A method of modeling a bone fracture healing model under the action of macrophages

Abstract

This invention provides a method for modeling a fracture healing model under the influence of macrophages. The steps are as follows: Step 1: Establish a mathematical model of fracture healing based on the ordinary differential equation of fracture healing; Step 2: Establish a fracture healing model under the influence of macrophages based on the regulatory effects of macrophages and their secreted cytokines on bone tissue cells. This invention provides a mathematical description of the complex process of fracture healing based on the interaction between the immune system and bone tissue cells in the human body, and has theoretical guiding significance for studying the mechanism of fracture healing and treating fractures.

Description

Technical Field

[0001] This invention relates to the field of biomedical engineering, and in particular to a method for modeling a fracture healing model under the action of macrophages. Background Technology

[0002] Fractures are a common injury, affecting millions, even tens of millions, of people annually. Often, delayed treatment after a fracture leads to delayed healing or nonunion, causing significant inconvenience and pain for the injured and imposing a substantial economic burden on society. Delayed or nonunion is influenced by a combination of factors, primarily mechanical, biological, and the geometry of the fracture site. While research on fracture healing is increasingly extensive and fruitful, studies on the impact of the immune system on fracture healing are still limited. However, recent experimental observations suggest that macrophages and their released factors play a crucial role in successful bone healing. Therefore, a better understanding of the role of macrophages in the fracture healing process is essential to prevent unsuccessful healing and to develop optimal treatments for fracture healing. Summary of the Invention

[0003] This invention addresses the problem that existing fracture healing models cannot simulate the regulatory role of macrophages and their secreted factors in fracture healing, and proposes a method for modeling fracture healing under the action of macrophages.

[0004] A method for modeling a fracture healing model induced by macrophages is implemented according to the following steps:

[0005] Step 1: Establish a basic fracture healing model based on accidental injury to human bone tissue and the subsequent healing process;

[0006] Step 2: Based on the regulatory effects of macrophages and their secreted cytokines on cells in bone tissue, establish a fracture healing model based on the action of macrophages.

[0007] The beneficial effects of this invention are as follows:

[0008] Traditional fracture healing models do not consider the influence of macrophages and their secreted cytokines on fracture healing. This invention, based on the metabolic processes of damaged bone tissue during healing, introduces a fracture healing model that describes the role of macrophages in fractures of varying degrees. For clinical trials, it can be used to detect the evolution of different fracture types and explore potential treatments that accelerate bone healing through the administration of anti-inflammatory drugs. Attached Figure Description

[0009] Figure 1This is a flowchart illustrating the basic intercellular dynamics during fracture healing.

[0010] Figure 2 This is a flowchart illustrating the dynamic process of macrophages (left) and bone tissue cells (right) during fracture healing. Detailed Implementation

[0011] Specific Implementation Method 1: A method for modeling a fracture healing model under the action of macrophages includes the following steps.

[0012] Step 1: Establish a basic fracture healing model based on accidental injury to human bone tissue and the subsequent healing process;

[0013] Step 2: Based on the regulatory effects of macrophages and their secreted cytokines on cells in bone tissue, establish a fracture healing model based on the action of macrophages.

[0014] Specific Implementation Method Two: This specific implementation method differs from Specific Implementation Method One in that the specific process of establishing the basic fracture healing model in step one is as follows:

[0015] During fracture healing, the dynamic healing process is controlled by the interaction of eight cell types and cytokines: primary cell debris (D), macrophages (M), inflammatory cytokines (C1), anti-inflammatory cytokines (C2), and mesenchymal stem cells (C5). m ), osteoblasts (C b ), fibrocartilage tissue (m c ) and woven bone (m b Each cell type represents a uniform concentration of cell nuclei within a given volume. Their interactions are as follows: Figure 1 As shown, cell dynamics are represented by round and solid arrows, molecular concentrations and their products are represented by octagonal and dashed arrows, tissue density and its synthesis are represented by rhomboid and dashed arrows, and debris removal and cytokine inhibition are represented by terminal dashed arrows.

