# Improving the Endoprosthesis Design and the Postoperative Therapy as a Means of Reducing Complications Risks after Total Hip Arthroplasty

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Constructive and Technological Factors Influencing the Development of Complications after THR

- Intraoperative (fractures of the hip, pelvis, damage to the great vessels, perforation of the femoral canal);
- Early postoperative (suppuration, thrombosis, thrombophlebitis, dislocation of the endoprosthesis head, neuritis, decompensation of concomitant pathology);
- Late postoperative (deep suppuration, periprosthetic fractures, aseptic loosening, instability of implants due to improper planning of the operation or as a result of operation, destruction of the endoprosthesis components).

- Polymers (polytetrafluoroethylene (PTFE), ultra-high molecular weight polyethylene (UHMWPE), cross-linked polyethylene (XLPE), highly cross-linked polyethylene (HXLPE), vitamin E-blended polymers, polyether-ether-ketone (PEEK), poly 2-methacryloyloxyethyl phosphorylcholine (PMPC), polycarbonate-urethane (PCU));
- Metals (Stainless steel, Cobalt-chromium-molybdenum (CoCrMo) alloys, Titanium alloys (Ti-6Al-4V), Zirconium alloy (Zr-2.5Nb));
- Metal alloy surface coatings (Titanium nitride (TiN), Silicon nitride (Si3N4), Diamond-like carbon (DLC), aluminum, nanocrystalline diamond (NCD));
- ceramics (aluminum ceramic, zirconia, zirconia-toughened alumina (ZTA), sapphire).

- hard-on-soft bearings (metal-on-polyethylene (MOP) is a metal femoral head and a polyethylene acetabular liner, ceramic-on-polyethene (COP) is a ceramic femoral head and a polyethylene acetabular liner);
- hard-on-hard bearings (metal-on-metal (MOM), ceramic-on-ceramic (COC), and ceramic-on-metal (COM) is a ceramic femoral head and a metal acetabular liner).

#### 2.2. Mechanobiological Models of Implant Osseointegration

^{2}(*) is the divergence grad (*); ${c}_{m},{c}_{c},{c}_{b}$ are the current concentrations, ${K}_{lm}=\frac{1}{{\alpha}_{m}},{K}_{lc}=\frac{1}{{\alpha}_{c}},{K}_{lb}=\frac{1}{{\alpha}_{b}}$ are the limiting concentrations, ${A}_{m},{A}_{c},{A}_{b}$ are the degrees of mesenchymal cells, chondrocytes and osteoblasts proliferation, respectively; ${m}_{c},{m}_{b}$, ${g}_{c},{g}_{b}$ are the matrix volumetric densities of the connective/cartilage tissue, bone tissue, chondrogenic and osteogenic growth factors, respectively; ${D}_{cm},{C}_{cm}$ are haptotactic and haptokinetic rates of cell migration; ${F}_{1},{F}_{2},{F}_{3}$are functions that link cell differentiation with the concentration of growth factors; ${P}_{cs},{P}_{bs}$ are constants representing connective/cartilage and bone matrix; ${Q}_{cd1},{Q}_{cd2},{Q}_{bd}$ are constants representing matrix degradation; ${D}_{gc},{D}_{gb}$ are the diffusion coefficients of chondrocytes and osteoblasts; ${E}_{gc},{E}_{gb}$ are functions that link the production of growth factors with the concentration of growth factors; ${d}_{gc},{d}_{gb}$ are decay constants. Sets of calculated model parameters:

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Model state variables | |||

Platelets population density | $T$ | $\mathrm{cells}\xb7\mathrm{m}{\mathrm{L}}^{-1}$ | |

Osteogenic cells population density | $C$ | $\mathrm{cells}\xb7\mathrm{m}{\mathrm{L}}^{-1}$ | |

Osteoblasts population density | $B$ | $\mathrm{cells}\xb7\mathrm{m}{\mathrm{L}}^{-1}$ | |

Type 1 growth factors concentration (PDGF, TGF-β) | ${f}_{1}$ | $\mathrm{ng}\xb7\mathrm{m}{\mathrm{L}}^{-1}$ | |

Type 2 growth factors concentration (BMP, superfamily TGF-β) | ${f}_{2}$ | $\mathrm{ng}\xb7\mathrm{m}{\mathrm{L}}^{-1}$ | |

