Damage Function of a Quasi-Brittle Material, Damage Rate, Acceleration and Jerk during Uniaxial Compression: Model and Application to Analysis of Trabecular Bone Tissue Destruction

A diversity of quasi-brittle materials can be observed in various engineering structures and natural objects (rocks, frozen soil, concrete, ceramics, bones, etc.). In order to predict the condition and safety of these objects, a large number of studies aimed at analyzing the strength of quasi-brittle materials has been conducted and presented in publications. However, at the modeling level, the problem of estimating the rate and acceleration of destruction of a quasi-brittle material under loading remains relevant. The purpose of the study was to substantiate the function of damage to a quasi-brittle material under uniaxial compression, determine the rate, acceleration and jerk of the damage process, and also to apply the results obtained to predicting the destruction of trabecular bone tissue. In accordance with the purpose of the study, the basic concepts of fracture mechanics and standard methods of mathematical modeling were used. The proposed model is based on the application of the previously obtained differentiable damage function without parameters. The results of the study are presented in the form of plots and analytical relations for computing the rate, acceleration and jerk of the damage process. Examples are given. The predicted peak of the combined effect of rate, acceleration and jerk of the damage process are found to be of practical interest as an additional criterion for destruction. The simulation results agree with the experimental data known from the available literature.

MATHEMATICAL MODELING OF CANCELLOUS BONE TISSUE ADAPTATION APPLIED TO THE HUMAN MAXILLODENTAL SYSTEM

The bone tissue in different parts of the skeleton conforms to Wolff’s law: it aims to become optimal for the loading which acts on the corresponding bone; the bone is remodelling by means of osteosynthesis and resorption mechanisms. The modern problems of biomechanics demand research on the history of formation of bone structures in the course of time at both physiological and pathological loadings. Ever changing loadings of different nature have influence on development and functioning of the trabecular bone tissue. The mandible is one of the most liable to external and internal changes bones. Very often one has to deal with pathological changes caused by incorrect loading of different regions of bone tissue due to dysfunction of a dentition, a temporomandibular joint and so on. For example, the Popov-Godon’s syndrome which connects with tooth loss is accompanied by pathological remodelling of the surrounding bone tissue. Thus, the mathematical modeling of the cancellous bone tissue behavior in the human maxillodental system is one of the most topical problems of biomechanics and medicine. Trabecular bone tissue is a heterogeneous, porous, anisotropic material. Heterogeneity of spongy structure can be described by methods of quantitative stereology. At the same time, structural features of the trabecular bone can be described by means of the fabric tensor. This is possible to implement if there is both a constitutive relation which connects the stress tensor, the fabric tensor, and the strain tensor, and kinetic equations which describe the evolution of the fabric tensor and bone density. An initial boundary value problem on the trabecular bone tissue remodelling is stated. The effective numerical algorithm allowing to solve the problem is developed. This algorithm is implemented as a complex of problem-oriented programs. Verification of the model and identification of its parameters are carried out. All numerical calculations are performed using the ANSYS software. Trabecular bone tissue evolution is demonstrated on the set of model examples when the stress–strain state is changed. The results demonstrate different character of influence of changes of loading conditions on process of structure formation which follows from Wolff’s law.

P0871THE IMPACT OF ENDOGENOUS PTH/PTH1R/ATF4 AXIS ON TRABECULAR AND CORTICAL BONE REMODELING AND BONE GROWTH OF YOUNG RATS WITH EXPERIMENTAL CHRONIC KIDNEY DISEASES