[0016] The ordinary differential equation for the change of primary cell debris (D) over time is:

[0017]

[0018] In the formula, k d The debridement rate represents the removal of primary cell debris;

[0019] The ordinary differential equation for the change of macrophages (M) over time is:

[0020]

[0021] In the formula, k0 is the mobility of M, and d0 is the efflux of M;

[0022] Mesenchymal stem cells (C m The time-varying ordinary differential equation is:

[0023]

[0024] In the formula, A m K lm F1 and F1 represent the mitotic rate of mesenchymal stem cells dependent on inflammatory cytokines, the upper limit of the population size of mesenchymal stem cells, and the differentiation rate of mesenchymal stem cells dependent on inflammatory cytokines, respectively.

[0025] osteoblasts (C b The time-varying ordinary differential equation is:

[0026]

[0027] In the formula, A b K lb F1, d b The mitotic rate of osteoblasts dependent on inflammatory cytokines, the upper limit of osteoblast population, the differentiation rate of osteoblasts dependent on inflammatory cytokines, and the natural mortality rate of osteoblasts were determined respectively.

[0028] The ordinary differential equation for the change of inflammatory cytokine (c1) over time is:

[0029]

[0030] In the formula, G3, k1, k2, These represent the inhibitory effect of inflammatory cytokines on the production of anti-inflammatory cytokines, the rate of secretion of inflammatory cytokines by primary cell debris, the rate of secretion of inflammatory cytokines by macrophages, and the decay rate of inflammatory cytokines, respectively.

[0031] The ordinary differential equation for the change of anti-inflammatory cytokine (c2) over time is:

[0032]

[0033] In the formula, G4 represents the inhibitory effect of anti-inflammatory cytokines on the production of anti-inflammatory cytokines, and k4 represents the rate at which mesenchymal stem cells secrete anti-inflammatory cytokines. Indicates the decay rate of anti-inflammatory cytokines;

[0034] Fibrocartilage tissue (m c The time-varying ordinary differential equation is:

[0035]

[0036] In the formula, pcs q cd1 q cd2 These represent the cartilage synthesis rate, cartilage degradation rate, and cartilage removal rate, respectively.

[0037] Woven bone (m) b The time-varying ordinary differential equation is:

[0038]

[0039] In the formula, p bs q bd These represent the synthesis rate of woven bone tissue and the degradation rate of woven bone tissue, respectively.

[0040] Specific Implementation Method Three: This specific implementation method differs from Specific Implementation Method One or Two in that: in step two, the fracture healing model based on the regulatory effect of macrophages and their secreted factors on bone tissue cells is established as follows:

[0041] During fracture healing under the action of macrophages, such as Figure 2 As shown, the immune cells involved in fracture healing are primary cell debris (D), unactivated macrophages (M0), classically activated macrophages (M1), alternately activated macrophages (M2), pro-inflammatory cytokines (c1), and anti-inflammatory cytokines (c2). The affected bone tissue cells are mesenchymal stem cells (C1, C2, and C3). m ), osteoblasts (C b ), fibrocartilage tissue (m c ), woven bone (m b );

[0042] The ordinary differential equation for the change of primary cell debris (D) over time is:

[0043]

[0044] In the formula, R D , These represent the saturation of phagocytosis rate of phagocytes, the fragment phagocytosis rate of M1, and the fragment phagocytosis rate of M2, respectively.

[0045] The ordinary differential equation for the change of unactivated macrophages (M0) over time is:

[0046]

[0047] In the formula, R M G1, G2, and d0 represent the maximum value of undifferentiated macrophages at the injury site, the inhibition rate of pro-inflammatory cytokines on the differentiation of M0 into M1, the inhibition rate of pro-inflammatory cytokines on the differentiation of M0 into M2, and the migration rate of M0, respectively.

[0048] The ordinary differential equations for the changes in classically activated macrophages (M1) and alternately activated macrophages (M2) over time are as follows:

[0049]

[0050]

[0051] In the formula, G1, G2, k 21 k 12 d1 and d2 represent the inhibition rates of pro-inflammatory cytokines on the differentiation of M0 into M1, the inhibition rates of pro-inflammatory cytokines on the differentiation of M0 into M2, the conversion rate from M2 to M1, the conversion rate from M1 to M2, the migration rate of M1, and the migration rate of M2, respectively.

