Advances in mechanobiological pharmacokinetic-pharmacodynamic models of osteoporosis treatment - Pathways to optimise and exploit existing therapies.

Osteoporosis (OP) is a chronic progressive bone disease which is characterised by reduction of bone matrix volume and changes in the bone matrix properties which can ultimately lead to bone fracture. The two major forms of OP are related to aging and/or menopause. With the worldwide increase of the elderly population, particularly age-related OP poses a serious health issue which puts large pressure on health care systems. A major challenge for development of new drug treatments for OP and comparison of drug efficacy with existing treatments is due to current regulatory requirements which demand testing of drugs based on bone mineral density (BMD) in phase 2 trials and fracture risk in phase 3 trials. This requires large clinical trials to be conducted and to be run for long time periods, which is very costly. This, together with the fact that there are already many drugs available for treatment of OP, makes the development of new drugs inhibitive. Furthermore, an increased trend of the use of different sequential drug therapies has been observed in OP management, such as sequential anabolic-anticatabolic drug treatment or switching from one anticatabolic drug to another. Running clinical trials for concurrent and sequential therapies is neither feasible nor practical due to large number of combinatorial possibilities. In silico mechanobiological pharmacokinetic-pharmacodynamic (PK-PD) models of OP treatments allow predictions beyond BMD, i.e. bone microdamage and degree of mineralisation can also be monitored. This will help to inform clinical drug usage and development by identifying the most promising scenarios to be tested clinically (confirmatory trials rather than exploratory only trials), optimise trial design and identify subgroups of the population that show benefit-risk profiles (both good and bad) that are different from the average patient. In this review, we provide examples of the predictive capabilities of mechanobiological PK-PD models. These include simulation results of PMO treatment with denosumab, implications of denosumab drug holidays and coupling of bone remodelling models with calcium and phosphate systems models that allows to investigate the effects of co-morbidities such as hyperparathyroidism and chronic kidney disease together with calcium and vitamin D status on drug efficacy.

An in silico approach to elucidate the pathways leading to primary osteoporosis: age-related vs. postmenopausal.

Numerical models of bone remodelling have traditionally been used to perform in silico tests of bone loss in postmenopausal women and also to simulate the response to different drug treatments. These models simulate the menopausal oestrogen decline by altering certain signalling pathways. However, they do not consider the simultaneous effect that ageing can have on cell function and bone remodelling, and thus on bone loss. Considering ageing and oestrogen decline together is important for designing osteoporosis treatments that can selectively counteract one or the other disease mechanism. A previously developed bone cell population model was adapted to consider the effect of ageing through: (1) the decrease of TGF- ß contained in the bone matrix and (2) an increased production of sclerostin by non-skeletal cells. Oestrogen deficiency is simulated in three different ways: (a) an increase in RANKL expression, (b) a decrease in OPG production, and (c) an increase in the responsiveness of osteoclasts to RANKL. The effect of ageing was validated using the cross-sectional study of (Riggs et al. in J Bone Miner Res 19: 1945-1954, 2004) on BMD of trabecular bone of the vertebral body of men. The joint effect of ageing and oestrogen deficiency was validated using these same clinical results but in women. In ageing, the effect of the increasing production of sclerostin is more important than the decrease of TGF- ß , while the three mechanisms used to simulate the effect of oestrogen deficiency produce almost identical responses. The results show that an early menopause leads to a lower average density in the fifth decade, but after the sixth decade the average density is independent of the age at menopause. Treatment of osteoporosis with denosumab was also simulated to conclude that the drug is not very effective if started before 10 years after menopause or before age 60.

Spatio-temporal simulations of bone remodelling using a bone cell population model based on cell availability.

