A Novel Multiscale Mathematical Model for Building Bone Substitute Materials for Children

Abstract

Bone is an engineering marvel that achieves a unique combination of stiffness and toughness exceeding that of synthesized materials. In orthopedics, we are currently challenged for the child population that needs a less stiff but a tougher bone substitute than adults. Recent evidence suggests that the relationship between inter-molecular connections that involve the two main bone building blocks, TropoCollagen molecules (TC) and carbonated Hydroxyapatite (cAp), and bone macroscopic mechanical properties, stiffness and toughness, are key to building bone substitute materials for children. The goal of our study is to establish how inter-molecular connections that occur during bone mineralization are related to macroscopic mechanical properties in child bones. Our aim is to link the biological alterations of the TC-cAp self assembly process happening during bone mineralization to the bone macroscopic mechanical properties’ alterations during aging. To do so, we have developed a multiscale mathematical model that includes collagen cross links (TC–TC interface) from experimental studies of bone samples to forecast bone macroscopic mechanical properties. Our results support that the Young’s modulus cannot be a linear parameter if we want to solve our system. In relation to bone substitute material with innovative properties for children, our results propose values of several biological parameters, such as the number of crystals and their size, and collagen crosslink maturity for the desired bone mechanical competence. Our novel mathematical model combines mineralization and macroscopic mechanical behavior of bone and is a step forward in building mechanically customized biomimetic bone grafts that would fit children’s orthopedic needs.

Predicting Bone Protein Expression: A Stiffness-Dependent Gene Regulation Model

“…WNT-β catenin pathway activated by stiffness). This pathway depicts how bone cell mechanoreceptors stimulation initiates bone mineralization [9][10][11][12][13]. In our modeling strategy, we globalize the entire pathway in terms of Stiffness, which means that a decrease in stiffness has to be understood in terms of inhibition of the canonical pathway itself.…”

“…The canonical mechanotransduction pathway (e.g. WNT-β catenin pathway) depicts how bone cell mechanoreceptors stimulation initiates bone mineralization [9][10][11][12][13]. It can be activated at different scales by (i) the stiffness of the extracellular bone matrix [14], (ii) shear forces coming from fluid movements surrounding the cell [15], (iii) vibration propagated along the bone diaphysis [4,16], (iv) tension coming from muscles' contractions [17], or (v) compression coming from body movements acting under gravity [18].…”

“…Regarding stiffness of the extracellular matrix, evidence proposed a cascade of transcription factor and protein production through activation of their corresponding genes : (i) bone GRN transcription factor called Runt-related transcription factor 2 (RUNX2), (ii) transcription factor called Osterix (OSX), and (iii) a Special AT-rich sequence-binding protein 2 (SATB2). Then, SATB2 initiates the production of the first enhancer of mineralization called Bone sialoprotein (BSP), which induces both the second enhancer called Bone alkaline phosphatase (ALP) and the two inhibitors of bone mineralization called osteocalcin (OC) and osteopontin (OPN) [9,[19][20][21]. In our previous work [8], we presented a model consisting of a system of nonlinear differential equations depicting the direct interactions between the genes coding for the transcription factors and those coding for the bone proteins.…”

Theoretical evidence of osteoblast self-inhibition after activation of the genetic regulatory network controlling mineralization

“…The canonical pathway of bone formation is when bone matrix stiffness activates the WNT-β cathenin pathway (Wingless/Beta Catenin pathway) to initiate bone mineralization [13,38,47,50,63]. For instance, the WNT-β cathenin pathway activates transcription factors (i.e.…”