[0052] The ordinary differential equation for the change of pro-inflammatory cytokine (c1) over time is:

[0053]

[0054] In the formula, H1, k0, k1, These represent the inhibitory effect of anti-inflammatory cytokines on pro-inflammatory cytokines, the secretion rate of pro-inflammatory cytokines by fragments, the rate of secretion of pro-inflammatory cytokines by classically activated macrophages, and the decay rate of pro-inflammatory cytokines, respectively.

[0055] The ordinary differential equation for the change of anti-inflammatory cytokine (c2) over time is:

[0056]

[0057] In the formula, H2, k2, k3, These represent the inhibitory effect of anti-inflammatory cytokines on anti-inflammatory cytokines, the rate of secretion of anti-inflammatory cytokines by alternately activated macrophages, the secretion rate of anti-inflammatory cytokines by mesenchymal stem cells, and the decay rate of anti-inflammatory cytokines, respectively.

[0058] Mesenchymal stem cells (C m The time-varying ordinary differential equation is:

[0059]

[0060] In the formula, A m K lm F1 and F1 represent the total proliferation rate of mesenchymal stem cells, the upper limit of the mesenchymal stem cell population, and the inhibitory effect of pro-inflammatory cytokines on mesenchymal stem cells, respectively.

[0061] osteoblasts (C b The time-varying ordinary differential equation is:

[0062]

[0063] In the formula, A b K lb F1, d b These represent the total osteoblast proliferation rate, the upper limit of the osteoblast population, the inhibitory effect of pro-inflammatory cytokines on mesenchymal stem cells, and the osteoblast differentiation rate, respectively.

[0064] Fibrocartilage tissue (m c The time-varying ordinary differential equation is:

[0065]

[0066] In the formula, p cs q cd1 q cd2 These represent the formation rate of fibrocartilage tissue, the degradation rate of fibrocartilage tissue, and the degradation rate of fibrocartilage tissue by osteoblasts, respectively.

[0067] Woven bone (m) b The time-varying ordinary differential equation is:

[0068]

[0069] In the formula, p bs q bd These represent the formation rate and degradation rate of woven bone, respectively.

Claims

1. A method for modeling a fracture healing model under the action of macrophages, characterized in that, The method for modeling a fracture healing model under the action of macrophages includes the following steps: Step 1: Establish a basic fracture healing model based on accidental injury to human bone tissue and the subsequent healing process; Step 2: Based on the regulatory effects of macrophages and their secreted cytokines on cells in bone tissue, establish a fracture healing model based on the action of macrophages; Step 1: The specific process of establishing a fracture healing model is as follows: During fracture healing, the dynamic healing process is controlled by the interaction of eight cell types and cytokines: primary cell debris (D), macrophages (M), pro-inflammatory cytokines (C1), anti-inflammatory cytokines (C2), and mesenchymal stem cells (C5). m ), osteoblasts (C b ), fibrocartilage tissue (m c ) and woven bone (m b ); The ordinary differential equation for the change of primary cell debris (D) over time is: wherein k d debridement rate representing the clearance of primary cell debris; The ordinary differential equation for the change of macrophages (M) over time is: In the formula, k0 is the mobility of M, and d0 is the efflux of M; Mesenchymal stem cells (C m ) Ordinary differential equations over time are: In the formula, A m , K lm , F1 respectively represent the proliferation rate of total mesenchymal stem cells, the upper limit of the population number of mesenchymal stem cells, and the inhibitory effect of pro-inflammatory cytokines on mesenchymal stem cells. Osteoblasts (C b ) The ordinary differential equation over time is: In the formula, A b , K lb , F1, d b respectively represent the total osteoblast proliferation rate, the upper limit of the osteoblast population, the inhibition of mesenchymal stem cells by pro-inflammatory cytokines, and the osteoblast differentiation rate. The ordinary differential equation for the change of pro-inflammatory cytokine (c1) over time is: In the formula, G3, k1, k2, These represent the inhibitory effect of pro-inflammatory cytokines on the production of anti-inflammatory cytokines, the rate of secretion of inflammatory cytokines by primary cell debris, the rate of secretion of inflammatory cytokines by macrophages, and the decay rate of pro-inflammatory cytokines, respectively. The ordinary differential equation for the change of anti-inflammatory cytokine (c2) over time is: In the formula, G4 represents the inhibitory effect of anti-inflammatory cytokines on their production, and k4 represents the rate at which mesenchymal stem cells secrete anti-inflammatory cytokines. Indicates the decay rate of anti-inflammatory cytokines; Fibrocartilage tissue (m c ) The ordinary differential equation over time is: wherein p cs , q cd1 , q cd2 respectively represent the generation rate of fibrocartilage tissue, the degradation rate of fibrocartilage tissue, and the degradation rate of fibrocartilage tissue by osteoblasts; Woven bone (m b ) The ordinary differential equation over time is: In the formula, p bs , q bd respectively represent the generation rate of woven bone, the degradation rate of woven bone.

