A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

Smart Sensors and Virtual Physiology Human Approach as a Basis of Personalized Therapies in Diabetes Mellitus

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient’s information to the models

Virtual Patients and Sensitivity Analysis of the Guyton Model of Blood Pressure Regulation: Towards Individualized Models of Whole-Body Physiology

Mathematical models that integrate multi-scale physiological data can offer insight into physiological and pathophysiological function, and may eventually assist in individualized predictive medicine. We present a methodology for performing systematic analyses of multi-parameter interactions in such complex, multi-scale models. Human physiology models are often based on or inspired by Arthur Guyton's whole-body circulatory regulation model. Despite the significance of this model, it has not been the subject of a systematic and comprehensive sensitivity study. Therefore, we use this model as a case study for our methodology. Our analysis of the Guyton model reveals how the multitude of model parameters combine to affect the model dynamics, and how interesting combinations of parameters may be identified. It also includes a “virtual population” from which “virtual individuals” can be chosen, on the basis of exhibiting conditions similar to those of a real-world patient. This lays the groundwork for using the Guyton model for in silico exploration of pathophysiological states and treatment strategies. The results presented here illustrate several potential uses for the entire dataset of sensitivity results and the “virtual individuals” that we have generated, which are included in the supplementary material. More generally, the presented methodology is applicable to modern, more complex multi-scale physiological models

SAPHIR - a multi-scale, multi-resolution modeling environment targeting blood pressure regulation and fluid homeostasis.

International audienceWe present progress on a comprehensive, modular, interactive modeling environment centered on overall regulation of blood pressure and body fluid homeostasis. We call the project SAPHIR, for "a Systems Approach for PHysiological Integration of Renal, cardiac, and respiratory functions". The project uses state-of-the-art multi-scale simulation methods. The basic core model will give succinct input-output (reduced-dimension) descriptions of all relevant organ systems and regulatory processes, and it will be modular, multi-resolution, and extensible, in the sense that detailed submodules of any process(es) can be "plugged-in" to the basic model in order to explore, eg. system-level implications of local perturbations. The goal is to keep the basic core model compact enough to insure fast execution time (in view of eventual use in the clinic) and yet to allow elaborate detailed modules of target tissues or organs in order to focus on the problem area while maintaining the system-level regulatory compensations

HumMod: A Modeling Environment for the Simulation of Integrative Human Physiology

Mathematical models and simulations are important tools in discovering key causal relationships governing physiological processes. Simulations guide and improve outcomes of medical interventions involving complex physiology. We developed HumMod, a Windows-based model of integrative human physiology. HumMod consists of 5000 variables describing cardiovascular, respiratory, renal, neural, endocrine, skeletal muscle, and metabolic physiology. The model is constructed from empirical data obtained from peer-reviewed physiological literature. All model details, including variables, parameters, and quantitative relationships, are described in Extensible Markup Language (XML) files. The executable (HumMod.exe) parses the XML and displays the results of the physiological simulations. The XML description of physiology in HumMod's modeling environment allows investigators to add detailed descriptions of human physiology to test new concepts. Additional or revised XML content is parsed and incorporated into the model. The model accurately predicts both qualitative and quantitative changes in clinical and experimental responses. The model is useful in understanding proposed physiological mechanisms and physiological interactions that are not evident, allowing one to observe higher level emergent properties of the complex physiological systems. HumMod has many uses, for instance, analysis of renal control of blood pressure, central role of the liver in creating and maintaining insulin resistance, and mechanisms causing orthostatic hypotension in astronauts. Users simulate different physiological and pathophysiological situations by interactively altering numerical parameters and viewing time-dependent responses. HumMod provides a modeling environment to understand the complex interactions of integrative physiology. HumMod can be downloaded at http://hummod.or

Requirements for the formal representation of pathophysiology mechanisms by clinicians

Knowledge of multiscale mechanisms in pathophysiology is the bedrock of clinical practice. If quantitative methods, predicting patient-specific behaviour of these pathophysiology mechanisms, are to be brought to bear on clinical decision-making, the Human Physiome community and Clinical community must share a common computational blueprint for pathophysiology mechanisms. A number of obstacles stand in the way of this sharing—not least the technical and operational challenges that must be overcome to ensure that (i) the explicit biological meanings of the Physiome's quantitative methods to represent mechanisms are open to articulation, verification and study by clinicians, and that (ii) clinicians are given the tools and training to explicitly express disease manifestations in direct contribution to modelling. To this end, the Physiome and Clinical communities must co-develop a common computational toolkit, based on this blueprint, to bridge the representation of knowledge of pathophysiology mechanisms (a) that is implicitly depicted in electronic health records and the literature, with (b) that found in mathematical models explicitly describing mechanisms. In particular, this paper makes use of a step-wise description of a specific disease mechanism as a means to elicit the requirements of representing pathophysiological meaning explicitly. The computational blueprint developed from these requirements addresses the Clinical community goals to (i) organize and manage healthcare resources in terms of relevant disease-related knowledge of mechanisms and (ii) train the next generation of physicians in the application of quantitative methods relevant to their research and practice

Object-oriented modeling and simulation of the closed loop cardiovascular system by using SIMSCAPE

The modeling of physiological systems via mathematical equations reflects the calculation procedure more than the structure of the real system modeled, with the simulation environment SIMULINK™ being one of the best suited to this strategy. Nevertheless, object-oriented modeling is spreading in current simulation environments through the use of the individual components of the model and its interconnections to define the underlying dynamic equations. In this paper we describe the use of the SIMSCAPE™ simulation environment in the object-oriented modeling of the closed loop cardiovascular system. The described approach represents a valuable tool in the teaching of physiology for graduate medical students

Toward Integration of Biological and Physiological Functions at Multiple Levels

An aim of systems physiology today can be stated as to establish logical and quantitative bridges between phenomenological attributes of physiological entities such as cells and organs and physical attributes of biological entities, i.e., biological molecules, allowing us to describe and better understand physiological functions in terms of underlying biological functions. This article illustrates possible schema that can be used for promoting systems physiology by integrating quantitative knowledge of biological and physiological functions at multiple levels of time and space with the use of information technology infrastructure. Emphasis will be made for systematic, modular, hierarchical, and standardized descriptions of mathematical models of the functions and advantages for the use of them