Background and Aims Chronic kidney disease - mineral bone disorder (CKD–MBD) is one of the major clinical complications in patients with chronic kidney disease (CKD). Bone remodeling has been suggested to play a fundamental role in the maintenance of skeletal integrity via a balance between the bone formation/resorption process. The parathyroid hormone (PTH) is a key hormone controlling bone metabolism. PTH is known to affect bone with a net catabolic and anabolic effect but the mechanisms responsible for these differing effects are poorly understood. Previously, we demonstrated the distinct effect of mild degree of CKD on trabecular and cortical bone strength in rapidly growing rats (Pawlak et al. PlosOne, 2016). The aim of the present study was to evaluate the effect of endogenous PTH, its receptor PTH1R and activating transcription factor 4 (ATF4) – the major regulators of the anabolic PTH response in osteoblasts on bone remodeling and growth of young rats with experimental CKD. Method Four-week old Wistar male rats were divided into 2 groups: with CKD induced by surgical 5/6 subtotal nephrectomy, and sham-operated (CON). After one (CON-1; CKD-1) and three months (CON-3; CKD-3) of the surgery the femurs were collected and their lengths were measured. The activity of alkaline phosphatase (ALP), a bone formation marker, and tartrate-resistant acid phosphatase (TRACP5b) reflecting bone resorption were determined in homogenates from trabecular and cortical left femurs. The expression of PTH1R and ATF4 gene was determined by QRT-PCR in right femurs. Serum PTH was analyzed using ELISA kit. Computations were performed using Statistica ver.10 computer software. Results Serum PTH was increased in CKD-3 compared to CKD-1, moreover the slight increase in PTH levels was noted in CKD-3 compared to appropriate controls (both p<0.05). The activity of ALP and TRACP5b in trabecular bone tissue were significantly lower in CKD-3 compared to CKD-1 rats (p<0.01 and p<0.05; respectively). There was a strong positive correlation between ALP and TRACP5b in this bone region (R =0.624, p =0.002), whereas both ALP and TRACP5b were inversely related to serum PTH (R = -0.534, p =0.012 and R = -0.636, p =0.002; respectively). The activity of TRACP5b in cortical bone tissue was significantly higher in CKD-3 compared to CKD-1 group (p<0.05), and it was positively associated with PTH levels (R =0.597, p =0.004). There was no difference in ALP activity between the studied groups, and ALP was not associated with TRACP5b in this bone region. The expression of ATF4 and PTH1R genes was significantly increased in the CKD-3 group compared with the appropriate control (p<0.01 and p<0.05; respectively) and with the CKD-1 group (p<0.05 and p<0.01; respectively). The expression of ATF4 was inversely correlated with ALP and TRACP5b in trabecular bone (R = -0.534, and R = -0.528, both p<0.05), whereas it was positively related to TRACP5b in cortical bone region (R =0.418, p<0.05). The femoral length was significantly increased during 3-month of CKD development (p<0.000), and it was positively associated with PTH levels (R =0.571, p =0.007), cortical TRACP5b activity (R =0.609, p =0.002) and tended to be related with ATF4 gene expression (R =0.409, p =0.065). In contrast, the femoral length was inversely related to ALP activity in trabecular bone tissue (R= -0.656, p =0.0007). Conclusion The endogenous PTH, through PTH1R/ATF4 axis, inhibited trabecular bone remodeling. In contrary, PTH/PTH1R/ATF4 system intensified bone resorption in cortical bone region. This opposite effect of PTH on bone remodeling was associated with the intensification of growth process in the long bones of young rats with CKD.

First Biomimetic Fixation for Resurfacing Arthroplasty: Investigation in Swine of a Prototype Partial Knee Endoprosthesis

Resurfacing hip and knee endoprostheses are generally embedded in shallow, prepared areas in the bone and secured with cement. Massive cement penetration into periarticular bone, although it provides sufficient primary fixation, leads to the progressive weakening of peri-implant bone and results in failures. The aim of this paper was to investigate in an animal model the first biomimetic fixation of components of resurfacing arthroplasty endoprostheses by means of the innovative multispiked connecting scaffold (MSC-Scaffold). The partial resurfacing knee arthroplasty (RKA) endoprosthesis working prototype with the MSC-Scaffold was designed for biomimetic fixation investigations using reverse engineering methods and manufactured by selective laser melting. After Ca-P surface modification of bone contacting surfaces of the MSC-Scaffold, the working prototypes were implanted in 10 swines. Radiological, histopathological, and micro-CT examinations were performed on retrieved bone-implant specimens. Clinical examination confirmed very good stability (4 in 5-point Likert scale) of the operated knee joints. Radiological examinations showed good implant fixation (radiolucency less than 2 mm) without any signs of migration. Spaces between the MSC-Scaffold spikes were penetrated by bone tissue. The histological sections showed newly formed trabecular bone tissue between the spikes, and the trabeculae of periscaffold bone were seen in contact with the spikes. The micro-CT results showed the highest percentage of bone tissue ingrowths into the MSC-Scaffold at a distance of 2.5÷3.0 mm from the spikes bases. The first biomimetic fixation for resurfacing arthroplasty was successfully verified in 10 swines investigations using RKA endoprosthesis working prototypes. The performed research shows that the MSC-Scaffold allows for cementless and biomimetic fixation of resurfacing endoprosthesis components in periarticular cancellous bone.