/* * Modeling the interactions between osteoblast and osteoclast * activities in bone remodeling * * Model Status * * This CellML model represents an extension of the core model * such that the receptor activator of NF-kB ligand (RANKL) is * being added at a constant rate from day 20 and osteoprotegerin * (OPG) is subsequently added 60 days later, also at a constant * rate. The model runs in both OpenCell and COR to recreate the * published results. The units are consistent throughout. * * Model Structure * * ABSTRACT: We propose a mathematical model explaining the interactions * between osteoblasts and osteoclasts, two cell types specialized * in the maintenance of the bone integrity. Bone is a dynamic, * living tissue whose structure and shape continuously evolves * during life. It has the ability to change architecture by removal * of old bone and replacement with newly formed bone in a localized * process called remodeling. The model described here is based * on the idea that the relative proportions of immature and mature * osteoblasts control the degree of osteoclastic activity. In * addition, osteoclasts control osteoblasts differentially depending * on their stage of differentiation. Despite the tremendous complexity * of the bone regulatory system and its fragmentary understanding, * we obtain surprisingly good correlations between the model simulations * and the experimental observations extracted from the literature. * The model results corroborate all behaviors of the bone remodeling * system that we have simulated, including the tight coupling * between osteoblasts and osteoclasts, the catabolic effect induced * by continuous administration of PTH, the catabolic action of * RANKL, as well as its reversal by soluble antagonist OPG. The * model is also able to simulate metabolic bone diseases such * as estrogen deficiency, vitamin D deficiency, senescence and * glucocorticoid excess. Conversely, possible routes for therapeutic * interventions are tested and evaluated. Our model confirms that * anti-resorptive therapies are unable to partially restore bone * loss, whereas bone formation therapies yield better results. * The model enables us to determine and evaluate potential therapies * based on their efficacy. In particular, the model predicts that * combinations of anti-resorptive and anabolic therapies provide * significant benefits compared with monotherapy, especially for * certain type of skeletal disease. Finally, the model clearly * indicates that increasing the size of the pool of preosteoblasts * is an essential ingredient for the therapeutic manipulation * of bone formation. This model was conceived as the first step * in a bone turnover modeling platform. These initial modeling * results are extremely encouraging and lead us to proceed with * additional explorations into bone turnover and skeletal remodeling. * * model diagram * * [[Image file: lemaire_2004_new.png]] * * Schematic diagram of the basic structure of the model. * * The original paper reference is cited below: * * Modeling the interactions between osteoblast and osteoclast * activities in bone remodeling, Vincent Lemaire, Frank L. Tobin, * Larry D. Greller, Carolyn R. Cho, and Larry J. Suva, 2004, Journal * of Theoretical Biology, 229, 293-309. PubMed ID: 15234198 */ import nsrunit; unit conversion on; unit day=86400 second^1; // unit picomole predefined unit cells = fundamental; unit picomole_cells=1E-12 mole^1*cells^1; unit picomole_picomole_cells=1 cells^(-1); unit picomole_day_picomole_cells=1.1574074E-5 second^(-1)*cells^(-1); // unit picomolar predefined unit flux=1.1574074E-14 meter^(-3)*second^(-1)*mole^1; unit first_order_rate_constant=1.1574074E-5 second^(-1); unit second_order_rate_constant=1.1574074E4 meter^3*second^(-1)*mole^(-1); math main { realDomain time day; time.min=0; extern time.max; extern time.delta; real R(time) picomolar; when(time=time.min) R=0; real DR flux; DR=7e-4; real pi_C(time) dimensionless; real DB first_order_rate_constant; real B(time) picomolar; when(time=time.min) B=0; real kB first_order_rate_constant; kB=0.189; real C(time) picomolar; when(time=time.min) C=0; real DC flux; DC=2.1e-3; real pi_L(time) dimensionless; real DA first_order_rate_constant; DA=0.7; real k1 second_order_rate_constant; k1=1e-2; real k2 first_order_rate_constant; k2=10; real k3 second_order_rate_constant; k3=5.8e-4; real k4 first_order_rate_constant; k4=1.7e-2; real K picomolar; K=10; real ko first_order_rate_constant; ko=0.35; real Io(time) flux; real IL(time) flux; real rL flux; rL=1e3; real KOP picomole_day_picomole_cells; KOP=2e5; real KLP picomole_picomole_cells; KLP=3e6; real pi_P dimensionless; real f0 dimensionless; f0=0.05; real dB first_order_rate_constant; dB=0.7; real IP flux; IP=0; real kP first_order_rate_constant; kP=86; real P picomolar; real P_0 picomolar; real P_s picomolar; real C_s picomolar; C_s=5e-3; real SP flux; SP=250; real k5 second_order_rate_constant; k5=0.02; real k6 first_order_rate_constant; k6=3; // // R:time=(DR*pi_C-DB/pi_C*R); // B:time=(DB/pi_C*R-kB*B); // C:time=(DC*pi_L-DA*pi_C*C); // pi_L=(k3/k4*KLP/(1 picomole_picomole_cells)*pi_P*B/(1+k3*K/k4+k1/(k2*ko)*(KOP/(1 picomole_picomole_cells)/pi_P*R+Io))*(1+IL/rL)); Io=(if (time>=(80 day)) (9E4 flux) else (0 flux)); IL=(if (time>=(20 day)) (1E4 flux) else (0 flux)); // DB=(f0*dB); pi_C=((C+f0*C_s)/(C+C_s)); pi_P=((P+P_0)/(P+P_s)); P=(IP/kP); P_0=(SP/kP); P_s=(k6/k5); }