Juliacon 2024

1 - Background and the Problem

Cardiovascular diseases stand as the foremost cause of death globally. Surgeries and treatments aimed at cardiovascular issues carry inherent risks and may not achieve desired clinical outcomes, influenced by patients' specific physical conditions. In the operating theatre, interventional cardiologists have access to increasingly sophisticated measurements for assessing patient vasculature. However, certain physiological quantities remain either indirectly measurable or are prone to measurement noises. Mathematical and computational models play a crucial role in supporting clinical diagnosis and decision-making through in silico Decision Support Systems. Yet, the integration of these in silico models into clinical practice is hindered by the challenge of personalisation - determining the required values for individual patients' model input parameters, some of which are bio-markers, based on measured clinical data. This process involves solving an inverse problem, marked by its complexity, uncertainty, and computational intensity.

2 - Methods

Recent advancements in computational data assimilation have led to the development of various cardiovascular models, utilising hemodynamics and other low-order models to quantitatively establish the interdependence of a patient’s systemic and pulmonary vasculature properties. We employ Zero-dimensional (0D) models, mapping physiological variables, such as pressure, volume, and flow, to electrical counterparts like voltage, charge, and current.

Each physiological compartment has a distinct representation with mechanical parameters portraying the "true" physiology of a patient. Structural identifiability analysis is employed to ascertain the estimability of parameters and necessary measurements for personalisation. Sensitivity analysis uncovers the most influential parameters affecting model outputs, while parameter orthogonality analysis examines the independent effects of individual parameters. Through a combination of sensitivity and orthogonality investigations, we identify a set of unique input parameters optimisable to a patient’s data using powerful techniques like the Unscented Kalman Filter (UKF). This comprehensive approach, as illustrated in the attached figure, enhances the precision of personalising complex cardiovascular models, advancing their clinical utility and effectiveness.

3 - The Julia Aspect

While the research conducted is incredibly applied, there is a computational workflow enabling the intersection between clinical practices and in-silico investigations. In the talk, we examine the different stages of the proposed personalisation workflow and highlight how Julia aids us at each stage. From utilising ModellingToolKit.jl to create cardiovascular models to using GlobalSensitivityAnalysis.jl for studying model uncertainty, along with other packages enabling the generation of personalised cardiovascular models.

We will spotlight some of the main challenges encountered in this process and how we've overcome them, such as performing parallel simulations on varying data types and accessing observed variables from MTK. This talk outlines a workflow for those interested in model analysis and emphasises how Julia can be utilised to produce clinically impactful work.

4 - Achievements and Impact

This study introduces a novel workflow efficiently identifying optimal bio-markers for cardiovascular personalisation, incorporating practical and structural identifiability, sensitivity analysis, orthogonality, and Kalman-based optimisation methods to determine the most informative and clinically usable model inputs. The outcome of our research is a more reliable and practically focused personalisation of complex cardiovascular models, empowering clinicians to provide tailored patient-specific treatments. This advancement has significant potential in enhancing cardiovascular diagnosis and ultimately improving patient outcomes. This talk aims to provide others with a workflow on utilising extensive model analysis packages to create a reliable interpretation of any model.