Cell Population Model Research Articles

Application of phase space file secondary computation method in cell dose distribution

Phase space files can store the particle information in one or more planes of radiation particles simulated by the Monte Carlo (MC) method. The secondary calculation method based on phase space files is commonly used to improve the efficiency of MC simulations. However, it is still unclear whether phase space files are applicable for microdosimetric evaluations. In this study, voxel-type and mesh-type monolayer cell population models of different sizes were constructed, and phase space files of secondary electrons generated by photons with different initial energies were obtained using the MC software -- PHITS. The overall average dose caused by the secondary electron phase space files in the region of interest and their microdosimetric distribution within cells were calculated and compared with the results caused by the initial photons under the same geometric conditions. The results showed that the adoption of secondary electron phase space files had almost no impact on the evaluation of macroscopic average dose, with deviations lower than 3% compared to the overall dose caused by the initial photons in the Petri dish. For microdosimetric distributions of the voxel-type model and the two different morphologies of mesh-type cell models, with a macroscopic accumulated dose of 1 mGy, the relative deviation of the cell dose distribution generated by the initial photons and the phase space files was below 10% and the total computation time of phase space files was below 2% of initial photon's. For accumulated doses of 10, 50, and 100 mGy, the relative deviation of the cell nucleus specific energy obtained by secondary electrons and initial photons was greater than 10%. As the size of the culture dish increased, the differences in cell dose distributions also increased, with the root mean square error (RMSE) and coefficient of variation (Cv) of dose distributions both exceeding 30%. In conclusion, this study assessed the effectiveness of the secondary calculation method utilizing phase space files for dose evaluation at the cellular scale. This research offers essential technical support and theoretical foundations for the utilization of this approach in microdosimetric investigations at the cellular level.

Numerical integration of mechanical forces in center-based models for biological cell populations

Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to many thousands or more, these models have to be numerically efficient, while being reasonably accurate on the level of individual cell trajectories. In this work, we increase the robustness, accuracy, and efficiency of the simulation of center-based models by choosing the time steps adaptively in the numerical method and comparing five different integration methods. We investigate the gain in using single rate time stepping based on local estimates of the numerical errors for the forward and backward Euler methods of first order accuracy and a Runge-Kutta method and the trapezoidal method of second order accuracy. Properties of the analytical solution such as convergence to steady state and conservation of the center of gravity are inherited by the numerical solutions. Furthermore, we propose a multirate time stepping scheme that simulates regions with high local force gradients (e.g. as they happen after cell division) with multiple smaller time steps within a larger single time step for regions with smoother forces. These methods are compared for a model system in numerical experiments. We conclude, for example, that the multirate forward Euler method performs better than the Runge-Kutta method for low accuracy requirements but for higher accuracy the latter method is preferred. Only with frequent cell divisions the method with a fixed time step is the best choice.

Dynamics of an age-structured tumor cell population model with nutrition

Dynamics of an age-structured tumor cell population model with nutrition

Derivation and simulation of a computational model of active cell populations: How overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces affect alignment.

Collective alignment of cell populations is a commonly observed phenomena in biology. An important example are aligning fibroblasts in healthy or scar tissue. In this work we derive and simulate a mechanistic agent-based model of the collective behaviour of actively moving and interacting cells, with a focus on understanding collective alignment. The derivation strategy is based on energy minimisation. The model ingredients are motivated by data on the behaviour of different populations of aligning fibroblasts and include: Self-propulsion, overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces. We find that there is an optimal ratio of self-propulsion speed and overlap avoidance that maximises collective alignment. Further we find that deformability aids alignment, and that cell-cell junctions by themselves hinder alignment. However, if cytoskeletal forces are transmitted via cell-cell junctions we observe strong collective alignment over large spatial scales.

A comparative study on the dose–effect of low-dose radiation based on microdosimetric analysis and single-cell sequencing technology

The biological mechanisms triggered by low-dose exposure still need to be explored in depth. In this study, the potential mechanisms of low-dose radiation when irradiating the BEAS-2B cell lines with a Cs-137 gamma-ray source were investigated through simulations and experiments. Monolayer cell population models were constructed for simulating and analyzing distributions of nucleus-specific energy within cell populations combined with the Monte Carlo method and microdosimetric analysis. Furthermore, the 10 × Genomics single-cell sequencing technology was employed to capture the heterogeneity of individual cell responses to low-dose radiation in the same irradiated sample. The numerical uncertainties can be found both in the specific energy distribution in microdosimetry and in differential gene expressions in radiation cytogenetics. Subsequently, the distribution of nucleus-specific energy was compared with the distribution of differential gene expressions to guide the selection of differential genes bioinformatics analysis. Dose inhomogeneity is pronounced at low doses, where an increase in dose corresponds to a decrease in the dispersion of cellular-specific energy distribution. Multiple screening of differential genes by microdosimetric features and statistical analysis indicate a number of potential pathways induced by low-dose exposure. It also provides a novel perspective on the selection of sensitive biomarkers that respond to low-dose radiation.

