Simulation of the nutrient supply in fracture healing

Potential use of barks of woody vascular plants in bone mending: A review

The use of synthetic drugs to overcome bone ailments causes severe side effects, but the application of herbals is helpful in maintaining bone health and accelerating bone mending. Currently, there is no oral allopathic medicine to hasten bone healing, though folk and traditional practices have adopted herbal to fasten the recovery from bone ailments. Earliest recovery is a universally desired phenomenon, especially for elderly people where many more cases of traumatic injuries are common along the compromised body immunity. The computerized database search engines, such as Google Scholar, PubMed, ScienceDirect, Springer Link, etc., and textbooks were used to collect all relevant information about barks for bone mending activity published from 1990 onwards using certain keywords such as bark, folklore/ traditional bone healing practices, and phytopharmacology. The results obtained were compiled to make this review and related information is tabulated herewith. Traditional herbal bone healing exists in every society in the world. The plant barks of a few species (e.g., Ficus religiosa, Prunus cerasoides, Terminalia arjuna, etc.) have outstanding significance for bone healing because of their special chemical composition and novel properties to reduce swelling, pain, soreness, and speedy recovery of functions. Mostly bark extracts are rich in polyphenols, and minerals, represented with antioxidant, immunostimulatory, antibacterial properties, etc. There is a diversity of bark utilization for bone healing from different plant species, globally, of which only a few have been phytopharmacologically deciphered. Validated bark ingredients as medicine or food supplements are more useful due to the least side effects. Entrepreneurs have a scope to use bioactive obtained from plant barks that have not been scientifically screened till now. The research focused on the commercial application of plant barks as green medicine needs fingerprints of bioactive and clinically validated data including the concentration of biomarkers in the blood (IC50) for reducing the healing period. Phytopharmacological screening of barks used in folk medicine and synthesizing the therapeutics at mega quantities in industries is an array of hopes for sustainable utilization of natural resources. The bio-stimulating knowledge of certain herbal ingredients will be helpful in the development of synergistic formulations for rapid bone mending.

A numerical bone regeneration model incorporating angiogenesis, considering oxygen-induced secretion of vascular endothelial growth factor and vascular remodeling

Angiogenesis is considered playing an important role in bone regeneration. Studies have shown that angiogenesis is affected by biological factors, oxygen tension, and blood flow. In this paper, we propose a bone regeneration model with angiogenesis based on the theories of mechanobiology regulation, vascular network modeling, oxygen-induced secretion of vascular endothelial growth factor (VEGF), and vascular remodeling. The results showed that this model can describe the distribution and concentration of vascular endothelial growth factor induced by oxygen tension during bone regeneration, the growth and remodeling of vascular tissue under the influence of vascular endothelial growth factor and mechanical loading, and the correspondence between vascular tissue and bone regeneration.

Recycled windshield glass as new material for producing ultrasonic phantoms of cortical bone-healing stages

The quantitative ultrasound technique was used to evaluate bone-mimicking phantoms; however, these phantoms do not mimic the intermediate stages of cortical bone healing. We propose using windshield glass as an original material to produce phantoms that mimic the characteristics of three different stages of cortical bone healing. This material was processed via a route that included breaking, grinding, compacting, drying, and sintering in four temperature groups: 625 °C, 645 °C, 657 °C, and 663 °C. The parameters evaluated were the ultrasonic longitudinal phase velocity (cL), corrected (αc) ultrasonic attenuation coefficient, and bulk density (ρs). The results showed that the mean values ofcL,αc,andρsvaried from 2, 398 to 4, 406 m·s^-1, 3 to 10 dB·cm^-1, and 1, 563 to 2, 089 kg·m^-3, respectively. The phantoms exhibited properties comparable with the three stages of cortical bone healing and can be employed in diagnostic and therapeutic studies using ultrasound.

Optimal time-dependent levels of weight-bearing for bone fracture healing under Ilizarov circular fixators

