Biological Flow Simulations Using Graphs

­Summary: A method for automate high-performance flow characteristics simulations using graph structures. This allows to quantify complex behaviour in large-scale biological networks.
A method to compute flow characteristics from 3D images of biological networks, such as the patient vasculature or airways. The geometrical features are automatically projected on a graph structure. Flow-dynamic equations are then solved using an electrical-analogue method for different configurations. This allows to account for physio-pathological behaviours of large and complex looped structures with high performance. The proposed approach can evaluate downstream effects of perturbations on any biological network. This can be of interest for surgical planning, for quantifying the overall vulnerability of a patient, and for statistical analyses in cohorts with similar biological features.
Modifications of flow dynamics characteristics of large biological structures, specifically blood flow and pressure in complex vascular networks, are commonly studied for understanding the onset of life-threatening diseases, such as atherosclerosis, stenosis, aneurysm, stroke, arterio-venous malformations, or neoplastic lesions. However, quantitative and continuous monitoring, alongside long-term predictions of such features represent an unmet clinical challenge.
For these reasons, computer-based numerical methods have been developed. However, conventional methods require accurate three-dimensional modelling, computationally intensive simulations, demanding hardware requirements and prohibitive computational time to accurately simulate for several physio-pathological scenarios on large-scale biological network.
The proposed technology linearly approximates pressure distributions and flow ratio characteristics in any branch of a patient-specific biological network, including anastomoses and looped structures, such as the complete circle of Willis in the brain, neoplastic blood vessels or pathological arterio-venous connections.
Simultaneous models with perturbed configurations of the biological network are simulated to extract corresponding biomarkers, e.g.  the resilience or susceptibility of a patient to a disease, with high performance for predictive clinical outcomes. Personalised screening programmes can stratify and compare the computed biomarkers against a population or a cohort of patients.
The implemented algorithm is automatic, stable, and computationally efficient, with nearly real-time performance on any imaging platform.
The technology is protected by US, European and Israeli patent applications and is available for licensing. Substantial funding has been secured for commercial translation. The code has been implemented following standard development practices and for being compliant with QMS criteria. Suitable commercial partners are sought for further implementation in a regulated software package and for commercialisation.
The Science
A 3D biological network, such as a vascular network, is extracted from a medical image (MR, CT scan, and the like) and is processed to automatically obtain a corresponding graph data structure. In particular, the latter can be a complete network without hierarchical constraints, to accurately model loops, anastomoses, and other complex configurations on large-scale.
Flow-dynamic equations are solved on the same graph data to obtain a biological characteristic, e.g. flow ratio and pressure distribution for each branch of the biological network. Specifically, the flow dynamic equations employ an electrical-analogue method, wherein each electrical equivalent component depends on geometric features and mechanical properties of the corresponding branch.
Simulations are automatically iterated over thousands of perturbed configurations of the graph data structure, modelling the effects of plausible variations, to ultimately calculate a patient-specific biomarker.

a) The figure shows the steps required for converting a 3D angiography to a vascular graph as analog-circuit.
b) The figure shows simulations on both the original and selectively perturbed graphs from Fig. a). Flow and pressure values are calculated for each branch.
c) Simulations are shown for 3 different anatomical phenotypes undergoing the same perturbation: flow and pressure distributions and hypertension histogram are calculated at increasing level of impairment, with resulting decreasing vascular network resilience
Patent Status
WO 2021/064372 A1 (PCT publication, now entered in EP, US and IL national phase)
Further Information
Moriconi, S. at al. (2019) "Towards Quantifying Neurovascular Resilience, in: Lecture Notes in Computer Science, vol 11794. pp. 149–157. doi:10.1007/978-3-030-33327-0_18
Patent Information:
For Information, Contact:
Lorenza Grechy
King's College London
Jorge Cardoso
Stefano Moriconi
Sebastien Ourselin
Parashkev Nachev