A mathematical model for describing the metastasis of cancer in bone tissue

Tumor growth for remodeling process: A 2D approach

This paper aims to present a comprehensive framework for coupling tumor-bone remodeling processes in a 2-dimensional geometry. This is achieved by introducing a bio-inspired damage that represents the growing tumor, which subsequently affects the main populations involved in the remodeling process, namely, osteoclasts, osteoblasts, and bone tissue. The model is constructed using a set of differential equations based on the Komarova's and Ayati's models, modified to incorporate the bio-inspired damage that may result in tumor mass formation. Three distinct models were developed. The first two models are based on the Komarova's governing equations, with one demonstrating an osteolytic behavior and the second one an osteoblastic model. The third model is a variation of Ayati's model, where the bio-inspired damage is induced through the paracrine and autocrine parameters, exhibiting an osteolytic behavior. The obtained results are consistent with existing literature, leading us to believe that our in-silico experiments will serve as a cornerstone for paving the way towards targeted interventions and personalized treatment strategies, ultimately improving the quality of life for those affected by these conditions.

Antigen receptor therapy in bone metastasis via optimal control for different human life stages

In this work we propose a bone metastasis model using power law growth functions in order to describe the biochemical interactions between bone cells and cancer cells. Experimental studies indicate that bone remodeling cycles are different for human life stages: childhood, young adulthood, and adulthood. In order to include such differences in our study, we estimate the model parameter values for each human life stage via bifurcation analysis. Results reveal an intrinsic relationship between the active period of remodeling cycles and the proliferation of cancer cells. Subsequently, using optimal control theory we analyze a possible antigen receptor therapy as a new treatment for bone metastasis. Theoretical results such as existence of optimal solutions are proved. Numerical simulations for late stages of bone metastasis are presented and a discussion of our results is carried out.

Toward a Mathematical Modeling of Diseases' Impact on Bone Remodeling: Technical Review

A wide variety of bone diseases have hitherto been discovered, such as osteoporosis, Paget's disease, osteopetrosis, and metastatic bone disease, which are not well defined in terms of changes in biochemical and mechanobiological regulatory factors. Some of these diseases are secondary to other pathologies, including cancer, or to some clinical treatments. To better understand bone behavior and prevent its deterioration, bone biomechanics have been the subject of mathematical modeling that exponentially increased over the last years. These models are becoming increasingly complex. The current paper provides a timely and critical analysis of previously developed bone remodeling mathematical models, particularly those addressing bone diseases. Besides, mechanistic pharmacokinetic/pharmacodynamic (PK/PD) models, which englobe bone disease and its treatment's effect on bone health. Therefore, the review starts by presenting bone remodeling cycle and mathematical models describing this process, followed by introducing some bone diseases and discussing models of pathological mechanisms affecting bone, and concludes with exhibiting the available bone treatment procedures considered in the PK/PD models.

A computational framework and sensitivity analysis for the hormonal treatment of bone

BACKGROUND

Osteoporosis is a bone disease identified by disordering of bone formation and resorption cells. It increases the risk of bone fragility and fracture. Autocrine and paracrine signalling of osteoclasts and osteoblasts plays an important role in the regulation of bone remodelling. Calcitonin is an approved pharmacologic agent for the treatment of osteoporosis.

METHODS

A novel mathematical model comprising the interaction among osteoclasts and osteoblasts cells with intermittent administration of calcitonin has been presented to study the dynamics of osteoporotic bone. The stability of model and sensitivity of parameters are also discussed.

FINDINGS

The population of osteoclastic and osteoblastic cells has been predicted via numerical simulation. The results of Monte Carlo sensitivity analysis are shown via tornado diagram.

INTERPRETATION

It is concluded that intermittent administration of calcitonin is an effective therapy for the treatment of osteoporosis.

Mathematical modelling of the role of Endo180 network in the development of metastatic bone disease in prostate cancer

Metastatic bone disease (MBD) is a common complication of advanced cancer and recent research suggests that Endo180 expression is dysregulated through the TGFβ-TGFβR-SMAD2/3 signalling pathway during the invasion of tumour cells in the development of MBD. We here provide a model for the dysregulation of the Endo180 network to demonstrate its vital contribution to bone destruction as well as tumour cell growth. The model consisted of a set of ordinary differential equations and reconstructed variations in the bone cells, resultant bone volume, and biochemical factors involved in the TGFβ-TGFβR-SMAD2/3 signalling pathway over time. The model also investigated the underlying mechanism in which the change of TGFβ affects the TGFβ-TGFβR-SMAD2/3 signalling pathway and the resultant Endo180 expression in osteoblastic and tumour cells. The model links the appearance of tumour cells with the inhibition of TGFβ binding to its receptors on osteoblastic cells, to affect TGFβ-TGFβR-SMAD2/3 signalling and Endo180 expression. Temporal variation in bone cells, bone volume, and the biochemical factors involved in the TGFβ-TGFβR-SMAD2/3 pathway as demonstrated in the model simulations agree with published experimental data. The model can be refined based on further discoveries but allows the influence of Endo180 network dysregulation on bone remodelling in MBD to be established. This model could aid in the development of Endo180 targeted therapies for MBD in the future.

Forecasting the critical role of intermittent therapies for the control of bone resorption

BACKGROUND

Osteoporosis is a chronic metabolic disease characterized by an imbalance of bone resorption and formation, leading to bone fragility and increased susceptibility to fracture. Parathyroid hormone is approved therapy for the treatment of osteoporosis.

METHODS

The intermittent therapy of parathyroid hormone requires accurate administration. Meta-analysis is conducted to draw a clear picture of the impact of intermittent therapy and dose rates relative to time, on the osteoporotic patients. A novel mathematical model is presented in this article synchronised with the parametric values, depicted from meta-analysis.

FINDINGS

Results obtained from the mathematical model are in close agreement with the results obtained from the clinical trials. The model can be used to forecast the drug potency and dosage rates, to control the vicious cycle of osteoporosis.

INTERPRETATIONS

The intermittent administration of parathyroid hormone, rather than the continuous administration, is more effective, furthermore it is also concluded that a mathematical model, linked with the extensive literature of clinical trials, using meta-analysis can help in drug administration and future clinical studies of drug development.

Emerging and Established Models of Bone Metastasis

Metastasis is the leading cause of cancer-related death and drives patient morbidity as well as healthcare costs. Bone is the primary site of metastasis for several cancers—breast and prostate cancers in particular. Efforts to treat bone metastases have been stymied by a lack of models to study the progression, cellular players, and signaling pathways driving bone metastasis. In this review, we examine newly described and classic models of bone metastasis. Through the use of current in vivo, microfluidic, and in silico computational bone metastasis models we may eventually understand how cells escape the primary tumor and how these circulating tumor cells then home to and colonize the bone marrow. Further, future models may uncover how cells enter and then escape dormancy to develop into overt metastases. Recreating the metastatic process will lead to the discovery of therapeutic targets for disrupting and treating bone metastasis.