Fibrin network volume fraction | ${v}_{f}$ | $\mathrm{m}{\mathrm{L}}^{-1}$ | |

Woven bone volume fraction | ${v}_{w}$ | $\mathrm{m}{\mathrm{L}}^{-1}$ | |

Lamellar bone volume fraction) | ${v}_{l}$ | $\mathrm{m}{\mathrm{L}}^{-1}$ | |

Concentration of adsorbed proteins (принимается в зависимoсти oт сoстoяния пoверхнoсти имплантата) | $p$ | - | $\mathsf{\mu}\mathrm{g}\xb7\mathrm{m}{\mathrm{m}}^{-2}$ |

Constant model parameters | |||

Platelet diffusion coefficient | ${D}_{T}$ | $1.365\times {10}^{-2}$ | $\mathrm{m}{\mathrm{m}}^{2}\xb7\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ |

Diffusion coefficient of osteogenic cells | ${D}_{C}$ | $0.133$ | $\mathrm{m}{\mathrm{m}}^{2}\xb7\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ |

Diffusion coefficient of type 1 growth factors | ${D}_{f1}$ | $0.3$ | $\mathrm{m}{\mathrm{m}}^{2}\xb7\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ |

Diffusion coefficient of type 2 growth factors | ${D}_{f2}$ | $0.1$ | $\mathrm{m}{\mathrm{m}}^{2}\xb7\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ |

The coefficient of chemotaxis along gradient of growth factors type 1 | ${K}_{1}$ | $0.667$ | $\mathrm{m}{\mathrm{m}}^{2}\xb7\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}\xb7{\left(\frac{\mathrm{ng}}{\mathrm{mL}}\right)}^{-1}$ |

The coefficient of chemotaxis along gradient of growth factors type 2 | ${K}_{2}$ | $0.167$ | $\mathrm{m}{\mathrm{m}}^{2}\xb7\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}\xb7{\left(\frac{\mathrm{ng}}{\mathrm{mL}}\right)}^{-1}$ |

Linear platelet taxis coefficient | ${H}_{T}$ | $0.333$ | $\mathrm{m}{\mathrm{m}}^{2}\xb7\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}\xb7\mathsf{\mu}{\mathrm{g}}^{-1}$ |

The coefficient of platelet death due to inflammation | ${A}_{T}$ | $0.067$ | ${\mathrm{day}}^{-1}$ |

The coefficient t of natural death of osteogenic cells | ${A}_{\mathrm{C}}$ | $2\times {10}^{-3}$ | ${\mathrm{day}}^{-1}$ |

The coefficient of differentiation of osteoblasts into osteocytes | ${A}_{B}$ | $6.67\times {10}^{-3}$ | ${\mathrm{day}}^{-1}$ |

Natural decay rate of type 1 growth factors | ${A}_{f1}$ | $10$ | ${\mathrm{day}}^{-1}$ |

Natural decay rate of type 2 growth factors | ${A}_{f2}$ | $10$ | ${\mathrm{day}}^{-1}$ |

The coefficient of influence the concentration of adsorbed proteins on the secretion of growth factors of type 1 | ${\alpha}_{T1}$ | $6.67\times {10}^{-5}$ | $\frac{\mathrm{ng}}{\mathrm{mL}}\xb7{\mathrm{day}}^{-1}\xb7{\left(\frac{\mathrm{cells}}{\mathrm{mL}}\right)}^{-1}$ |

The coefficient of natural secretion of growth factors type 1 | ${\alpha}_{T2}$ | ${10}^{-5}$ | $\frac{\mathrm{ng}}{\mathrm{mL}}\xb7{\mathrm{day}}^{-1}\xb7{\left(\frac{\mathrm{cells}}{\mathrm{mL}}\right)}^{-1}$ |

The coefficient of natural proliferation of osteogenic cells | ${\alpha}_{C0}$ | $0.25$ | ${\mathrm{day}}^{-1}$ |

The coefficient of enhancing the proliferation of osteogenic cells by growth factors | ${\alpha}_{C}$ | $0.25$ | ${\mathrm{day}}^{-1}$ |

The coefficient of influence of growth factors type 1 on the proliferation of osteoblasts | ${\alpha}_{CB}$ | $0.5$ | ${\mathrm{day}}^{-1}$ |

The coefficient of natural secretion of type 2 growth factors in the environment of osteogenic cells | ${\alpha}_{C2}$ | $2.5\times {10}^{-3}$ | $\frac{\mathrm{ng}}{\mathrm{mL}}\xb7{\mathrm{day}}^{-1}\xb7{\left(\frac{\mathrm{cells}}{\mathrm{mL}}\right)}^{-1}$ |

The coefficient of natural secretion of type 2 growth factors in the environment of osteoblasts | ${\alpha}_{B2}$ | $2.5\times {10}^{-3}$ | |