Here we developed a spatio-temporal bone remodeling model to simulate the action of Basic Multicelluar Units (BMUs). This model is based on two major extensions of a temporal-only bone cell population model (BCPM). First, the differentiation into mature resorbing osteoclasts and mature forming osteoblasts from their respective precursor cells was modelled as an intermittent process based on precursor cells availability. Second, the interaction between neighbouring BMUs was considered based on a "metabolic cost" argument which warrants that no new BMU will be activated in the neighbourhood of an existing BMU. With the proposed model we have simulated the phases of the remodelling process obtaining average periods similar to those found in the literature: resorption ( ∼ 22 days)-reversal (∼8 days)-formation (∼65 days)-quiescence (560-600 days) and an average BMU activation frequency of ∼1.6 BMUs/year/mm3. We further show here that the resorption and formation phases of the BMU become coordinated only by the presence of TGF-ß (transforming growth factor ß), i.e., a major coupling factor stored in the bone matrix. TGF-ß is released through resorption so upregulating osteoclast apoptosis and accumulation of osteoblast precursors, i.e., facilitating the transition from the resorption to the formation phase at a given remodelling site. Finally, we demonstrate that this model can explain targeted bone remodelling as the BMUs are steered towards damaged bone areas in order to commence bone matrix repair.

Mechanistic PK-PD model of alendronate treatment of postmenopausal osteoporosis predicts bone site-specific response.

Alendronate is the most widely used drug for postmenopausal osteoporosis (PMO). It inhibits bone resorption, affecting osteoclasts. Pharmacokinetics (PK) and pharmacodynamics (PD) of alendronate have been widely studied, but few mathematical models exist to simulate its effect. In this work, we have developed a PK model for alendronate, valid for short- and long-term treatments, and a mechanistic PK-PD model for the treatment of PMO to predict bone density gain (BDG) at the hip and lumbar spine. According to our results, at least three compartments are required in the PK model to predict the effect of alendronate in both the short and long terms. Clinical data of a 2-year treatment of alendronate, reproduced by our PK-PD model, demonstrate that bone response is site specific (hip: 7% BDG, lumbar spine: 4% BDG). We identified that this BDG is mainly due to an increase in tissue mineralization and a decrease in porosity. The difference in BDG between sites is linked to the different loading and dependence of the released alendronate on the bone-specific surface and porosity. Osteoclast population diminishes quickly within the first month of alendronate treatment. Osteoblast population lags behind but also falls due to coupling of resorption and formation. Two dosing regimens were studied (70 mg weekly and 10 mg daily), and both showed very similar BDG evolution, indicating that alendronate accumulates quickly in bone and saturates. The proposed PK-PD model could provide a valuable tool to analyze the effect of alendronate and to design patient-specific treatments, including drug combinations.

Assessment of Strategies for Safe Drug Discontinuation and Transition of Denosumab Treatment in PMO-Insights From a Mechanistic PK/PD Model of Bone Turnover.

Denosumab (Dmab) treatment against postmenopausal osteoporosis (PMO) has proven very efficient in increasing bone mineral density (BMD) and reducing the risk of bone fractures. However, concerns have been recently raised regarding safety when drug treatment is discontinued. Mechanistic pharmacokinetic-pharmacodynamic (PK-PD) models are the most sophisticated tools to develop patient specific drug treatments of PMO to restore bone mass. However, only a few PK-PD models have addressed the effect of Dmab drug holidays on changes in BMD. We showed that using a standard bone cell population model (BCPM) of bone remodelling it is not possible to account for the spike in osteoclast numbers observed after Dmab discontinuation. We show that inclusion of a variable osteoclast precursor pool in BCPMs is essential to predict the experimentally observed rapid rise in osteoclast numbers and the associated increases in bone resorption. This new model also showed that Dmab withdrawal leads to a rapid increase of damage in the bone matrix, which in turn decreases the local safety factor for fatigue failure. Our simulation results show that changes in BMD strongly depend on Dmab concentration in the central compartment. Consequently, bone weight (BW) might play an important factor in calculating effective Dmab doses. The currently clinically prescribed constant Dmab dose of 60 mg injected every 6 months is less effective in increasing BMD for patients with high BW (2.5% for 80 kg in contrast to 8% for 60 kg after 6 years of treatment). However, bone loss observed 24 months after Dmab withdrawal is less pronounced in patients with high BW (3.5% for 80kg and 8.5% for 60 kg). Finally, we studied how to safely discontinue Dmab treatment by exploring several transitional and combined drug treatment strategies. Our simulation results indicate that using transitional reduced Dmab doses are not effective in reducing rapid bone loss. However, we identify that use of a bisphosphonate (BP) is highly effective in avoiding rapid bone loss and increase in bone tissue damage compared to abrupt withdrawal of Dmab. Furthermore, the final values of BMD and damage were not sensitive to the time of administration of the BP.

