Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Metallic glass fiber-reinforced Zr-based bulk metallic glass

A novel Zr-based bulk metallic glass composite was fabricated using stainless steel capillaries as the reinforcement. Large plasticity (14%) was achieved in the composite with a reinforcement volume fraction of 38%. The high plasticity observed can be attributed to the formation of small glass fibers encapsulated by the steel capillaries, which promotes multiple shear bands in both metallic glass matrix and the fibers themselves. A new parameter was also proposed to approximately evaluate the reinforcement efficiency.

The relationship between deformity correction and clinical outcomes after thoracoscopic scoliosis surgery : a prospective series of one hundred patients

Prospective clinical case series of 100 patients receiving thoracoscopic anterior scoliosis correction surgery. The objective was to evaluate the relationship between clinical outcomes of thoracoscopic anterior scoliosis surgery and deformity correction using the Scoliosis Research Society (SRS) outcomes instrument questionnaire. The surgical treatment of scoliosis is quantitatively assessed in the clinic using radiographic measures of deformity correction, as well as the rib hump, but it is important to understand the extent to which these quantitative measures correlate with self-reported improvements in patients’ quality of life following surgery. A series of 100 consecutive adolescent idiopathic scoliosis patients received a single anterior rod via a thoracoscopic approach at the Mater Children’s Hospital, Brisbane, Australia. Patients completed SRS outcomes questionnaires pre-operatively and at 24 months post-operatively. There were 94 females and 6 males with a mean age of 16.1 years. The mean Cobb angle improved from 52º pre-operatively to 25º post-operatively (52%) and the mean rib hump improved from 16º to 8º (51%). The mean total SRS score for the cohort was 99.4/120. None of the deformity related parameters in the multiple regression were significant. However, patients with the lowest post-operative major Cobb angles reported significantly higher SRS scores than those with the highest post-operative Cobb angles, but there was no difference on the basis of rib hump correction. There were no significant differences between patients with either rod fractures or screw-related complications compared to those without complications.

Paediatric spinal deformity research at the Mater Children's Hospital, Brisbane, Australia.

The Paediatric Spine Research group was formed in 2002 to perform high quality research into the prevention and management of spinal deformity, with an emphasis on scoliosis. The group has successfully built collaborative bridges between the scientific and research expertise at QUT, and the clinical skills and experience of the spinal orthopaedic surgeons at the Mater Children’s Hospital in Brisbane. Clinical and biomechanical research is now possible as a result of the development of detailed databases of patients who have innovative and unique surgical interventions for spinal deformity such as thoracoscopic scoliosis correction, thoracoscopic staple insertion for juvenile idiopathic scoliosis and minimally invasive growing rods. The Mater in Brisbane provides these unique datasets of spinal deformity surgery patients, whose procedures are not being performed anywhere else in the Southern Hemisphere. The most detailed is a database of thoracoscopic scoliosis correction surgery which now contains 180 patients with electronic collections of X-Rays, photographs and patient questionnaires. With ethics approval, a subset of these patients has had CT scans, and a further subset have had MRI scans with and without a compressive load to simulate the erect standing position. This database has to date contributed to 17 international refereed journal papers, a further 7 journal papers either under review or in final preparation, 53 national conference presentations and 35 international conference presentations. Major findings from selected journal publications will be presented. It is anticipated that as the surgical databases grow they will continue to provide invaluable clinical data which will feed into clinically relevant projects driven by both medical and engineering researchers whose findings will benefit spinal deformity patients and scientific knowledge worldwide.