An in silico approach to elucidate the pathways leading to primary osteoporosis: age-related vs. postmenopausal

Numerical models of bone remodelling have traditionally been used to perform in silico tests of bone loss in postmenopausal women and also to simulate the response to different drug treatments. These models simulate the menopausal oestrogen decline by altering certain signalling pathways. However, they do not consider the simultaneous effect that ageing can have on cell function and bone remodelling, and thus on bone loss. Considering ageing and oestrogen decline together is important for designing osteoporosis treatments that can selectively counteract one or the other disease mechanism. A previously developed bone cell population model was adapted to consider the effect of ageing through: (1) the decrease of TGF-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} contained in the bone matrix and (2) an increased production of sclerostin by non-skeletal cells. Oestrogen deficiency is simulated in three different ways: (a) an increase in RANKL expression, (b) a decrease in OPG production, and (c) an increase in the responsiveness of osteoclasts to RANKL. The effect of ageing was validated using the cross-sectional study of (Riggs et al. in J Bone Miner Res 19: 1945-1954, 2004) on BMD of trabecular bone of the vertebral body of men. The joint effect of ageing and oestrogen deficiency was validated using these same clinical results but in women. In ageing, the effect of the increasing production of sclerostin is more important than the decrease of TGF-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document}, while the three mechanisms used to simulate the effect of oestrogen deficiency produce almost identical responses. The results show that an early menopause leads to a lower average density in the fifth decade, but after the sixth decade the average density is independent of the age at menopause. Treatment of osteoporosis with denosumab was also simulated to conclude that the drug is not very effective if started before 10 years after menopause or before age 60.

Selective elimination of tumorigenic cells from mixed culture of normal and tumorigenic cells using hybrid liposomes aimed at realizing of cell therapy

While induced pluripotent stem (iPS) cells are expected to be a cell source for regenerative medicine, they also have tumorigenic properties owing to their proliferative potential. During the manufacturing of regenerative medicine products, undifferentiated iPS cells and malignant transformed cells may be mixed in the cell culture population. Therefore, it is essential to eliminate tumorigenic cells selectively. In this study, a mixed culture of normal human fetal hepatocytes (Hc cells) and human hepatocellular carcinoma cells (HuH-7 cells) was used as a cell population model to be used as regenerative medicine products, and the selective elimination of HuH-7 cells by hybrid liposomes (HL) was analyzed. HL tended to fuse and accumulate more in HuH-7 cells due to larger fluidity of plasma membrane for HuH-7 cells than that for Hc cells. In a mixed culture of Hc and HuH-7 cells, HL selectively eliminated HuH-7 cells while allowing Hc cells to remain viable. In addition, HL treatment for the mixed culture of Hc and HuH-7 cells suppressed the tumorigenicity of HuH-7 cells. Therefore, HL selectively fused and accumulated in tumorigenic cells in a mixed cell culture of normal and tumorigenic cells, and eliminated tumorigenic cells while allowing normal cells to remain viable. The results of this study suggest the potential of HL in eliminating tumorigenic cells during the manufacturing of regenerative medicine products. Thus, HL could be expected to contribute to the development of safe regenerative medical products.

Theoretical understanding of evolutionary dosing following tumor dynamics

Recent preclinical and clinical studies have suggested that evolution-based cancer therapies exploiting intratumor competition can significantly delay resistance. Various mathematical and computational models have been used to explain the effectiveness of particular treatment strategies. However, this evolutionary approach often assumes only preexisting resistance, although acquired resistance and cancer phenotype plasticity can dramatically affect treatment outcomes. We theoretically investigate whether an evolutionary therapy that capitalizes on plasticity could delay resistance. In particular, we propose a time-dependent evolutionary dose that can modulate the evolving competition among drug-sensitive, drug-resistant, and plastic cells. We assume a Lotka–Volterra type competition model of cancer cell populations with constant carrying capacity to analyze the dynamics of tumor growth to show that some tumors can be controlled with proper dosing, which balances the competition between different cell species so that they coexist in a stable tumor below a tolerable burden. The emergence of a new resistant species may further increase the tumor volume, which can be nullified by lowering the dose. In contrast, increasing the tumor volume due to new metastatic formation requires a higher dose. Additionally, we propose tumor-dynamics-driven adaptive scheduling consisting of subsequent treatment holidays and low- and high-dose periods. This approach can contain the tumor at variable volumes below the tolerable burden, which may facilitates reiteration of the treatment strategy in the case of any evolutionary changes. Overall, this study provides a theoretical understanding of the evolutionary dosing that can delay resistance.