Evolution of relaxation properties of callus tissue during bone transport.

Callus tissue exhibits a viscoelastic behavior that has a strong influence on the distribution of stresses and their evolution with time and, thus, it can affect tissue differentiation during distraction procedures. For this reason, a deep knowledge of that viscoelastic behavior can be very useful to improve current protocols of bone distraction and bone transport. Monitoring stress relaxation of the callus during distraction osteogenesis allows characterizing its viscoelastic behavior. Different procedures have been used in the literature to fit the response of a given viscoelastic model to the force relaxation curve. However, these procedures do not ensure the uniqueness of that fit, which is of the utmost importance for statistical purposes. This work uses a fitting procedure already validated for other tissues that ensures that uniqueness. Very importantly too, the procedure presented here allows obtaining more information from the stress relaxation tests, distinguishing relaxation in different time scales, which provides a deeper insight into the viscoelastic behavior and its evolution over time. As it was observed in the results, relaxation is faster at the first days after osteotomy and becomes slower and more gradual with time. This fact can be directly linked to the temporal evolution of the callus composition (water, organic phase, and mineral content) and also to the progression of tissue differentiation, with a prevalence of hard tissues as time passes.

Combined Effects of Exercise and Denosumab Treatment on Local Failure in Post-menopausal Osteoporosis-Insights from Bone Remodelling Simulations Accounting for Mineralisation and Damage.

Denosumab has been shown to increase bone mineral density (BMD) and reduce the fracture risk in patients with post-menopausal osteoporosis (PMO). Increase in BMD is linked with an increase in bone matrix mineralisation due to suppression of bone remodelling. However, denosumab anti-resorptive action also leads to an increase in fatigue microdamage, which may ultimately lead to an increased fracture risk. A novel mechanobiological model of bone remodelling was developed to investigate how these counter-acting mechanisms are affected both by exercise and long-term denosumab treatment. This model incorporates Frost's mechanostat feedback, a bone mineralisation algorithm and an evolution law for microdamage accumulation. Mechanical disuse and microdamage were assumed to stimulate RANKL production, which modulates activation frequency of basic multicellular units in bone remodelling. This mechanical feedback mechanism controls removal of excess bone mass and microdamage. Furthermore, a novel measure of bone local failure due to instantaneous overloading was developed. Numerical simulations indicate that trabecular bone volume fraction and bone matrix damage are determined by the respective bone turnover and homeostatic loading conditions. PMO patients treated with the currently WHO-approved dose of denosumab (60 mg administrated every 6 months) exhibit increased BMD, increased bone ash fraction and damage. In untreated patients, BMD will significantly decrease, as will ash fraction; while damage will increase. The model predicted that, depending on the time elapsed between the onset of PMO and the beginning of treatment, BMD slowly converges to the same steady-state value, while damage is low in patients treated soon after the onset of the disease and high in patients having PMO for a longer period. The simulations show that late treatment PMO patients have a significantly higher risk of local failure compared to patients that are treated soon after the onset of the disease. Furthermore, overloading resulted in an increase of BMD, but also in a faster increase of damage, which may consequently promote the risk of fracture, specially in late treatment scenarios. In case of mechanical disuse, the model predicted reduced BMD gains due to denosumab, while no significant change in damage occurred, thus leading to an increased risk of local failure compared to habitual loading.

A novel algorithm to resolve lack of convergence and checkerboard instability in bone adaptation simulations using non-local averaging.

Checkerboard is a typical instability in finite element (FE) simulations of bone adaptation and topology optimization in general. It consists in a patchwork pattern with elements of alternating stiffness, producing lack of convergence and instabilities in the predicted bone density. Averaging techniques have been proposed to solve this problem. One of the most acknowledged techniques (node based formulation) has severe drawbacks such as: high sensitivity to mesh density and type of element integration (full vs reduced) and, more importantly, oscillatory solutions also leading to lack of convergence. We propose a new solution consisting in a non-local smoothing technique. It defines, as the mechanical stimulus governing bone adaptation in a certain integration point of the mesh, the average of the stimuli obtained in the neighbour integration points. That average is weighted with a decay function of the distance to the centre of the neighbourhood. The new technique has been shown to overcome all the referred problems and perform in a robust way. It was tested on a hollow cylinder, resembling the diaphysis of a long bone, subjected to bending or torsion. Checkerboard instability was eliminated and local convergence of bone adaptation was achieved rapidly, in contrast to the other averaging technique and to the model without control of checkerboard instability. The new algorithm was also tested with good results on the same geometry but in a model containing a void, which produces a stress concentration that usually leads to checkerboard instability, like in other applications such as simulations of bone-implant interfaces.