Patient-specific computational biomechanics for simulating adolescent scoliosis surgery : predicted vs clinical correction for a preliminary series of six patients

Scoliosis is a spinal deformity that requires surgical correction in progressive cases. In order to optimize surgical outcomes, patient-specific finite element models are being developed by our group. In this paper, a single rod anterior correction procedure is simulated for a group of six scoliosis patients. For each patient, personalised model geometry was derived from low-dose CT scans, and clinically measured intra-operative corrective forces were applied. However, tissue material properties were not patient-specific, being derived from existing literature. Clinically, the patient group had a mean initial Cobb angle of 47.3 degrees, which was corrected to 17.5 degrees after surgery. The mean simulated post-operative Cobb angle for the group was 18.1 degrees. Although this represents good agreement between clinical and simulated corrections, the discrepancy between clinical and simulated Cobb angle for individual patients varied between -10.3 and +8.6 degrees, with only three of the six patients matching the clinical result to within accepted Cobb measurement error of +-5 degrees. The results of this study suggest that spinal tissue material properties play an important role in governing the correction obtained during surgery, and that patient-specific modelling approaches must address the question of how to prescribe patient-specific soft tissue properties for spine surgery simulation.

Mesenchymal stem cells

Cell based therapies as they apply to tissue engineering and regenerative medicine, require cells capable of self renewal and differentiation, and a prerequisite is to be able to prepare an effective dose of ex vivo expanded cells for autologous transplants. The in vivo identification of a source of physiologically relevant cell types suitable for cell therapies therefore figures as an integral part of tissue engineering. Stem cells serve as a reserve for biological repair, having the potential to differentiate into a number of specialised cell types within the body; they therefore represent the most useful candidates for cell based therapies. The primary goal of stem cell research is to produce cells that are both patient specific, as well as having properties suitable for the specific conditions for which they are intended to remedy. From a purely scientific perspective, stem cells allow scientists to gain a deeper understanding of developmental biology and regenerative therapies. Stem cells have acquired a number of uses for applications in regenerative medicine, immunotherapy, gene therapy, but it is in the area of tissue engineering that they generate most excitement, primarily as a result of their capacity for self-renewal and pluripotency. A unique feature of stem cells is their ability to maintain an uncommitted quiescent state in vivo and then, once triggered by conditions such as disease, injury or natural wear or tear, serve as a reservoir and natural support system to replenish lost cells. Although these cells retain the plasticity to differentiate into various tissues, being able to control this differentiation process is still one of the biggest challenges facing stem cell research. In an effort to harness the potential of these cells a number of studies have been conducted using both embryonic/foetal and adult stem cells. The use of embryonic stem cells (ESC) have been hampered by strong ethical and political concerns, this despite their perceived versatility due to their pluripotency. Ethical issues aside, other concerns raised with ESCs relates to the possibility of tumorigenesis, immune rejection and complications with immunosuppressive therapies, all of which adds layers of complications to the application ESC in research and which has led to the search for alternative sources for stem cells. The adult tissues in higher organisms harbours cells, termed adult stem cells, and these cells are reminiscent of unprogrammed stem cells. A number of sources of adult stem cells have been described. Bone marrow is by far the most accessible source of two potent populations of adult stem