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

Abstract

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.

Keywords: bone; bone disease; bone remodeling; drug interventions; mathematical modeling; mechanobiology.

FIGURE 1

Schematic representation of the different overlapping phases of bone remodeling process. Activation phase: excitation of embedded osteocytes leading to recruit resorbing cells by means of biochemical factors. Resorption phase: bone matrix resorption accompanied by osteoblasts’ recruitment. Formation phase: blocked osteoclasts’ activity accompanied by progressive osteoid synthesis. Termination phase: mineralization of the formed bone matrix and completion of the remodeling process.

FIGURE 2

Schematic illustration of the biochemical interactions and feedback loops within a bone remodeling process in the presence of prostate cancer (PC) cells that were adopted in the mathematical model. OBu, uncommitted osteoblasts; OBp, preosteoblasts; OBa, active osteoblasts; OCp, preosteoclasts; OCa; active osteoclasts; OCap, apoptotic osteoclasts; PCe, early PC cells; PCI, late PC cells; BONEt, total bone; BONEp, bone production; and BONEr, bone resorption.

FIGURE 3

Schematic illustration of the biochemical interactions during the bone remodeling process after the adhesion of myeloma cells into the bone microenvironment. Interleukin-6 (IL-6) expression and multiple myeloma–bone marrow stromal cell (MM–BMSC) adhesion are the central factors controlling the process.

FIGURE 4

Schematic illustration of the biochemical interactions during the bone remodeling process after the adhesion of myeloma cells into the bone microenvironment. Interleukin-6 (IL-6) expression, multiple myeloma–bone marrow stromal cell (MM–BMSC) adhesion, and small leucine-rich proteoglycan (SLRP) expression are the central factors controlling the process.