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.

翻译：个性化医疗的目标之一是为每位患者量身定制诊断方案。在实践中，诊断通过测量称为生物标志物的指标来实施，这些指标能够反映疾病的存在与发展进程。在高血压等常见心血管疾病中，与患者临床表现密切相关的生物标志物可通过计算模型进行预测。计算模型的个性化意味着需考虑患者特定的血流条件，例如无法先验获知的血管顺应性，以及可通过影像学测量的患者几何形态等参数。因此，患者需要通过一组可测量与不可测量的参数来准确定义计算模型；否则，计算模型将缺乏个性化特征，意味着其预测结果可能产生较大误差。为实现计算模型的个性化，需要从数据中提取充分的信息。当前实现该目标的方法存在两大局限：或因依赖收敛缓慢的优化方法而效率低下，或因采用"黑箱"深度学习算法而难以解释。本文提出一种基于可微分0D-1D纳维-斯托克斯降阶模型求解器的个性化诊断流程，结合利用求解器梯度信息的快速参数推断方法。该方法通过可微分特性实现了参数推断与敏感性分析的加速，同时保持了成熟数学模型与数值方法的高可解释性，从而融合了两种范式的优势。通过在不同几何构型上与成熟流程的对比验证了所提求解器的性能，并成功实现了多种参数推断流程。