cells, namely haematopoietic stem cells (HSCs) and bone marrow mesenchymal stem cells (BMSCs). Autologously harvested adult stem cells can, in contrast to embryonic stem cells, readily be used in autografts, since immune rejection is not an issue; and their use in scientific research has not attracted the ethical concerns which have been the case with embryonic stem cells. The major limitation to their use, however, is the fact that adult stem cells are exceedingly rare in most tissues. This fact makes identifying and isolating these cells problematic; bone marrow being perhaps the only notable exception. Unlike the case of HSCs, there are as yet no rigorous criteria for characterizing MSCs. Changing acuity about the pluripotency of MSCs in recent studies has expanded their potential application; however, the underlying molecular pathways which impart the features distinctive to MSCs remain elusive. Furthermore, the sparse in vivo distribution of these cells imposes a clear limitation to their study in vitro. Also, when MSCs are cultured in vitro, there is a loss of the in vivo microenvironment, resulting in a progressive decline in proliferation potential and multipotentiality. This is further exacerbated with increased passage numbers in culture, characterized by the onset of senescence related changes. As a consequence, it is necessary to establish protocols for generating large numbers of MSCs but without affecting their differentiation potential. MSCs are capable of differentiating into mesenchymal tissue lineages, including bone, cartilage, fat, tendon, muscle, and marrow stroma. Recent findings indicate that adult bone marrow may also contain cells that can differentiate into the mature, nonhematopoietic cells of a number of tissues, including cells of the liver, kidney, lung, skin, gastrointestinal tract, and myocytes of heart and skeletal muscle. MSCs can readily be expanded in vitro and can be genetically modified by viral vectors and be induced to differentiate into specific cell lineages by changing the microenvironment–properties which makes these cells ideal vehicles for cellular gene therapy. MSCs can also exert profound immunosuppressive effects via modulation of both cellular and innate immune pathways, and this property allows them to overcome the issue of immune rejection. Despite the many attractive features associated with MSCs, there are still many hurdles to overcome before these cells are readily available for use in clinical applications. The main concern relates to in vivo characterization and identification of MSCs. The lack of a universal biomarker, sparse in vivo distribution, and a steady age related decline in their numbers, makes it an obvious need to decipher the reprogramming pathways and critical molecular players which govern the characteristics unique to MSCs. This book presents a comprehensive insight into the biology of adult stem cells and their utility in current regeneration therapies. The adult stem cell populations reviewed in this book include bone marrow derived MSCs, adipose derived stem cells (ASCs), umbilical cord blood stem cells, and placental stem cells. The features such as MSC circulation and trafficking, neuroprotective properties, and the nurturing roles and differentiation potential of multiple lineages have been discussed in details. In terms of therapeutic applications, the strengths of MSCs have been presented and their roles in disease treatments such as osteoarthritis, Huntington’s disease, periodontal regeneration, and pancreatic islet transplantation have been discussed. An analysis comparing osteoblast differentiation of umbilical cord blood stem cells and MSCs has been reviewed, as has a comparison of human placental stem cells and ASCs, in terms of isolation, identification and therapeutic applications of ASC in bone, cartilage regeneration, as well as myocardial regeneration. It is my sincere hope that this book will update the reader as to the research progress of MSC biology and potential use of these cells in clinical applications. It will be the best reward to all contributors of this book, if their efforts herein may in some way help the readers in any part of their study, research, and career development.