It is known that weight-bearing exercises under Ilizarov circular fixators (ICF) could enhance bone fracture healing by mechano-regulation. However, interfragmentary movements at the fracture site induced by weight-bearing may inhibit angiogenesis and ultimately delay the healing process. To tackle this challenge, a computational model is presented in this study which considers the spatial and temporal changes in mechanical properties of fracture callus to predict optimal levels of weight-bearing during fracture healing under ICF. The study takes sheep fractures as example and shows that the developed model has the capability of predicting patient specific, time-dependent optimal levels of weight-bearing which enhances mechano-regulation mediated healing without hindering the angiogenesis process. The results demonstrate that allowable level of weight-bearing and timings depend on fracture gap size. For normal body weights (BW) and moderate fracture gap sizes (e.g. 3 mm), weight-bearing with 30% BW could start by week 4 post-operation and gradually increase to 100% BW by week 11. In contrast, for relatively large fracture gap sizes (i.e. 6 mm), weight-bearing is recommended to commence in later stages of healing (e.g. week 11 post-operation). Furthermore, increasing ICF stiffness (e.g. using half pins instead of pretension wires) can increase the level of weight-bearing significantly in the early stages up to a certain time point (e.g. week 8 post-operation) beyond which no noticeable benefits could be achieved. The findings of this study have potential applications in designing post-operative weight bearing exercises.

Domain-independent simulation of physiologically relevant callus shape in mechanoregulated models of fracture healing

Mechanoregulatory models have been used to predict the progression of bone fracture healing for more than two decades. However, many published studies share the same fundamental limitation: callus development proceeds within a pre-defined domain that both restricts and directs healing and leads to some non-physiologic healing patterns. To address this limitation, we added two spatial proximity functions to an existing mechanoregulatory model of fracture healing to control the localization of callus within the healing domain. We tested the performance of the new model in an idealized ovine tibial osteotomy with medial plate fixation using three sizes of healing domains and multiple variations of the spatial proximity functions. All model variations produced outward callus growth and bridging weighted toward the far cortex, which is consistent with in vivo healing. With and without the proximity functions, there were marked differences in the predicted callus volume and shape. With no proximity functions, the callus produced was strongly domain dependent, with a 15% difference in volume between the smallest and largest initialization domains. With proximity function control, callus growth was restricted to near the fracture line and there was only 2% difference in volume between domain sizes. Superimposing both proximity functions - one to control outward growth and one representing a decay in periosteal activity away from the fracture - produced a predicted callus size that was within the physiologic range for sheep and had a realistic morphology when compared with fluorescent dye co-localization with calcium deposition over time and histology.

Morphology of bony callus growth in healing of a sheep tibial osteotomy

Long bone fractures typically heal via formation of an external callus, which helps stabilise the bone fragments. Callus composition and morphology influence the mechanical environment, which in turn regulates the progression of healing. Therefore characterising callus development over time is crucial in understanding this mechanobiological regulation. Although bony callus is often assumed to grow towards the fracture from either side, this is not consistent with observations from large animal studies and clinical cases. Therefore, we sought to quantify the morphology of bony callus over time in a large animal model. Sheep tibiae were x-rayed weekly over eight weeks following an osteotomy (n=5), with fixation allowing up to 10% axial displacement under normal weight-bearing. After scaling radiographs by known landmarks and normalising greyscales, bony callus boundaries were defined by manual segmentation. The lateral callus area and coordinates of its centroid were calculated from each image. The external callus initially formed adjacent to the osteotomy site. Over the first four weeks, callus growth from its outer surfaces was characterised by its centre of area moving outwards and away from the osteotomy, on both proximal and distal fragments. Subsequent weeks showed consolidation and resorption from the outer surface of the callus. Our approach allowed bony callus development to be tracked in individuals throughout healing. Contrary to the view that periosteal bone formation originates distant from the fracture, our data showed bony callus adjacent to the defect from early stages, followed by approximately concentric growth. This discrepancy highlights the need for data specific to experimental conditions, and particularly early stages of healing, for evaluating theoretical models of mechanical regulation.

Effect of ultrasound on bone fracture healing: A computational mechanobioregulatory model

Bone healing process is a complicated phenomenon regulated by biochemical and mechanical signals. Experimental studies have shown that ultrasound (US) accelerates bone ossification and has a multiple influence on cell differentiation and angiogenesis. In a recent work of the authors, a bioregulatory model for providing bone-healing predictions was addressed, taking into account for the first time the salutary effect of US on the involved angiogenesis. In the present work, a mechanobioregulatory model of bone solidification under the US presence incorporating also the mechanical environment on the regeneration process, which is known to affect cellular processes, is presented. An iterative procedure is adopted, where the finite element method is employed to compute the mechanical stimuli at the linear elastic phases of the poroelastic callus region and a coupled system of partial differential equations to simulate the enhancement by the US cell angiogenesis process and thus the oxygen concentration in the fractured area. Numerical simulations with and without the presence of US that illustrate the influence of progenitor cells' origin in the healing pattern and the healing rate and simultaneously demonstrate the salutary effect of US on bone repair are presented and discussed.