Modeling and analysis of a multilayer solid tumour with cell physiological age and resource limitations

We study an avascular spherical solid tumour model with cell physiological age and resource constraints in vivo. We divide the tumour cells into three components: proliferating cells, quiescent cells and dead cells in necrotic core. We assume that the division rate of proliferating cells is nonlinear due to the nutritional and spatial constraints. The proportion of newborn tumour cells entering directly into quiescent state is considered, since this proportion can respond to the therapeutic effect of drug. We establish a nonlinear age-structured tumour cell population model. We investigate the existence and uniqueness of the model solution and explore the local and global stabilities of the tumour-free steady state. The existence and local stability of the tumour steady state are studied. Finally, some numerical simulations are performed to verify the theoretical results and to investigate the effects of different parameters on the model.

Pharmacodynamic Age Structured Population Model For Cell Trafficking

ObjectivesCell trafficking encompasses movement of the immune system cells (e.g., granulocytes, lymphocytes) between the blood and the extravascular tissues (e.g., lymph nodes). Corticosteroids are known to suppress cell trafficking. The age-structured cell population models introduce the transit time as a structure that allows one to quantify the distribution of times the immune cells spend in the blood and the extravascular tissues. The objective of this work is to develop an age-structured cell population model describing drug effects on cell trafficking and to implement the model in pharmacometric software to enable parameter estimation and simulations. MethodsWe adopted the well-known McKendrick age-structured population model to describe the age distributions in two cell populations: blood cells and cells in the extravascular space. The hazard of cell recirculation from the extravascular tissues was age dependent and described by the Weibull function with the shape ν and scale β parameters. The drug effect on cell trafficking was modeled as the product of the Emax function of the drug plasma concentration and the Weibull hazard. The model was implemented in NONMEM 7.5.1. The model was applied to the basophil data in 34 healthy subjects who received a single intramuscular or oral dose of 6 mg dexamethasone (DEX). A recently published pharmacokinetic model was applied to describe DEX plasma concentration. Typical values of parameter estimates were further used to simulate the DEX effect of the basophil mean transit time in the extravascular tissues. ResultsSimulations of basophil time courses for varying ν demonstrated that the rebound in the blood count data following drug administration is only possible for ν >1. The estimates of model parameters were ν = 3.02, β = 0.00863 1/h, and IC50 = 7.47 ng/mL. The calculated baseline mean transit times of basophils in the blood 7.2 h and extravascular tissues 104.9 h agree with the values reported in the literature. ConclusionsWe introduced an age-structured population model to describe cell trafficking between the blood and extravascular tissues. The model was adopted to account for the inhibitory drug effect on the cell recirculation. We showed that the age structure is essential to explain the rebound observed in the blood count response to a single dose drug administration. The model was validated using the basophil responses to DEX treatment in healthy subjects.

Modelling how plant cell-cycle progression leads to cell size regulation.

Populations of cells typically maintain a consistent size, despite cell division rarely being precisely symmetrical. Therefore, cells must possess a mechanism of "size control", whereby the cell volume at birth affects cell-cycle progression. While size control mechanisms have been elucidated in a number of other organisms, it is not yet clear how this mechanism functions in plants. Here, we present a mathematical model of the key interactions in the plant cell cycle. Model simulations reveal that the network of interactions exhibits limit-cycle solutions, with biological switches underpinning both the G1/S and G2/M cell-cycle transitions. Embedding this network model within growing cells, we test hypotheses as to how cell-cycle progression can depend on cell size. We investigate two different mechanisms at both the G1/S and G2/M transitions: (i) differential expression of cell-cycle activator and inhibitor proteins (with synthesis of inhibitor proteins being independent of cell size), and (ii) equal inheritance of inhibitor proteins after cell division. The model demonstrates that both these mechanisms can lead to larger daughter cells progressing through the cell cycle more rapidly, and can thus contribute to cell-size control. To test how these features enable size homeostasis over multiple generations, we then simulated these mechanisms in a cell-population model with multiple rounds of cell division. These simulations suggested that integration of size-control mechanisms at both G1/S and G2/M provides long-term cell-size homeostasis. We concluded that while both size independence and equal inheritance of inhibitor proteins can reduce variations in cell size across individual cell-cycle phases, combining size-control mechanisms at both G1/S and G2/M is essential to maintain size homeostasis over multiple generations. Thus, our study reveals how features of the cell-cycle network enable cell-cycle progression to depend on cell size, and provides a mechanistic understanding of how plant cell populations maintain consistent size over generations.