Overview of mesenchymal stem cells

Stem cells are unprogrammed cells which possess plasticity and self renewal capability. The term of stem cell was first used to describe cells committed to give rise to germline cells, and to describe proposed progenitor cells of the blood system [1]. A unique feature of stem cell is to remain quiescent in vivo in an uncommitted state. They serve as reservoir or natural support system to replenish cells lost due to disease, injury or aging. When triggered by appropriate signals these cells divide and may become specialized, committed cells; however being able to control this differentiation process still remains one of the biggest challenge in stem cell research [2]. The cell division of stem cells is a distinct aspect of their biology, since this division may be either symmetric or asymmetric. Symmetric division takes place when the stem cells divides and forms two new daughter cells. Asymmetric division is thought to take place only under certain conditions where stem cells divides and gives rise to a daughter cell which remains primitive and does not proliferate, and one committed progenitor cell, which heads down a path of differentiation. Asymmetric division of stem cells helps reparative process, and also ensures that the stem cells pool does not decrease, whereas symmetric division is responsible for stem cells undergoing self renewal and proliferation. The factors which prompt the stem cells to undergo asymmetric division are, however, not well understood, but it is clear that the delicate balance between the self renewal and differentiation is what maintains tissue homeostasis.

Periodontal regeneration and mesenchymal stem cells

The ultimate goal of periodontal therapy is to regenerate periodontal supporting tissues, but this is hard to achieve as the results of periodontal techniques for regeneration are clinically unpredictable. Stem cells owing to their plasticity and proliferation potential provides a new paradigm for periodontal regeneration. Stem cells from mesenchyme can self renew and generate new dental tissues (including dentin and cementum), alveolar bone and periodontal ligament, and thus they have great potential in periodontal regeneration. This chapter presents an insight into mesenchymal stem cells and their potential use in periodontal regeneration. In this chapter the cellular and molecular biology in periodontal regeneration will be introduced, followed by a range of conventional surgical procedures for periodontal regeneration will be discussed. Mesenchymal stem cells applied in regenerated periodontal tissue and their biological characterizations in vitro will be also introduced. Lastly, the use of mesenchymal stem cell to repair periodontal tissues in large animal models will be also reviewed.

A material model for flexural crack simulation in reinforced concrete elements using ABAQUS

This paper presents a material model to simulate load induced cracking in Reinforced Concrete (RC) elements in ABAQUS finite element package. Two numerical material models are used and combined to simulate complete stress-strain behaviour of concrete under compression and tension including damage properties. Both numerical techniques used in the present material model are capable of developing the stress-strain curves including strain softening regimes only using ultimate compressive strength of concrete, which is easily and practically obtainable for many of the existing RC structures or those to be built. Therefore, the method proposed in this paper is valuable in assessing existing RC structures in the absence of more detailed test results. The numerical models are slightly modified from the original versions to be comparable with the damaged plasticity model used in ABAQUS. The model is validated using different experiment results for RC beam elements presented in the literature. The results indicate a good agreement with load vs. displacement curve and observed crack patterns.

A biomechanical investigation of vertebral staples for fusionless scoliosis correction

Background: Fusionless scoliosis surgery is an early-stage treatment for idiopathic scoliosis which claims potential advantages over current fusion-based surgical procedures. Anterior vertebral stapling using a shape memory alloy staple is one such approach. Despite increasing interest in this technique, little is known about the effects on the spine following insertion, or the mechanism of action of the staple. The purpose of this study was to investigate the biomechanical consequences of staple insertion in the anterior thoracic spine, using in vitro experiments on an immature bovine model. Methods: Individual calf spine thoracic motion segments were tested in flexion, extension, lateral bending and axial rotation. Changes in motion segment rotational stiffness following staple insertion were measured on a series of 14 specimens. Strain gauges were attached to three of the staples in the series to measure forces transmitted through the staple during loading. A micro-CT scan of a single specimen was performed after loading to qualitatively examine damage to the vertebral bone caused by the staple. Findings: Small but statistically significant decreases in bending stiffness occurred in flexion,extension, lateral bending away from the staple, and axial rotation away from the staple. Each strain-gauged staple showed a baseline compressive loading following insertion which was seen to gradually decrease during testing. Post-test micro-CT showed substantial bone and growth plate damage near the staple. Interpretation: Based on our findings it is possible that growth modulation following staple insertion is due to tissue damage rather than sustained mechanical compression of the motion segment.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson‟s ratio f 0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 m with a von Mises model, and from 0.09 to 0.02 m with Drucker-Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.

What aspects of the scoliosis correction are most important to the teenager who has keyhole scoliosis correction surgery? A prospective series of 100 patients

Introduction. Surgical treatment of scoliosis is assessed in the spine clinic by the surgeon making numerous measurements on X-Rays as well as the rib hump. But it is important to understand which of these measures correlate with self-reported improvements in patients’ quality of life following surgery. The objective of this study was to examine the relationship between patient satisfaction after thoracoscopic (keyhole) anterior scoliosis surgery and standard deformity correction measures using the Scoliosis Research Society (SRS) adolescent questionnaire. Methods. A series of 100 consecutive adolescent idiopathic scoliosis patients received a single anterior rod via a keyhole approach at the Mater Children’s Hospital, Brisbane. Patients completed SRS outcomes questionnaires before surgery and again at 24 months after surgery. Multiple regression and t-tests were used to investigate the relationship between SRS scores and deformity correction achieved after surgery. Results. There were 94 females and 6 males with a mean age of 16.1 years. The mean Cobb angle improved from 52º pre-operatively to 21º for the instrumented levels post-operatively (59% correction) and the mean rib hump improved from 16º to 8º (51% correction). The mean total SRS score for the cohort was 99.4/120 which indicated a high level of satisfaction with the results of their scoliosis surgery. None of the deformity related parameters in the multiple regressions were significant. However, the twenty patients with the smallest Cobb angles after surgery reported significantly higher SRS scores than the twenty patients with the largest Cobb angles after surgery, but there was no difference on the basis of rib hump correction. Discussion. Patients undergoing thoracoscopic (keyhole) anterior scoliosis correction report good SRS scores which are comparable to those in previous studies. We suggest that the absence of any statistically significant difference in SRS scores between patients with and without rod or screw complications is because these complications are not associated with any clinically significant loss of correction in our patient group. The Cobb angle after surgery was the only significant predictor of patient satisfaction when comparing subgroups of patients with the largest and smallest Cobb angles after surgery.

