A mathematical model of Bacteroides thetaiotaomicron, Methanobrevibacter smithii, and Eubacterium rectale interactions in the human gut.

The human gut microbiota is a complex ecosystem that affects a range of human physiology. In order to explore the dynamics of the human gut microbiota, we used a system of ordinary differential equations to model mathematically the biomass of three microorganism populations: Bacteroides thetaiotaomicron, Eubacterium rectale, and Methanobrevibacter smithii. Additionally, we modeled the concentrations of relevant nutrients necessary to sustain these populations over time.

Considerations for Modeling Proteus mirabilis Swarming.

In this chapter we provide some initial guidance to experimentalists on how they might go about creating mathematical representations of their systems under study. Because the interests and goals of different researchers can differ, we try to provide broad instruction on the creation and use of mathematical models. We provide a brief overview of some modeling that has been done with Proteus mirabilis colonies, and discuss the goals of modeling.

Modeling the Effects of Multiple Myeloma on Kidney Function.

Multiple myeloma (MM), a plasma cell cancer, is associated with many health challenges, including damage to the kidney by tubulointerstitial fibrosis. We develop a mathematical model which captures the qualitative behavior of the cell and protein populations involved. Specifically, we model the interaction between cells in the proximal tubule of the kidney, free light chains, renal fibroblasts, and myeloma cells.

Modeling the effect of blunt impact on mitochondrial function in cartilage: implications for development of osteoarthritis.

Objective: Osteoarthritis (OA) is a disease characterized by degeneration of joint cartilage. It is associated with pain and disability and is the result of either age and activity related joint wear or an injury. Non-invasive treatment options are scarce and prevention and early intervention methods are practically non-existent.

Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model.

Post-traumatic osteoarthritis affects almost 20% of the adult US population. An injurious impact applies a significant amount of physical stress on articular cartilage and can initiate a cascade of biochemical reactions that can lead to the development of osteoarthritis. In our effort to understand the underlying biochemical mechanisms of this debilitating disease, we have constructed a multiscale mathematical model of the process with three components: cellular, chemical, and mechanical.

Mathematics as a conduit for translational research in post-traumatic osteoarthritis.

Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients.

Complementary models reveal cellular responses to contact stresses that contribute to post-traumatic osteoarthritis.

Two categories of joint overloading cause post-traumatic osteoarthritis (PTOA): single acute traumatic loads/impactions and repetitive overloading due to incongruity/instability. We developed and refined three classes of complementary models to define relationships between joint overloading and progressive cartilage loss across the spectrum of acute injuries and chronic joint abnormalities: explant and whole joint models that allow probing of cellular responses to mechanical injury and contact stresses, animal models that enable study of PTOA pathways in living joints and pre-clinical testing of treatments, and patient-specific computational models that define the overloading that causes OA in humans. We coordinated methodologies across models so that results from each informed the others, maximizing the benefit of this complementary approach.

Corrigendum: "A Validated Model of the Pro- and Anti-Inflammatory Cytokine Balancing Act in Articular Cartilage Lesion Formation".

[This corrects the article on p. 25 in vol. 3, PMID: 25806365.

A validated model of the pro- and anti-inflammatory cytokine balancing act in articular cartilage lesion formation.

Traumatic injuries of articular cartilage result in the formation of a cartilage lesion and contribute to cartilage degeneration and the risk of osteoarthritis (OA). A better understanding of the framework for the formation of a cartilage lesion formation would be helpful in therapy development. Toward this end, we present an age and space-structured model of articular cartilage lesion formation after a single blunt impact.

Modeling and simulation of the effects of cyclic loading on articular cartilage lesion formation.

We present a model of articular cartilage lesion formation to simulate the effects of cyclic loading. This model extends and modifies the reaction-diffusion-delay model by Graham et al., 2012 for the spread of a lesion formed though a single traumatic event.

The role of osteocytes in targeted bone remodeling: a mathematical model.

Until recently many studies of bone remodeling at the cellular level have focused on the behavior of mature osteoblasts and osteoclasts, and their respective precursor cells, with the role of osteocytes and bone lining cells left largely unexplored. This is particularly true with respect to the mathematical modeling of bone remodeling. However, there is increasing evidence that osteocytes play important roles in the cycle of targeted bone remodeling, in serving as a significant source of RANKL to support osteoclastogenesis, and in secreting the bone formation inhibitor sclerostin.

Towards a new spatial representation of bone remodeling.

Irregular bone remodeling is associated with a number of bone diseases such as osteoporosis and multiple myeloma. Computational and mathematical modeling can aid in therapy and treatment as well as understanding fundamental biology. Different approaches to modeling give insight into different aspects of a phenomena so it is useful to have an arsenal of various computational and mathematical models.

Reaction-diffusion-delay model for EPO/TNF-α interaction in articular cartilage lesion abatement.

Background: Injuries to articular cartilage result in the development of lesions that form on the surface of the cartilage. Such lesions are associated with articular cartilage degeneration and osteoarthritis. The typical injury response often causes collateral damage, primarily an effect of inflammation, which results in the spread of lesions beyond the region where the initial injury occurs.

Microbial dormancy in batch cultures as a function of substrate-dependent mortality.

We present models and computational studies of dormancy in batch cultures to try to understand the relationship between reculturing time and death penalty for low substrate and the relative advantage of fast versus slow reawakening on the part of the bacteria. We find that the advantage goes to the faster waker for shorter reculturing times and lower mortality under low substrate, and moves to the slower waker as reculturing times and death penalty increase. The advantage returns again to the fast waker for very high death penalties.

A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease.

Background: Multiple myeloma is a hematologic malignancy associated with the development of a destructive osteolytic bone disease.

Results: Mathematical models are developed for normal bone remodeling and for the dysregulated bone remodeling that occurs in myeloma bone disease. The models examine the critical signaling between osteoclasts (bone resorption) and osteoblasts (bone formation).

A spatial model of tumor-host interaction: application of chemotherapy.

In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. When no treatment is applied the model reproduces the typical dynamics of early tumor growth.

A structured-population model of Proteus mirabilis swarm-colony development.

In this paper we present continuous age- and space-structured models and numerical computations of Proteus mirabilis swarm-colony development. We base the mathematical representation of the cell-cycle dynamics of Proteus mirabilis on those developed by Esipov and Shapiro, which are the best understood aspects of the system, and we make minimum assumptions about less-understood mechanisms, such as precise forms of the spatial diffusion. The models in this paper have explicit age-structure and, when solved numerically, display both the temporal and spatial regularity seen in experiments, whereas the Esipov and Shapiro model, when solved accurately, shows only the temporal regularity.