Microdosimetric assessment about proton spread-out Bragg peak at different depths based on the normal human mesh-type cell population model.

Objective.In clinical proton therapy, the spread-out Bragg peak (SOBP) is commonly used to fit the target shape. Dose depositions at microscopic sites vary, even with a consistent absorbed dose (D) in SOBP. In the present study, monolayer mesh-type cell population models were developed for microdosimetric assessment at different SOBP depths.Approach.Normal human bronchial epithelial (BEAS-2B) and hepatocytes (L-O2) mesh-type cell models were constructed based on fluorescence tomography images of normal human cells. Particle transport simulation in cell populations was performed coupled with Monte Carlo software PHITS. The relationship between microdosimetry and macrodosimetry of SOBP at different depths was described by analyzing the microdosimetric indicators such as specific energyz,specific energy distributionfz,D,and relative standard deviationσz/z¯within cells. Additionally, the microdosimetric distributions characteristics and their contributing factors were also discussed.Main results.The microscopic dose distribution is strongly influenced by cellular size, shape, and material. The mean specific energyz¯of nucleus and cytoplasm in the cell population is greater than the overall absorbed dose of the cell population model (Dp), with a maximumz¯/Dpof 1.1. The cellular dose distribution is different between the BEAS-2B mesh-type model and its concentric ellipsoid geometry-type model, which difference inz¯is about 10.3% for the nucleus and about 7.5% for the cytoplasm with the SOBP depth of 15 cm. WhenD= 2 Gy, the maximumzof L-O2 nucleus reaches 2.8 Gy andσz/z¯is 5.1% at the mid-depth SOBP (16-18 cm); while the maximumzof the BEAS-2B nucleus reaches 2.2 Gy with only 2.7% ofσz/z¯.Significance.The significant variation of microdosimetric distributions of SOBP different depths indicates the necessity to use mesh-type cell population models, which have the potential to be compared with biological results and build the bio-physical model.

Self-Regulated Symmetry Breaking Model for Stem Cell Differentiation.

In conventional disorder-order phase transitions, a system shifts from a highly symmetric state, where all states are equally accessible (disorder) to a less symmetric state with a limited number of available states (order). This transition may occur by varying a control parameter that represents the intrinsic noise of the system. It has been suggested that stem cell differentiation can be considered as a sequence of such symmetry-breaking events. Pluripotent stem cells, with their capacity to develop into any specialized cell type, are considered highly symmetric systems. In contrast, differentiated cells have lower symmetry, as they can only carry out a limited number of functions. For this hypothesis to be valid, differentiation should emerge collectively in stem cell populations. Additionally, such populations must have the ability to self-regulate intrinsic noise and navigate through a critical point where spontaneous symmetry breaking (differentiation) occurs. This study presents a mean-field model for stem cell populations that considers the interplay of cell-cell cooperativity, cell-to-cell variability, and finite-size effects. By introducing a feedback mechanism to control intrinsic noise, the model can self-tune through different bifurcation points, facilitating spontaneous symmetry breaking. Standard stability analysis showed that the system can potentially differentiate into several cell types mathematically expressed as stable nodes and limit cycles. The existence of a Hopf bifurcation in our model is discussed in light of stem cell differentiation.