Are drug holidays a safe option in treatment of osteoporosis? - Insights from an in silico mechanistic PK-PD model of denosumab treatment of postmenopausal osteoporosis.

Recent reviews by the clinical bone research community suggest caution with prescription of drug holidays for patients with postmenopausal osteoporosis (PMO) treated with denosumab for an extended period of time. Main reasons for this suggestion are based on the fact that discontinuation of denosumab treatment leads to a relapse of osteoclastic bone resorption and a loss of bone mineral density (BMD) to pre-treatment levels at only 12-28 months. The question remains what is the best treatment option for cases where it is required to discontinue and/or reduce the drug dose and what are the consequences on BMD and bone turnover markers (BTMs). The latter questions are difficult to be addressed using clinical trials alone given the large number of parameter combinations involved to answer this problem. In this paper, we apply a recently developed in silico mechanistic pharmacokinetic-pharmacodynamic (PK-PD) model of the effect of denosumab on bone remodelling in PMO. To address the above clinical relevant questions, we design a wide range of current and virtual treatment regimens to study the effect of drug holiday duration and therapy resumption on the evolution of BTMs, BMD and mineral content. Our numerical simulation results indicate the symptomatic effect of denosumab, which is lost once treatment is stopped. This effect is most clearly seen on rapid loss of BMD to pre-treatment levels 12 months after the last injection (8% and 3.6% per year in the lumbar spine and femoral neck, respectively). Also, we identify that independently of the duration of drug holiday (i.e. 12, 16 or 18 months) resuming treatment can restore BMD quite effectively. However, the latter result does not consider the possibility of potential fractures that can occur during the drug holiday. Finally, we identify a treatment case most promising for achieving maintenance of BMD and mineral content, while moderately increasing BTMs. The latter case uses no drug holiday, but reduces the most commonly prescribed denosumab dose (60 mg every 6 months) by half at same interval.

Effects of long-term treatment of denosumab on bone mineral density: insights from an in-silico model of bone mineralization.

Denosumab is one of the most commonly prescribed anti-resorptive drugs for the treatment of postmenopausal osteoporosis. The therapeutic effect of denosumab is to inhibit osteoclast differentiation and consequently bone resorption. Gains in bone mineral density (BMD) are achieved based on the ability of the bone matrix to undergo secondary mineralization. Experimental data show that the increase of BMD after commencing denosumab treatment are bone site specific. In this paper, we developed a comprehensive mechanistic pharmacokinetic-pharmacodymamic (PK-PD) model of the effect of denosumab on bone remodeling in postmenopausal osteoporosis (PMO). The PD model is based on a bone cell population model describing the bone remodeling process at the tissue scale. The conceptual model of the bone mineralization process, originally proposed by Boivin and Meunier, is quantitatively incorporated using a FIFO (First-In-First-Out) queue algorithm. The latter takes into account the balance of mineral within bone tissue due to the mineralization process, distinguishing the primary and secondary phases and removal of bone matrix due to bone resorption. The numerical simulations show that the model is able to predict the bone-site specific increase in BMD as was observed in the experimental data of Bone et al. 2008 for a typical denosumab administration pattern of 60 mg every 6 months. At the hip a 5 % increase in BMD was observed, while at the lumbar spine a 7.5 % increase of BMD was achieved after a 2 year treatment period. The difference in BMD is due to the fact that bone turnover at the hip is lower compared to lumbar spine and consequently has less potential for secondary mineralization. Parametric studies revealed that the rate of bone mineralization is an essential parameter regulating BMD gains. If mineralization is neglected only minimal increases in BMD are observed.