The measurement of applied forces during anterior single rod surgical correction of adolescent idiopathic scoliosis

INTRODUCTION. Following anterior thoracoscopic instrumentation and fusion for the treatment of thoracic AIS, implant related complications have been reported as high as 20.8%. Currently the magnitudes of the forces applied to the spine during anterior scoliosis surgery are unknown. The aim of this study was to measure the segmental compressive forces applied during anterior single rod instrumentation in a series of adolescent idiopathic scoliosis patients. METHODS. A force transducer was designed, constructed and retrofitted to a surgical cable compression tool, routinely used to apply segmental compression during anterior scoliosis correction. Transducer output was continuously logged during the compression of each spinal joint, the output at completion converted to an applied compression force using calibration data. The angle between adjacent vertebral body screws was also measured on intra-operative frontal plane fluoroscope images taken both before and after each joint compression. The difference in angle between the two images was calculated as an estimate for the achieved correction at each spinal joint. RESULTS. Force measurements were obtained for 15 scoliosis patients (Aged 11-19 years) with single thoracic curves (Cobb angles 47˚- 67˚). In total, 95 spinal joints were instrumented. The average force applied for a single joint was 540 N (± 229 N)ranging between 88 N and 1018 N. Experimental error in the force measurement, determined from transducer calibration was ± 43 N. A trend for higher forces applied at joints close to the apex of the scoliosis was observed. The average joint correction angle measured by fluoroscope imaging was 4.8˚ (±2.6˚, range 0˚-12.6˚). CONCLUSION. This study has quantified in-vivo, the intra-operative correction forces applied by the surgeon during anterior single rod instrumentation. This data provides a useful contribution towards an improved understanding of the biomechanics of scoliosis correction. In particular, this data will be used as input for developing patient-specific finite element simulations of scoliosis correction surgery.

Is there a difference between narrowing of the spinal canal and neurological deficits comparing Denis and Magerl classifications?

We have read with great interest the retrospective study by Caffaro and Avanzi1 evaluating the relation between narrowing of the spinal canal and neurological deficits in patients with burst-type fractures of the spine. The authors are to be commended for obtaining detailed neurological and radiological data in a large cohort of 227 patients. The authors conclude: “The percentage of narrowing of the spinal canal proved to be a pre-disposing factor for the severity of the neurological status in thoracolumbar and lumbar burst-type fractures according to the classifications of Denis and Magerl.” Although this conclusion is mainly in accordance with previous findings, we would like to comment on the methodological approach applied in the current study.

Interactive image manipulation for surgical planning

The Australian e-Health Research Centre in collaboration with the Queensland University of Technology's Paediatric Spine Research Group is developing software for visualisation and manipulation of large three-dimensional (3D) medical image data sets. The software allows the extraction of anatomical data from individual patients for use in preoperative planning. State-of-the-art computer technology makes it possible to slice through the image dataset at any angle, or manipulate 3D representations of the data instantly. Although the software was initially developed to support planning for scoliosis surgery, it can be applied to any dataset whether obtained from computed tomography, magnetic resonance imaging or any other imaging modality.