Low-energy electron microdosimetry assessment based on the two-dimensional monolayer human normal mesh-type cell population model

In radiobiology, in vitro irradiation experiments on cells are often conducted to investigate the relationship between radiation dose and biological effects, where the phenotypic indicators of cells in culture are generally measured with macroscopic dosimetric indicators of the absorbed dose. The intracellular transport behavior of low-energy electrons are of particular importance. Considering the states of cells in culture, two-dimensional monolayer mesh-type cell population models were constructed in this work based on two human mesh-type cell models to evaluate the microdosimetric distribution of monoenergetic electrons with two energy levels in the cell population. Two-dimensional monolayer mesh-type and equivalent-volume concentric sphere cell population models of two cell lines, i.e., BEAS-2B and FHs74Int, with different cell numbers and shapes were constructed. Monte Carlo toolkit, GATE, was used as the simulation platform. The impacts of different deposition doses from the 100 keV and 200 keV monoenergetic electron beams on the average specific energy z‾ of the nucleus and cytoplasm, the specific energy frequency function f(z,D), and their relative standard deviation σz/z‾ were assessed. Under the same irradiation conditions, the mesh-type and equivalent-volume sphere cell population models showed small differences in f(z,D), whereas the z‾ of the nucleus and cytoplasm differed significantly. As the cumulative absorbed dose reached the mGy level under the irradiation of the monoenergetic electron beam with an initial energy of 100 keV, the nucleus z‾ of the FHs74Int circular mesh-type population model with 848 cells was 19.88 mGy, whereas the nucleus z‾ of the concentric sphere cell population model was 23.96 mGy. The lower dose (∼mGy level) under the same geometry resulted in a more pronounced uncertainty in the absorbed dose value. Specifically, take the FHs74Int quadrate mesh-type population model with 484 cells as an example, the σz/z‾ were 3.61% and 23.35%, respectively, at the ∼Gy and ∼mGy levels under electrons with the initial energy of 200 keV. In addition, the volume and shape of the cell population impact the specific energy distribution. Through the constructed two-dimensional monolayer mesh-type cell population model, this work quantitatively demonstrates that the dose distribution within subcellular regions under low-energy electron irradiation for low-dose level is significantly affected by the cell volume and shape. This study provides a viable means of simulating and quantifying the energy deposition distribution of radiation within the culture dish based on radiobiological cell irradiation scenarios, which can provide method and data support to build biophysical models.

Spatio-temporal simulations of bone remodelling using a bone cell population model based on cell availability.

Here we developed a spatio-temporal bone remodeling model to simulate the action of Basic Multicelluar Units (BMUs). This model is based on two major extensions of a temporal-only bone cell population model (BCPM). First, the differentiation into mature resorbing osteoclasts and mature forming osteoblasts from their respective precursor cells was modelled as an intermittent process based on precursor cells availability. Second, the interaction between neighbouring BMUs was considered based on a "metabolic cost" argument which warrants that no new BMU will be activated in the neighbourhood of an existing BMU. With the proposed model we have simulated the phases of the remodelling process obtaining average periods similar to those found in the literature: resorption ( days)-reversal (∼8days)-formation (∼65days)-quiescence (560-600days) and an average BMU activation frequency of ∼1.6BMUs/year/mm3. We further show here that the resorption and formation phases of the BMU become coordinated only by the presence of TGF-β (transforming growth factor β), i.e., a major coupling factor stored in the bone matrix. TGF-β is released through resorption so upregulating osteoclast apoptosis and accumulation of osteoblast precursors, i.e., facilitating the transition from the resorption to the formation phase at a given remodelling site. Finally, we demonstrate that this model can explain targeted bone remodelling as the BMUs are steered towards damaged bone areas in order to commence bone matrix repair.

Effect of Antiviral Therapy for HCV Treatment in the Presence of Hepatocyte Growth Factor

The effect of antiviral therapy during Hepatitis C Virus (HCV) infection is the focus of this study. HCV infection destroys healthy hepatocyte cells in the human liver, causing cirrhosis and hepatocellular carcinoma. We introduce a cell-population model representing the long-term dynamics of HCV infection in response to antiviral drug therapies. The proliferation of existing cells can create hepatocyte cells in the system. Such models are based on the dynamics of susceptible hepatocytes, infected hepatocytes and HCV with interactive dynamics, which can give a complete understanding of the host dynamics of the system in the presence of antiviral drug therapy. Infection-free equilibrium and endemic equilibrium are two equilibrium states in the absence of drugs. The existence and stability conditions for both systems are presented. We also construct an optimal control system to find the optimal control strategy. Numerical results show that the effects of the proliferation rate and infection rate are critical for the changes in the dynamics of the model. The impact of different weight factors on the optimal control problem is analysed through numerical simulation.

Convergence rate for the incompressible limit of nonlinear diffusion–advection equations

The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cellpopulation models to free boundary problems of Hele–Shaw type. Although a vast literature is available on this singular limit, little is known on the convergence rate of the solutions. In this work, we compute the convergence rate in a negative Sobolev norm and, upon interpolating with BV-uniform bounds, we deduce a convergence rate in appropriate Lebesgue spaces.