Comparison of the volumetric composition of lamellar bone and the woven bone of calluses.

Woven tissue is mainly present in the bone callus, formed very rapidly either after a fracture or in distraction processes. This high formation speed is probably responsible for its disorganized microstructure and this, in turn, for its low stiffness. Nonetheless, the singular volumetric composition of this tissue may also play a key role in its mechanical properties. The volumetric composition of woven tissue extracted from the bone transport callus of sheep was investigated and compared with that of the lamellar tissue extracted from the cortical shell of the same bone. Significant differences were found in the mineral and water contents, but they can be due to the different ages of both tissues, which affects the mineral/water ratio. However, the content in organic phase remains more or less constant throughout the mineralization process and has proven to be a good variable to measure the different composition of both tissues, being that content significantly higher in woven tissue. This may be linked to the abnormally high concentration of osteocytes in this tissue, which is likely a consequence of the more abundant presence of osteoblasts secreting osteoid and burying other osteoblasts, which then differentiate into osteocytes. This would explain the high formation rate of woven tissue, useful to recover the short-term stability of the bone. Nonetheless, the more abundant presence of organic phase prevents the woven tissue from reaching a stiffness similar to that of lamellar tissue in the long term, when it is fully mineralized.

Comparison of different constitutive models to characterize the viscoelastic properties of human abdominal adipose tissue. A pilot study.

Knowing the mechanical properties of human adipose tissue is key to simulate surgeries such as liposuction, mammoplasty and many plastic surgeries in which the subcutaneous fat is present. One of the most important surgeries, for its incidence, is the breast reconstruction surgery that follows a mastectomy. In this case, achieving a deformed shape similar to the healthy breast is crucial. The reconstruction is most commonly made using autologous tissue, taken from the patient's abdomen. The amount of autologous tissue and its mechanical properties have a strong influence on the shape of the reconstructed breast. In this work, the viscoelastic mechanical properties of the human adipose tissue have been studied. Uniaxial compression stress relaxation tests were performed in adipose tissue specimens extracted from the human abdomen. Two different viscoelastic models were used to fit to the experimental tests: a quasi-linear viscoelastic (QLV) model and an internal variables viscoelastic (IVV) model; each one with four different hyperelastic strain energy density functions to characterise the elastic response: a 5-terms polynomial function, a first order Ogden function, an isotropic Gasser-Ogden-Holzapfel function and a combination of a neoHookean and an exponential function. The IVV model with the Ogden function was the best combination to fit the experimental tests. The viscoelastic properties are not important in the simulation of the static deformed shape of the breast, but they are needed in a relaxation test performed under finite strain rate, particularly, to derive the long-term behaviour (as time tends to infinity), needed to estimate the static deformed shape of the breast. The so obtained stiffness was compared with previous results given in the literature for adipose tissue of different regions, which exhibited a wide dispersion.

Effect of freezing storage time on the elastic and viscous properties of the porcine TMJ disc.

The correct characterisation of the articular disc of the temporomandibular joint (TMJ) is key to study the masticatory biomechanics. For the interval from extraction until testing, freezing is the most used preservation technique for biological tissues, but its influence on their behaviour is still unclear. An important error can be committed in the characterisation of such tissues if freezing has any effect on their mechanical properties. Thus, the aim of this study was to determine whether the freezing storage time causes any change in the mechanical properties of the TMJ discs. To check that, the specimens were stored in a -20°C freezer during different time intervals: 1 day, 1 week, 1 month and 3 months. Fresh specimens, tested right after extraction, were used as the control group. Compressive stress relaxation tests were carried out on the specimens and a quasi-linear viscoelastic (QLV) model was used to fit the experimental curves. A statistical analysis detected significant differences among the groups. Post-hoc tests determined that freezing the specimens more than 30 days may lead to changes in the viscoelastic properties of the tissue.

Is cannulated-screw fixation an alternative to plate osteosynthesis in open book fractures? A biomechanical analysis.

