A mathematical model for foreign body reactions in 2D

Models for Implant-Induced Capsular Contracture Post Breast Cancer Surgery

Capsular contracture is a painful deformation of scar-tissue that may form around an implant in post-breast cancer reconstruction or cosmetic surgery. Inflammation due to surgical trauma or contamination in the tissue around the implant could account for recruitment of immune cells, and transdifferentiation of resident fibroblasts into cells that deposit abnormally thick collagen. Here we examine this hypothesis using a mathematical model for interacting macrophages, fibroblasts, myofibroblasts, and collagen. Our model demonstrates that cellular response can, together with inflammatory cell recruitment, account for prognoses.

Interaction of Ceramic Implant Materials with Immune System

The immuno-compatibility of implant materials is a key issue for both initial and long-term implant integration. Ceramic implants have several advantages that make them highly promising for long-term medical solutions. These beneficial characteristics include such things as the material availability, possibility to manufacture various shapes and surface structures, osteo-inductivity and osteo-conductivity, low level of corrosion and general biocompatibility. The immuno-compatibility of an implant essentially depends on the interaction with local resident immune cells and, first of all, macrophages. However, in the case of ceramics, these interactions are insufficiently understood and require intensive experimental examinations. Our review summarizes the state of the art in variants of ceramic implants: mechanical properties, different chemical modifications of the basic material, surface structures and modifications, implant shapes and porosity. We collected the available information about the interaction of ceramics with the immune system and highlighted the studies that reported ceramic-specific local or systemic effects on the immune system. We disclosed the gaps in knowledge and outlined the perspectives for the identification to ceramic-specific interactions with the immune system using advanced quantitative technologies. We discussed the approaches for ceramic implant modification and pointed out the need for data integration using mathematic modelling of the multiple ceramic implant characteristics and their contribution for long-term implant bio- and immuno-compatibility.

Mathematical modelling of the restenosis process after stent implantation

The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion-reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors.

Computational modeling of phagocyte transmigration for foreign body responses to subcutaneous biomaterial implants in mice

BACKGROUND

Computational modeling and simulation play an important role in analyzing the behavior of complex biological systems in response to the implantation of biomedical devices. Quantitative computational modeling discloses the nature of foreign body responses. Such understanding will shed insight on the cause of foreign body responses, which will lead to improved biomaterial design and will reduce foreign body reactions. One of the major obstacles in computational modeling is to build a mathematical model that represents the biological system and to quantitatively define the model parameters.

RESULTS

In this paper, we considered quantitative inter connections and logical relationships among diverse proteins and cells, which have been reported in biological experiments and literature. Based on the established biological discovery, we have built a mathematical model while unveiling the key components that contribute to biomaterial-mediated inflammatory responses. For the parameter estimation of the mathematical model, we proposed a global optimization algorithm, called Discrete Selection Levenberg-Marquardt (DSLM). This is an extension of Levenberg-Marquardt (LM) algorithm which is a gradient-based local optimization algorithm. The proposed DSLM suggests a new approach for the selection of optimal parameters in the discrete space with fast computational convergence.

CONCLUSIONS

The computational modeling not only provides critical clues to recognize current knowledge of fibrosis development but also enables the prediction of yet-to-be observed biological phenomena.

A computational model of fibroblast and macrophage spatial/temporal dynamics in foreign body reactions

The implantation of medical devices often triggers several immune responses, one kind of which is categorized as foreign body reactions. It is well established that macrophages and many other cells participate in the complex processes of foreign body reactions, and cause severe inflammations and fibrotic capsule formation in surrounding tissues. However, the detailed mechanisms of macrophage responses, recruitment and activation, in foreign body reactions are not totally understood. In the meantime, mathematical models have been proposed to systematically decipher the behavior of this complex system of multiple cells, proteins and biochemical processes in wound healing responses. Based on these early works, this study introduces a mathematical model in two spatial dimensions to investigate the transient behavior of macrophages, fibroblasts and their interactions during the formation of fibrotic tissue. We find that the simulation results are consistent with the experimental observations. These findings support that the model can reveal quantitative insights for studying foreign body reaction processes.

A Predictive Tool for Foreign Body Fibrotic Reactions Using 2-Dimensional Computational Model

It is well established that implanted medical devices often trigger immunological and inflammatory reactions. Such foreign body-mediated tissue responses may result in fibrotic tissue formation surrounding the implants. Despite of intensive research in the area of wound healing, few methods are currently available to systematically predict the quantitative behavior of the complex system of multiple cells, proteins and enzymes during foreign body-associated fibrotic reactions. This study introduces a kinetics-based predictive tool to analyze outcomes of reactions of various cells/proteins and biochemical processes and to understand transient behavior during the entire implant healing period up to several months in time. A computational model in two spatial dimensions is constructed to investigate the time dynamics as well as spatial variation of fibrotic reaction kinetics. Our results have shown that this model can be used to predict many features in a systematic way and also complement the traditional immunological methodology by experiments or empirical data predictions.