Three-dimensional computational model simulating the fracture healing process with both biphasic poroelastic finite element analysis and fuzzy logic control

A dynamic model regulated by both biphasic poroelastic finite element analysis and fuzzy logic control was established. Fuzzy logic control was an easy and comprehensive way to simulate the tissue differentiation process, and it is convenient for researchers and medical experts to communicate with one another to change the fuzzy logic rules and improve the simulation of the tissue differentiation process. In this study, a three-dimensional fracture healing model with two different interfragmentary movements (case A: 0.25 mm and case B: 1.25 mm) was analysed with the new set-up computational model. As the healing process proceeded, both simulated interfragmentary movements predicted a decrease and the time that the decrease started for case B was later than that for case A. Compared with experimental results, both cases corresponded with experimental data well. The newly established dynamic model can simulate the healing process under different mechanical environments and has the potential to extend to the multiscale healing model, which is essential for reducing the animal experiments and helping to characterise the complex dynamic interaction between tissue differentiations within the callus region.

A theoretical analysis and finite element simulation of fixator-bone system stiffness on healing progression

INTRODUCTION

The unilateral external fixator has become a quick and easy application for fracture stabilization of the extremities; the main value for evaluation of mechanical stability of the external fixator is stiffness. The stiffness property of the external fixator affects the local biomechanical environment of fractured bone.

METHODS

In this study, a theoretical model with changing Young's modulus of the callus is established by using the Castigliano's theory, investigating compression stiffness, torsional stiffness and bending stiffness of the fixator-bone system during the healing process. The effects of pin deviation angle on three stiffness methods are also investigated. In addition, finite element simulation is discussed regarding the stress distribution between the fixator and bone.

RESULTS

The results reveal the three stiffness evaluation methods are similar for the fixator-bone system. Finite element simulation shows that with increased healing time, the transmission of the load between the fixator and bone are different. In addition, the finite element analyses verify the conclusions obtained from the theoretical model.

CONCLUSIONS

This work helps orthopedic doctors to monitor the progression of fracture healing and determine the appropriate time for removal of a fixation device and provide important theoretical methodology.

Novel systems for the application of isolated tensile, compressive, and shearing stimulation of distraction callus tissue

Background

Distraction osteogenesis is a procedure widely used for the correction of large bone defects. However, a high complication rate persists, likely due to insufficient stability during maturation. Numerical fracture healing models predict bone regeneration under different mechanical conditions allowing fixation stiffness optimization. However, most models apply a linear elastic material law inappropriate for the transient stresses/strains present during limb lengthening or segment transport. They are also often validated using in vivo osteotomy models lacking precise mechanical regulation due to the unavoidable stimulation of secondary interfragmentary motion during ambulation under finitely stiff fixation. Therefore, in order to create a robust numerical model of distraction osteogenesis, it is necessary to both characterize the new tissue’s viscoelasticity during distraction and determine the influence of strictly isolated stimulation in each loading mode (tension, compression, and shear) to account for potential differences in mechanical and histological response.

Aim

Two electromechanical fixators with integrated load cells were designed to precisely perform and monitor in vivo lateral distraction and isolated stimulation in sheep tibiae using a mobile, hydroxyapatite-coated titanium plate. The novel surgical procedure circumvents osteotomy, eliminating the undesirable and unquantifiable mechanical stimulation during ambulation.

Methods

After a 10-day post-surgery latency period, two 0.275 mm distraction steps were performed daily for 10 days. The load cell collected data before, during, and after each distraction step and was terminated after no less than one minute from the time of distraction. A 7-day consolidation period separated the distraction phase and 18-day stimulation phase. Stimulation was carried out in isolated tension, compression, or shear while recording force/time data. Each stimulation session consisted of 120 cycles with a magnitude of either 0.1 mm or 0.6 mm in the tension and compression groups and 1.0 mm in the shear group. The animals were euthanized after a 3-day holding period following stimulation.

Results

Our initial results show that the tissue progressively stiffens and maintains an increasingly large residual traction. The force curves during compressive stimulation show a progressive drift from compression toward tension. We hypothesize that this behavior may be due to the preferential flow of fluid outward from the tissue and a greater resistance to reabsorption during the plate’s return to the starting position.