OBJECTIVES: The current biomechanical work compares the symphyseal and sacroiliac stability obtained with two systems of bone osteosynthesis. The two methods of fixation compared were the 6-hole suprapubic non-locked plate and pubic fixation with two cannulated screws, a novel technique that can be applied percutaneously in the clinical practice. The aim of this study was to examine the validity of the use of two-cannulated-screws osteosynthesis in order to minimize the secondary effects of open fixation, especially in patients in whom an open reduction is contraindicated. MATERIALS AND METHODS: A biomechanical study was designed in 9 fresh, human pelvis specimens, simulating an AO B1.1 type injury, using both fixation systems sequentially in each specimen. In both parts of the test, the specimens were subjected to an axial load of 300N. Displacements and rotations between the different pelvic elements were studied by means of a discrete set of points. The absence of differences between the two systems has been set as the null hypothesis. RESULTS: There were significant differences in favor of the cross-cannulated screws in most of the displacements measured at the pubic symphysis and sacroiliac joint. CONCLUSIONS: Fixation of the AO B1.1 type fractures with cross cannulated screws restores the biomechanical behavior of the pubic symphysis, obtaining better stability than fixation with the 6-hole non-locked plate. To date, no comparative, biomechanical studies have been conducted with these two systems of osteosynthesis. This study demonstrates that cross-cannulated screws fixation of the pubic symphysis in AO B1.1 pelvic fractures should be considered as an alternative to the conventional plating system.

Aplicación de la mecánica de fluidos y la simulación: tracto urinario y catéteres ureterales / Application of fluid mechanics and simulation: urinary tract and ureteral catheters

El comportamiento de la orina durante su transporte, desde la pelvis renal hasta la vejiga, tiene un gran interés para los urólogos. El conocimiento de las diferentes variables físicas y su interrelación, en movimientos fisiológicos y patologías, ayudará a un mejor diagnóstico y tratamiento. El objetivo de este capítulo es exponer y acercar al mundo clínico los conceptos físicos y sus relaciones básicas más relevantes en el transporte de orina. Para ello, se explica el movimiento de la orina durante una peristalsis, una obstrucción ureteral y un uréter tutorizado con un catéter ureteral. Esta explicación se basa en dos herramientas muy utilizadas en bioingeniería: el análisis teórico a través de la Teoría de los Medios Continuos y la Mecánica de Fluidos y la simulación computacional que ofrece una solución práctica de cada uno de los escenarios. Además, se repasan otras aportaciones de la bioingeniería al campo de la Urología, como la simulación física o las técnicas de fabricación aditiva y sustractiva. Finalmente, se enumeran las limitaciones actuales de estas herramientas y las líneas de desarrollo tecnológico con más proyección. CONCLUSIÓN: Se pretende que este capítulo ayude a los urólogos a comprender algunos conceptos importantes de bioingeniería, fomentando la colaboración multidisciplinar para ofrecer herramientas complementarias que les ayuden en el diagnóstico y el tratamiento de enfermedades

The mechanics of urine during its transport from the renal pelvis to the bladder is of great interest for urologists. The knowledge of the different physical variables and their interrelationship, both in physiologic movements and pathologies, will help a better diagnosis and treatment. The objective of this chapter is to show the physics principles and their most relevant basic relations in urine transport, and to bring them over the clinical world. For that, we explain the movement of urine during peristalsis, ureteral obstruction and in a ureter with a stent. This explanation is based in two tools used in bioengineering: the theoretical analysis through the Theory of concontinuous media and Ffluid mechanics and computational simulation that offers a practical solution for each scenario. Moreover, we review other contributions of bioengineering to the field of Urology, such as physical simulation or additive and subtractive manufacturing techniques. Finally, we list the current limitations for these tools and the technological development lines with more future projection. CONCLUSIONS: In this chapter we aim to help urologists to understand some important concepts of bioengineering, promoting multidisciplinary cooperation to offer complementary tools that help in diagnosis and treatment of diseases

On the Use of Bone Remodelling Models to Estimate the Density Distribution of Bones. Uniqueness of the Solution.

Bone remodelling models are widely used in a phenomenological manner to estimate numerically the distribution of apparent density in bones from the loads they are daily subjected to. These simulations start from an arbitrary initial distribution, usually homogeneous, and the density changes locally until a bone remodelling equilibrium is achieved. The bone response to mechanical stimulus is traditionally formulated with a mathematical relation that considers the existence of a range of stimulus, called dead or lazy zone, for which no net bone mass change occurs. Implementing a relation like that leads to different solutions depending on the starting density. The non-uniqueness of the solution has been shown in this paper using two different bone remodelling models: one isotropic and another anisotropic. It has also been shown that the problem of non-uniqueness is only mitigated by removing the dead zone, but it is not completely solved unless the bone formation and bone resorption rates are limited to certain maximum values.

