Cesar Pichardo-Almarza

On the formalization of multi-scale and multi-science processes for integrative biology

The aim of this work is to introduce the general concept of ‘Bond Graph’ (BG) techniques applied in the context of multi-physics and multi-scale processes. BG modelling has a natural place in these developments. BGs are inherently coherent as the relationships defined between the ‘elements’ of the graph are strictly defined by causality rules and power (energy) conservation. BGs clearly show how power flows between components of the systems they represent. The ‘effort’ and ‘flow’ variables enable bidirectional information flow in the BG model. When the power level of a system is low, BGs degenerate into signal flow graphs in which information is mainly one-dimensional and power is minimal, i.e. they find a natural limitation when dealing with populations of individuals or purely kinetic models, as the concept of energy conservation in these systems is no longer relevant. The aim of this work is twofold: on the one hand, we will introduce the general concept of BG techniques applied in the context of multi-science and multi-scale models and, on the other hand, we will highlight some of the most promising features in the BG methodology by comparing with examples developed using well-established modelling techniques/software that could suggest developments or refinements to the current state-of-the-art tools, by providing a consistent framework from a structural and energetic point of view.

Towards personalised management of atherosclerosis via computational models in vascular clinics: technology based on patient-specific simulation approach.

The development of a new technology based on patient-specific modelling for personalised healthcare in the case of atherosclerosis is presented. Atherosclerosis is the main cause of death in the world and it has become a burden on clinical services as it manifests itself in many diverse forms, such as coronary artery disease, cerebrovascular disease/stroke and peripheral arterial disease. It is also a multifactorial, chronic and systemic process that lasts for a lifetime, putting enormous financial and clinical pressure on national health systems. In this Letter, the postulate is that the development of new technologies for healthcare using computer simulations can, in the future, be developed as in-silico management and support systems. These new technologies will be based on predictive models (including the integration of observations, theories and predictions across a range of temporal and spatial scales, scientific disciplines, key risk factors and anatomical sub-systems) combined with digital patient data and visualisation tools. Although the problem is extremely complex, a simulation workflow and an exemplar application of this type of technology for clinical use is presented, which is currently being developed by a multidisciplinary team following the requirements and constraints of the Vascular Service Unit at the University College Hospital, London.

Development of a Patient-Specific Multi-Scale Model to Understand Atherosclerosis and Calcification Locations: Comparison with In vivo Data in an Aortic Dissection

Vascular calcification results in stiffening of the aorta and is associated with hypertension and atherosclerosis. Atherogenesis is a complex, multifactorial, and systemic process; the result of a number of factors, each operating simultaneously at several spatial and temporal scales. The ability to predict sites of atherogenesis would be of great use to clinicians in order to improve diagnostic and treatment planning. In this paper, we present a mathematical model as a tool to understand why atherosclerotic plaque and calcifications occur in specific locations. This model is then used to analyze vascular calcification and atherosclerotic areas in an aortic dissection patient using a mechanistic, multi-scale modeling approach, coupling patient-specific, fluid-structure interaction simulations with a model of endothelial mechanotransduction. A number of hemodynamic factors based on state-of-the-art literature are used as inputs to the endothelial permeability model, in order to investigate plaque and calcification distributions, which are compared with clinical imaging data. A significantly improved correlation between elevated hydraulic conductivity or volume flux and the presence of calcification and plaques was achieved by using a shear index comprising both mean and oscillatory shear components (HOLMES) and a non-Newtonian viscosity model as inputs, as compared to widely used hemodynamic indicators. The proposed approach shows promise as a predictive tool. The improvements obtained using the combined biomechanical/biochemical modeling approach highlight the benefits of mechanistic modeling as a powerful tool to understand complex phenomena and provides insight into the relative importance of key hemodynamic parameters.

Predicting Atherosclerotic Plaque Location in an Iliac Bifurcation Using a Hybrid CFD/Biomechanical Approach

Experimental evidence indicates that haemodynamic stimuli influence some properties of the arterial endothelium, such as cell geometry and permeability, leading to possible accumulation of blood-borne macromolecules and initiation of atherosclerosis. Patient-specific computational models are able to capture complex haemodynamic characteristics to explore and analyse the development of these diseases in silico. Patient-specific models are particularly beneficial in the case of aortic dissection (AD), a condition in which the aortic wall is split in two, creating a true and a false lumen. In this condition, the proportion of blood through the main vessel and the main aortic branches is substantially modified and malperfusion (lack of blood supply) of the downstream vessels is often observed. Furthermore, AD alters the haemodynamics downstream of the lesion, potentially leading to the formation of atherosclerotic plaques at the iliac bifurcation. In order to correctly approximate the haemodynamic changes and analyse the role they play in the development of atherosclerosis formations in AD patients, a combined multiscale methodology is required. In this study, both, blood flow through an iliac bifurcation of a patient suffering from type-B aortic dissection and endothelium behavior are analysed, in order to investigate atherosclerosis formation.