Global stability of a HCV dynamics model with cellular proliferation and delay

In this work, we propose and investigate a delay cell population model of hepatitis C virus (HCV) infection with cellular proliferation, absorption effect and a nonlinear incidence function. First of all, after having shown the existence of the local solutions of our model, we show the existence of the global solutions and positivity. Moreover, we determine the uninfected equilibrium point and the basic reproduction rate R0, which is a threshold number in mathematical epidemiology. After showing the existence and uniqueness of the infected equilibrium point, we proceed to the study of the local and global stability of this equilibrium. We show that if R0 < 1, the uninfected equilibrium point is globally asymptotically stable, which means that the disease will disappear and if R0 > 1, we have a unique infected equilibrium that is globally asymptotically stable under some conditions. Finally, we perform some numerical simulations to illustrate the obtained theoretical results.

Assessment of Strategies for Safe Drug Discontinuation and Transition of Denosumab Treatment in PMO-Insights From a Mechanistic PK/PD Model of Bone Turnover.

Denosumab (Dmab) treatment against postmenopausal osteoporosis (PMO) has proven very efficient in increasing bone mineral density (BMD) and reducing the risk of bone fractures. However, concerns have been recently raised regarding safety when drug treatment is discontinued. Mechanistic pharmacokinetic-pharmacodynamic (PK-PD) models are the most sophisticated tools to develop patient specific drug treatments of PMO to restore bone mass. However, only a few PK-PD models have addressed the effect of Dmab drug holidays on changes in BMD. We showed that using a standard bone cell population model (BCPM) of bone remodelling it is not possible to account for the spike in osteoclast numbers observed after Dmab discontinuation. We show that inclusion of a variable osteoclast precursor pool in BCPMs is essential to predict the experimentally observed rapid rise in osteoclast numbers and the associated increases in bone resorption. This new model also showed that Dmab withdrawal leads to a rapid increase of damage in the bone matrix, which in turn decreases the local safety factor for fatigue failure. Our simulation results show that changes in BMD strongly depend on Dmab concentration in the central compartment. Consequently, bone weight (BW) might play an important factor in calculating effective Dmab doses. The currently clinically prescribed constant Dmab dose of 60 mg injected every 6 months is less effective in increasing BMD for patients with high BW (2.5% for 80 kg in contrast to 8% for 60 kg after 6 years of treatment). However, bone loss observed 24 months after Dmab withdrawal is less pronounced in patients with high BW (3.5% for 80kg and 8.5% for 60 kg). Finally, we studied how to safely discontinue Dmab treatment by exploring several transitional and combined drug treatment strategies. Our simulation results indicate that using transitional reduced Dmab doses are not effective in reducing rapid bone loss. However, we identify that use of a bisphosphonate (BP) is highly effective in avoiding rapid bone loss and increase in bone tissue damage compared to abrupt withdrawal of Dmab. Furthermore, the final values of BMD and damage were not sensitive to the time of administration of the BP.

A unified framework of cell population dynamics and mechanical stimulus using a discrete approach in bone remodelling

Multiphysics models have become a key tool in understanding the way different phenomenon are related in bone remodeling and various approaches have been proposed, yet, to the best of the author’s knowledge there is no model able to link a cell population model with a mechanical stimulus model using a discrete approach, which allows for an easy implementation. This article couples two classical models, the cell population model from Komarova and the Nackenhorst model in a 2D domain, where correlations between the mechanical loading and the cell population dynamics can be established, furthermore the effect of different paracrine and autocrine regulators is seen on the overall density of a portion of trabecular bone. A discretization is performed using frame 1D finite elements, representing the trabecular structure. The Nackenhorst model is implemented by using the finite element method to calculate the strain energy as the main mechanical stimulus that determines the bone mass density evolution in time. This density is normalized to be added to the bone mass percentage proposed by the Komarova model, where coupling terms have been added as well that guarantee a stable response. In the simulations, the equations were solved employing the finite element method with a user subroutine implemented in ABAQUS (2017) and by applying a direct formulation. The methodology presented can model the cell dynamics occurring in bone remodelling in accordance with the asynchronous nature of this process, yet allowing to differentiate zones with higher density, the main trabecular groups are obtained for the proximal femur. Finally, the model is tested in pathological cases, such as osteoporosis and osteopetrosis, yielding results similar to the pathology behavior. Furthermore, the discrete modelling technique is shown to be of use in this particular application.