The coefficient of influence of type 2 growth factors on bone synthesis | ${\alpha}_{w}$ | ${10}^{-7}$ | ${\mathrm{day}}^{-1}\xb7{\left(\frac{\mathrm{cells}}{\mathrm{mL}}\right)}^{-1}$ |

$\mathrm{Bone}\text{}\mathrm{remodeling}\text{}\mathrm{coefficient}\text{}(\mathrm{determined}\text{}\mathrm{by}\text{}\mathrm{numerical}\text{}\mathrm{simulation}\text{}\mathrm{to}\text{}\mathrm{achieve}\text{}{v}_{l}09$ within one year) | $\gamma $ | - | - |

Additional concentration of adsorbed proteins in the platelet environment | ${\beta}_{T1}$ | $0.1$ | $\mathsf{\mu}\mathrm{g}\xb7{\left({\mathrm{mm}}^{2}\right)}^{-1}$ |

Additional concentration of type 1 growth factors in the platelet environment | ${\beta}_{T2}$ | $10$ | $\mathrm{ng}\xb7{\mathrm{mL}}^{-1}$ |

Additional concentration of type 2 growth factors in the environment of osteogenic cells | ${\beta}_{C2}$ | $10$ | $\mathrm{ng}\xb7{\mathrm{mL}}^{-1}$ |

Additional concentration of type 2 growth factors in the environment of osteoblasts | ${\beta}_{B2}$ | $10$ | $\mathrm{ng}\xb7{\mathrm{mL}}^{-1}$ |

Additional concentration of growth factors affecting the proliferation of osteogenic cells | ${\beta}_{C}$ | $10$ | $\mathrm{ng}\xb7{\mathrm{mL}}^{-1}$ |

Additional concentration of growth factors affecting the proliferation of osteoblasts | ${\beta}_{CB}$ | $10$ | $\mathrm{ng}\xb7{\mathrm{mL}}^{-1}$ |

Additional concentration of type 2 growth factors affecting bone formation | ${\beta}_{w}$ | $10$ | $\mathrm{ng}\xb7{\mathrm{mL}}^{-1}$ |

Limiting cell density | $N$ | ${10}^{6}$ | $\mathrm{cells}\xb7{\mathrm{mL}}^{-1}$ |

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**Figure 2.**The improved ceramic head: (

**a**) general view of the experimental sample; (

**b**) elements of the internal structure (description of elements indicated by numbers is given in the text below).

**Figure 3.**Change in platelet population density: (

**a**) $p\left(x\right)={p}_{10}\xb7{e}^{-2x}$; (

**b**) $p\left(x\right)={p}_{20}\xb7{e}^{-2x}$.

**Figure 4.**Dynamics of the processes of changes in the concentration of osteogenic cells in the periprosthetic space under different modes of implant osseointegration.

**Figure 5.**Dynamics of the processes of changes in the concentration of osteoblasts in the periprosthetic space under different modes of implant osseointegration.

**Figure 6.**Changes in the state variables of the Equations (24)–(28) depending on the parameters that determine the natural death of osteogenic cells and the influence of type 1 growth factors on the proliferation of osteoblasts: (

**a**) Osteogenic cells population density; (

**b**) Osteoblasts population density; (

**c**) Fibrin network volume fraction); (

**d**) Woven bone volume fraction; (

**e**) Lamellar bone volume fraction.

**Figure 7.**Change in the state variables of the Equations (24)–(28) depending on the diffusion coefficient of osteogenic cells: (

**a**) Osteogenic cells population density; (

**b**) Osteoblasts population density; (

**c**) Fibrin network volume fraction); (

**d**) Woven bone volume fraction; (

**e**) Lamellar bone volume fraction.

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**MDPI and ACS Style**

Popov, V.L.; Poliakov, A.M.; Pakhaliuk, V.I.
Improving the Endoprosthesis Design and the Postoperative Therapy as a Means of Reducing Complications Risks after Total Hip Arthroplasty. *Lubricants* **2022**, *10*, 38.
https://doi.org/10.3390/lubricants10030038

**AMA Style**

Popov VL, Poliakov AM, Pakhaliuk VI.
Improving the Endoprosthesis Design and the Postoperative Therapy as a Means of Reducing Complications Risks after Total Hip Arthroplasty. *Lubricants*. 2022; 10(3):38.
https://doi.org/10.3390/lubricants10030038

**Chicago/Turabian Style**

Popov, Valentin L., Aleksandr M. Poliakov, and Vladimir I. Pakhaliuk.
2022. "Improving the Endoprosthesis Design and the Postoperative Therapy as a Means of Reducing Complications Risks after Total Hip Arthroplasty" *Lubricants* 10, no. 3: 38.
https://doi.org/10.3390/lubricants10030038