A multiscale modelling approach to understand atherosclerosis formation: A patient-specific case study in the aortic bifurcation

Atherogenesis, the formation of plaques in the wall of blood vessels, starts as a result of lipid accumulation (low-density lipoprotein cholesterol) in the vessel wall. Such accumulation is related to the site of endothelial mechanotransduction, the endothelial response to mechanical stimuli and haemodynamics, which determines biochemical processes regulating the vessel wall permeability. This interaction between biomechanical and biochemical phenomena is complex, spanning different biological scales and is patient-specific, requiring tools able to capture such mathematical and biological complexity in a unified framework. Mathematical models offer an elegant and efficient way of doing this, by taking into account multifactorial and multiscale processes and mechanisms, in order to capture the fundamentals of plaque formation in individual patients. In this study, a mathematical model to understand plaque and calcification locations is presented: this model provides a strong interpretability and physical meaning through a multiscale, complex index or metric (the penetration site of low-density lipoprotein cholesterol, expressed as volumetric flux). Computed tomography scans of the aortic bifurcation and iliac arteries are analysed and compared with the results of the multifactorial model. The results indicate that the model shows potential to predict the majority of the plaque locations, also not predicting regions where plaques are absent. The promising results from this case study provide a proof of concept that can be applied to a larger patient population.

Patient-Specific, Multi-Scale Modeling of Neointimal Hyperplasia in Vein Grafts

Neointimal hyperplasia is amongst the major causes of failure of bypass grafts. The disease progression varies from patient to patient due to a range of different factors. In this paper, a mathematical model will be used to understand neointimal hyperplasia in individual patients, combining information from biological experiments and patient-specific data to analyze some aspects of the disease, particularly with regard to mechanical stimuli due to shear stresses on the vessel wall. By combining a biochemical model of cell growth and a patient-specific computational fluid dynamics analysis of blood flow in the lumen, remodeling of the blood vessel is studied by means of a novel computational framework. The framework was used to analyze two vein graft bypasses from one patient: a femoro-popliteal and a femoro-distal bypass. The remodeling of the vessel wall and analysis of the flow for each case was then compared to clinical data and discussed as a potential tool for a better understanding of the disease. Simulation results from this first computational approach showed an overall agreement on the locations of hyperplasia in these patients and demonstrated the potential of using new integrative modeling tools to understand disease progression.

A Multiscale and Patient-Specific Computational Framework of Atherosclerosis Formation and Progression: A Case Study in the Aorta and Peripheral Arteries

Abstract Atherosclerosis is the main cause of mortality and morbidity in the western world. Atherosclerosis is a chronic disease defined by life-long processes, with multiple actors playing a role at different biological and time scales. Patient-specific in silico models and simulations can help to understand better the mechanisms of atherosclerosis formation, potentially improving patient management. A conceptual and computational multiscale framework for the modelling of atherosclerosis formation at its early stage was created from the integration of a fluid mechanics model and a biochemical model. The fluid mechanics model describes the interaction between arterial endothelium and blood flow using an artery-specific approach. The low density lipoprotein (LDL) oxidation and consequent immune reaction leading to chronic inflammatory process at the basis of plaque formation was described in the biochemical model. The integration of these modelling approaches led to the creation of a computational framework, an effective tool for the modelling of atherosclerosis plaque development. The model presented in this study was able to capture key features of atherogenesis such as the location of pro-atherogenic areas and to reproduce the formation of plaques detectable from in vivo observations. This framework is being currently tested at University College Hospital (UCH).

Understanding the Effect of Statins and Patient Adherence in Atherosclerosis via a Quantitative Systems Pharmacology Model Using a Novel, Hybrid, and Multi-Scale Approach

Background and Objective: Statins are one of the most prescribed drugs to treat atherosclerosis. They inhibit the hepatic HMG-CoA reductase, causing a reduction of circulating cholesterol and LDL levels. Statins have had undeniable success; however, the benefits of statin therapy crystallize only if patients adhere to the prescribed treatment, which is far away from reality since adherence decreases with time with around half of patients discontinue statin therapy within the first year. The objective of this work is to; firstly, demonstrate a formal in-silico methodology based on a hybrid, multiscale mathematical model used to study the effect of statin treatment on atherosclerosis under different patient scenarios, including cases where the influence of medication adherence is examined and secondly, to propose a flexible simulation framework that allows extensions or simplifications, allowing the possibility to design other complex simulation strategies, both interesting features for software development. Methods: Different mathematical modeling paradigms are used to present the relevant dynamic behavior observed in biological/physiological data and clinical trials. A combination of continuous and discrete event models are coupled to simulate the pharmacokinetics (PK) of statins, their pharmacodynamic (PD) effect on lipoproteins levels (e.g., LDL) and relevant inflammatory pathways whilst simultaneously studying the dynamic effect of flow-related variables on atherosclerosis progression. Results: Different scenarios were tested showing the impact of: (1) patient variability: a virtual population shows differences in plaque growth for different individuals could be as high as 100%; (2) statin effect on atherosclerosis: it is shown how a patient with a 1-year statin treatment will reduce his plaque growth by 2–3% in a 2-year period; (3) medical adherence: we show that a patient missing 10% of the total number of doses could increase the plaque growth by ~1% (after 2 years) compared to the same “regular” patient under a 1-year treatment with statins. Conclusions: The results in this paper describe the effect of pharmacological intervention combined with biological/physiological or behavioral factors in atherosclerosis progression and treatment in specific patients. It also provides an exemplar of basic research that can be practically developed into an application software.