Multiscale Modeling of Bone Healing: Toward a Systems Biology Approach

Bone is a living part of the body that can, in most situations, heal itself after fracture. However, in some situations, healing may fail. Compromised conditions, such as large bone defects, aging, immuno-deficiency, or genetic disorders, might lead to delayed or non-unions. Treatment strategies for those conditions remain a clinical challenge, emphasizing the need to better understand the mechanisms behind endogenous bone regeneration. Bone healing is a complex process that involves the coordination of multiple events at different length and time scales. Computer models have been able to provide great insights into the interactions occurring within and across the different scales (organ, tissue, cellular, intracellular) using different modeling approaches [partial differential equations (PDEs), agent-based models, and finite element techniques]. In this review, we summarize the latest advances in computer models of bone healing with a focus on multiscale approaches and how they have contributed to understand the emergence of tissue formation patterns as a result of processes taking place at the lower length scales.

Dietary Recommendations in Fracture Healing in Traditional Persian Medicine: A Historical Review of Literature

BACKGROUND

Fracture repair is a complex process. An inappropriate diet is a contributing risk factor for fracture nonunion. The aim of this study was to extract dietary recommendations for fracture healing according to traditional Persian medicine (TPM) literature.

METHOD

The contents relevant to diets in fracture healing were selected from main textbooks in TPM like Al Qanon fi Al-teb ( The Canon). Other reference textbooks in traditional medicine were also used for a comprehensive study in this respect. Finally content analysis was used for summarizing and describing the results.

FINDINGS

Food stuffs are classified in TPM according to their nutritive value, their assimilability, and the quality of achieved chyme. Some light meals like chicken soup are recommended for the early days of fracture and high-nutrient and dense foods such as goat's or sheep's head and nuts are advised in following days for fracture healing acceleration and callus formation. Several recommendations are also provided for pacing the healing process.

CONCLUSION

A comparison of Avicenna and other Persian sage's recommended regimens with the recent evidence revealed the potential positive effects of their regimen for bone healing acceleration. It can shed light on a part of history of orthopedics and add to current knowledge about bone fracture and its management.

Computational modeling of bone fracture non-unions: four clinically relevant case studies

The human skeleton has a remarkable regeneration capacity. Nevertheless, 5-10 % of the bone fractures fails to heal and develops into a non-union which is a challenging orthopedic complication requiring complex and expensive treatment. This review paper will discuss four different computational models, each capturing a particular clinical case of non-union: non-union induced by reaming of the marrow canal and periosteal stripping, non-union due to a large interfragmentary gap, non-union due to a genetic disorder [i.e. NF1 related congenital pseudoarthrosis of the tibia (CPT)] and non-union due to mechanical overload. Together, the four computational models are able to capture the etiology of a wide range of fracture non-union types and design novel treatment strategies thereof. Further research is required to corroborate the computational models in both animal and human settings and translate them from bench to bed side.

Mechanical regulation of bone regeneration: theories, models, and experiments

How mechanical forces influence the regeneration of bone remains an open question. Their effect has been demonstrated experimentally, which has allowed mathematical theories of mechanically driven tissue differentiation to be developed. Many simulations driven by these theories have been presented, however, validation of these models has remained difficult due to the number of independent parameters considered. An overview of these theories and models is presented along with a review of experimental studies and the factors they consider. Finally limitations of current experimental data and how this influences modeling are discussed and potential solutions are proposed.

Substrate stiffness and oxygen as regulators of stem cell differentiation during skeletal tissue regeneration: a mechanobiological model

Extrinsic mechanical signals have been implicated as key regulators of mesenchymal stem cell (MSC) differentiation. It has been possible to test different hypotheses for mechano-regulated MSC differentiation by attempting to simulate regenerative events such as bone fracture repair, where repeatable spatial and temporal patterns of tissue differentiation occur. More recently, in vitro studies have identified other environmental cues such as substrate stiffness and oxygen tension as key regulators of MSC differentiation; however it remains unclear if and how such cues determine stem cell fate in vivo. As part of this study, a computational model was developed to test the hypothesis that substrate stiffness and oxygen tension regulate stem cell differentiation during fracture healing. Rather than assuming mechanical signals act directly on stem cells to determine their differentiation pathway, it is postulated that they act indirectly to regulate angiogenesis and hence partially determine the local oxygen environment within a regenerating tissue. Chondrogenesis of MSCs was hypothesized to occur in low oxygen regions, while in well vascularised regions of the regenerating tissue a soft local substrate was hypothesised to facilitate adipogenesis while a stiff substrate facilitated osteogenesis. Predictions from the model were compared to both experimental data and to predictions of a well established computational mechanobiological model where tissue differentiation is assumed to be regulated directly by the local mechanical environment. The model predicted all the major events of fracture repair, including cartilaginous bridging, endosteal and periosteal bony bridging and bone remodelling. It therefore provides support for the hypothesis that substrate stiffness and oxygen play a key role in regulating MSC fate during regenerative events such as fracture healing.