2. The method for modeling a fracture healing model under the action of macrophages according to claim 1, characterized in that, The specific process for establishing the fracture healing model under the action of macrophages is as follows: In the fracture healing process mediated by macrophages, the immune cells involved in fracture healing are primary cell debris (D), unactivated macrophages (M0), classically activated macrophages (M1), alternately activated macrophages (M2), pro-inflammatory cytokines (c1), and anti-inflammatory cytokines (c2); the affected bone tissue cells are mesenchymal stem cells (C1, C2, C3, C4, C5, C6, C7, C8, C9 ... m ), osteoblasts (C b ), fibrocartilage tissue (m c ), woven bone (m b ); The ordinary differential equation for the change of primary cell debris (D) over time is: In the formula, R D , These represent the saturation of phagocytosis rate of phagocytes, the fragment phagocytosis rate of M1, and the fragment phagocytosis rate of M2, respectively. The ordinary differential equation for the change of unactivated macrophages (M0) over time is: In the formula, R M G1, G2, and d0 represent the maximum value of undifferentiated macrophages at the injury site, the inhibition rate of pro-inflammatory cytokines on the differentiation of M0 into M1, the inhibition rate of pro-inflammatory cytokines on the differentiation of M0 into M2, and the migration rate of M0, respectively. The ordinary differential equations for the changes in classically activated macrophages (M1) and alternately activated macrophages (M2) over time are as follows: In the formula, G1, G2, k 21 k 12 d1 and d2 represent the inhibition rates of pro-inflammatory cytokines on the differentiation of M0 into M1, the inhibition rates of pro-inflammatory cytokines on the differentiation of M0 into M2, the conversion rate from M2 to M1, the conversion rate from M1 to M2, the migration rate of M1, and the migration rate of M2, respectively. The ordinary differential equation for the change of pro-inflammatory cytokine (c1) over time is: In the formula, H1, k0, k1, These represent the inhibitory effect of anti-inflammatory cytokines on pro-inflammatory cytokines, the secretion rate of pro-inflammatory cytokines by fragments, the rate of secretion of inflammatory cytokines by primary cell fragments, and the decay rate of pro-inflammatory cytokines, respectively. The ordinary differential equation for the change of anti-inflammatory cytokine (c2) over time is: In the formula, H2, k2, k3, These represent the inhibitory effect of anti-inflammatory cytokines on anti-inflammatory cytokines, the rate of macrophage secretion of inflammatory cytokines, the secretion rate of mesenchymal stem cells of anti-inflammatory cytokines, and the attenuation rate of anti-inflammatory cytokines, respectively. Mesenchymal stem cells (C m The time-varying ordinary differential equation is: In the formula, A m K lm F1 and F1 represent the total proliferation rate of mesenchymal stem cells, the upper limit of the population size of mesenchymal stem cells, and the inhibitory effect of pro-inflammatory cytokines on mesenchymal stem cells, respectively. osteoblasts (C b The time-varying ordinary differential equation is: In the formula, A b K lb F1, d b These represent the total osteoblast proliferation rate, the upper limit of the osteoblast population, the inhibitory effect of pro-inflammatory cytokines on mesenchymal stem cells, and the osteoblast differentiation rate, respectively. Fibrocartilage tissue (m c The time-varying ordinary differential equation is: In the formula, p cs q cd1 q cd2 These represent the formation rate of fibrocartilage tissue, the degradation rate of fibrocartilage tissue, and the degradation rate of fibrocartilage tissue by osteoblasts, respectively. Woven bone (m) b The time-varying ordinary differential equation is: In the formula, p bs q bd These represent the formation rate and degradation rate of woven bone, respectively.

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