A polynomial hyperelastic model for the mixture of fat and glandular tissue in female breast.

In the breast of adult women, glandular and fat tissues are intermingled and cannot be clearly distinguished. This work studies if this mixture can be treated as a homogenized tissue. A mechanical model is proposed for the mixture of tissues as a function of the fat content. Different distributions of individual tissues and geometries have been tried to verify the validity of the mixture model. A multiscale modelling approach was applied in a finite element model of a representative volume element (RVE) of tissue, formed by randomly assigning fat or glandular elements to the mesh. Both types of tissues have been assumed as isotropic, quasi-incompressible hyperelastic materials, modelled with a polynomial strain energy function, like the homogenized model. The RVE was subjected to several load cases from which the constants of the polynomial function of the homogenized tissue were fitted in the least squares sense. The results confirm that the fat volume ratio is a key factor in determining the properties of the homogenized tissue, but the spatial distribution of fat is not so important. Finally, a simplified model of a breast was developed to check the validity of the homogenized model in a geometry similar to the actual one.

Percutaneous iliosacral fixation in external rotational pelvic fractures. A biomechanical analysis.

INTRODUCTION: Although the gold standard in open book pelvic fractures remains the pubic symphysis (PS) plate fixation, the clinical outcomes are not satisfactory, despite the excellent anatomical reduction assessed radiologically. Some authors suggest that residual instability of the posterior pelvic elements may be responsible for the chronic pain and the early osteoarthritic changes in the sacroiliac joint (SIJ). OBJECTIVE: To evaluate whether the isolated posterior fixation with one or two iliosacral screws (ISSs) is sufficient to provide adequate stability for the treatment of Burgess Young APC-II (YB APC-II) type of pelvic ring injuries. METHODS: Biomechanical experimental study using 7 fresh human pelvises, where an YB APC-II pelvic injury was previously implemented. The isolated posterior fixation of the pelvic ring with 1 or 2 ISSs directed in the S1 vertebra body was analysed in each specimen following an axial load of 300N. The different displacement of the SIJ and of the PS were analysed in all three spatial axes, using the validated optical measurement system 3D PONTOS 5M. A multivariate version of Friedman test (non-parametric ANOVA for repeated measures) was performed. RESULTS: The isolated fixation of the SIJ with 1 ISS did not show any differences with respect to the intact pelvis (p=0.851). Regarding the PS, both type of fixations (with 1 or 2 ISSs) confirmed an acceptable correction and adequate control of the PS even though with some differences compared to the intact pelvis (p=0.01). The presence of the second ISS found not to offer any significant additional benefit. The three-dimensional analysis of the behaviour of the pelvic elements, in these two different types of fixation, did not show any statistical significant differences (p=0.645). CONCLUSION: The posterior fixation with ISS can represent an alternative option for treatment of pelvic injuries associated with rotational instability. Further prospective clinical studies are necessary to determine, the influence of the residual pubic symphysis mobility in the every day life, when the above-mentioned technique is applied.

Finite element analysis of the human mastication cycle.

The aim of this paper is to propose a biomechanical model that could serve as a tool to overcome some difficulties encountered in experimental studies of the mandible. One of these difficulties is the inaccessibility of the temporomandibular joint (TMJ) and the lateral pterygoid muscle. The focus of this model is to study the stresses in the joint and the influence of the lateral pterygoid muscle on the mandible movement. A finite element model of the mandible, including the TMJ, was built to simulate the process of unilateral mastication. Different activation patterns of the left and right pterygoid muscles were tried. The maximum stresses in the articular disc and in the whole mandible during a complete mastication cycle were reached during the instant of centric occlusion. The simulations show a great influence of the coordination of the right and left lateral pterygoid muscles on the movement of the jaw during mastication. An asynchronous activation of the lateral pterygoid muscles is needed to achieve a normal movement of the jaw during mastication.