Accelerated Patient-Specific Calibration via Differentiable Hemodynamics Simulations
Diego Renner, Georgios Kissas
TL;DR
The paper tackles the challenge of patient-specific calibration in cardiovascular diagnostics by introducing a fast, differentiable 1D reduced-order solver for pulse-wave propagation. Implemented in JAX as jaxFlowSim, it combines a reduced-order Navier–Stokes model with a MUSCL finite-volume scheme and differentiable boundaries (including Windkessel outflow) to enable gradient-based parameter inference and sensitivity analysis while preserving interpretability. The authors validate the approach against openBF with subpercent pressure errors, demonstrate linear scalability with network size, and show both deterministic and probabilistic inference can be performed efficiently through automatic differentiation and gradient-based optimization or Bayesian methods. This differentiable solver has the potential to enable solver-in-the-loop calibration for personalized medical decision support, offering a practical path toward faster, data-informed cardiovascular diagnostics on realistic vascular networks.
Abstract
One of the goals of personalized medicine is to tailor diagnostics to individual patients. Diagnostics are performed in practice by measuring quantities, called biomarkers, that indicate the existence and progress of a disease. In common cardiovascular diseases, such as hypertension, biomarkers that are closely related to the clinical representation of a patient can be predicted using computational models. Personalizing computational models translates to considering patient-specific flow conditions, for example, the compliance of blood vessels that cannot be a priori known and quantities such as the patient geometry that can be measured using imaging. Therefore, a patient is identified by a set of measurable and nonmeasurable parameters needed to well-define a computational model; else, the computational model is not personalized, meaning it is prone to large prediction errors. Therefore, to personalize a computational model, sufficient information needs to be extracted from the data. The current methods by which this is done are either inefficient, due to relying on slow-converging optimization methods, or hard to interpret, due to using `black box` deep-learning algorithms. We propose a personalized diagnostic procedure based on a differentiable 0D-1D Navier-Stokes reduced order model solver and fast parameter inference methods that take advantage of gradients through the solver. By providing a faster method for performing parameter inference and sensitivity analysis through differentiability while maintaining the interpretability of well-understood mathematical models and numerical methods, the best of both worlds is combined. The performance of the proposed solver is validated against a well-established process on different geometries, and different parameter inference processes are successfully performed.