Influence of high-frequency cyclical stimulation on the bone fracture-healing process: mathematical and experimental models

Mechanical stimulation affects the evolution of healthy and fractured bone. However, the effect of applying cyclical mechanical stimuli on bone healing has not yet been fully clarified. The aim of the present study was to determine the influence of a high-frequency and low-magnitude cyclical displacement of the fractured fragments on the bone-healing process. This subject is studied experimentally and computationally for a sheep long bone. On the one hand, the mathematical computational study indicates that mechanical stimulation at high frequencies can stimulate and accelerate the process of chondrogenesis and endochondral ossification and consequently the bony union of the fracture. This is probably achieved by the interstitial fluid flow, which can move nutrients and waste from one place to another in the callus. This movement of fluid modifies the mechanical stimulus on the cells attached to the extracellular matrix. On the other hand, the experimental study was carried out using two sheep groups. In the first group, static fixators were implanted, while, in the second one, identical devices were used, but with an additional vibrator. This vibrator allowed a cyclic displacement with low magnitude and high frequency (LMHF) to be applied to the fractured zone every day; the frequency of stimulation was chosen from mechano-biological model predictions. Analysing the results obtained for the control and stimulated groups, we observed improvements in the bone-healing process in the stimulated group. Therefore, in this study, we show the potential of computer mechano-biological models to guide and define better mechanical conditions for experiments in order to improve bone fracture healing. In fact, both experimental and computational studies indicated improvements in the healing process in the LMHF mechanically stimulated fractures. In both studies, these improvements could be associated with the promotion of endochondral ossification and an increase in the rate of cell proliferation and tissue synthesis.

The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules

During secondary bone healing, different tissue types are formed within the fracture callus depending on the local mechanical and biological environment. Our aim was to understand the temporal succession of these tissue patterns for a normal bone healing progression by means of a basic mechanobiological model. The experimental data stemmed from an extensive, previously published animal experiment on sheep with a 3 mm tibial osteotomy. Using recent experimental data, the development of the hard callus was modelled as a porous material with increasing stiffness and decreasing porosity. A basic phenomenological model was employed with a small number of simulation parameters, which allowed comprehensive parameter studies. The model distinguished between the formation of new bone via endochondral and intramembranous ossification. To evaluate the outcome of the computer simulations, the tissue images of the simulations were compared with experimentally derived tissue images for a normal healing progression in sheep. Parameter studies of the threshold values for the regulation of tissue formation were performed, and the source of the biological stimulation (comprising e.g. stem cells) was varied. It was found that the formation of the hard callus could be reproduced in silico for a wide range of threshold values. However, the bridging of the fracture gap by cartilage on the periosteal side was observed only (i) for a rather specific choice of the threshold values for tissue differentiation and (ii) when assuming a strong source of biological stimulation at the periosteum.

A hybrid bioregulatory model of angiogenesis during bone fracture healing

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.

Low oxygen tension is a more potent promoter of chondrogenic differentiation than dynamic compression

During fracture healing and microfracture treatment of cartilage defects mesenchymal stem cells (MSCs) infiltrate the wound site, proliferate extensively and differentiate along a cartilaginous or an osteogenic lineage in response to local environmental cues. MSCs may be able to directly sense their mechanical environment or alternatively, the mechanical environment could act indirectly to regulate MSC differentiation by inhibiting angiogenesis and diminishing the supply of oxygen and other regulatory factors. Dynamic compression has been shown to regulate chondrogenesis of MSCs. In addition, previous studies have shown that a low oxygen environment promotes in vitro chondrogenesis of MSCs. The hypothesis of this study is that a low oxygen environment is a more potent promoter of chondrogenic differentiation of MSCs embedded in agarose hydrogels compared to dynamic compression. In MSC-seeded constructs supplemented with TGF-beta3, GAG and collagen accumulation was higher in low oxygen conditions compared to normoxia. For normoxic and low oxygen culture GAG accumulation within the agarose hydrogel was inhomogeneous, with low levels of GAG measured in the annulus of constructs maintained in normoxic conditions. Dynamic compression did not significantly increase GAG or collagen accumulation in normoxia. However under low oxygen conditions, dynamic compression reduced GAG accumulation compared to free-swelling controls, but remained higher than comparable constructs maintained in normoxic conditions. This study demonstrates that continuous exposure to low oxygen tension is a more potent pro-chondrogenic stimulus than 1h/day of dynamic compression for porcine MSCs embedded in agarose hydrogels.