmic NADH cycles. The degree of overshoot is determined by competing timescales associated with the exchange rates of lactate and pyruvate with the media and their interconversion rates catalyzed by lactate dehydrogenase. Applying control theory to the data enables the inference of the exchange and conversion rates of pyruvate and lactate, allowing predictions of the contribution of lactate to mitochondrial respiration. Our work indicates that the oocytes maintain a homeostatic respiration rate across nutrient conditions by modulating the contribution of lactate to mitochondrial respiration.

Purpose: RF-induced heating remains a major barrier to MRI access for patients with epicardial cardiac implantable electronic devices (CIEDs). Although ISO/TS 10974 Tier-3 transfer function (TF) methods are established for unbranched leads, no analogous framework exists for bifurcated leads, in which branch asymmetry and inter-branch coupling may substantially alter heating. We developed and validated a cumulative transfer function (cTF) framework to address this gap. Methods: Following ISO/TS 10974 Tier-3 formalism, we measured, calibrated, and validated cTFs for a commercial 35 cm bipolar epicardial lead at 1.5 T. The framework explicitly accounts for branch-specific response and cross-branch coupling. Validation was performed with 24 canonical lead configurations in a homogeneous phantom and, without recalibration, in a heterogeneous anthropomorphic pediatric phantom with clinically derived trajectories. A single-branch TF approximation served as a comparator. The validated cTF was applied to predict RF heating across adult and pediatric human models at multiple imaging landmarks. Results: Compared with the single-branch TF approximation, the cTF reduced prediction error by nearly 70% in the primary validation dataset. In secondary validation, the cTF maintained low error across clinically relevant trajectories and imaging landmarks. In human models, the framework revealed marked anatomy- and landmark-dependent variation in predicted heating for the tested 35 cm lead, with low predicted heating in pediatric models and substantially higher heating in selected adult chest and upper abdominal imaging scenarios. Conclusion: The cTF provides a validated framework for RF-heating assessment of bifurcated leads and substantially improves prediction accuracy over single-branch TF approximations that neglect branch coupling.

Objective: This study aims to develop and validate a quantitative, depth-resolved anisotropy imaging framework that extends ARFI-based focal degree-of-anisotropy (DoA) estimation into two-dimensional mapping by modeling the depth-dependent relationship between shear modulus ratio (SMR) and peak displacement ratio (PDR). Methods: We propose APRIL (Adaptive Polynomial Regression for anisotropy Imaging via ARFI-induced DispLacements), a framework for quantitative, depth-resolved DoA imaging that adaptively selects polynomial regression or shape-preserving spline interpolation based on excitation PSF asymmetry. Training data were generated using an LS-DYNA3D + Field II simulation pipeline in homogeneous transversely isotropic media (SMR 0.9-4.9). Testing included shifted SMRs under varied acoustic conditions and three heterogeneous inclusion configurations (anisotropic inclusion in isotropic background and vice versa). Experimental validation was performed in an in-vivo murine tumor model over the time, ex-vivo chicken breast, and tissue-mimicking gelatin phantoms, using a Verasonics system with an L11-5v transducer. Results: APRIL achieved depth-resolved SMR prediction errors below 9% over 10-30 mm, with highest accuracy in the focal region (MAE 2.3%, RMSE < 0.1) and stable performance across PSF transition zones. In heterogeneous phantoms, it reconstructed anisotropy maps with SSIM up to 86% and MPE below 7%, accurately delineating inclusion boundaries. Under acoustic parameter variations, mean absolute errors remained below 10%, demonstrating robustness to system and tissue heterogeneity. Conclusion: APRIL enables robust, two-dimensional anisotropy imaging beyond focal estimates. Significance: The method provides a physically grounded and generalizable framework for clinically viable anisotropy biomarkers in muscle, tendon, kidney, tumor and breast tissues.