Abstract: Image-based modeling of tumor growth combines methods from cancer simulation and medical imaging. In this context, we present a novel approach to adapt a healthy brain atlas to MR images of tumor patients. In order to establish correspondence between a healthy atlas and a pathologic patient image, tumor growth modeling in combination with registration algorithms is employed. In a first step, the tumor is grown in the atlas based on a new multiscale, multiphysics model including growth simulation from the cellular level up to the biomechanical level, accounting for cell proliferation and tissue deformations. Large-scale deformations are handled with an Eulerian approach for finite element computations, which can operate directly on the image voxel mesh. Subsequently, dense correspondence between the modified atlas and patient image is established using nonrigid registration. The method offers opportunities in atlas-based segmentation of tumor-bearing brain images as well as for improved patient-specific simulation and prognosis of tumor progression.
Abstract: A mechanical balance between intraocular pressure and tissue stiffness defines the refractive shape of the human cornea. More and more daily surgical procedures modify that shape to achieve vision correction, which increases the demand for a profound understanding of the tissue mechanics. The wide variety of published mechanical properties foreshadows the difficulty of this task. The aim of this study is to show that such problems may arise from using the inverse method for fitting material models with multiple coefficients to a limited number (usually one) of experimental data. Using multiple sets of experimental data for the fitting process is proposed as a possible solution.
Abstract: Craniosynostosis consists of a premature fusion of the sutures in an infant skull that restricts skull and brain growth. During the last decades, there has been a rapid increase of fundamentally diverse surgical treatment methods. At present, the surgical outcome has been assessed using global variables such as cephalic index, head circumference, and intracranial volume. However, these variables have failed in describing the local deformations and morphological changes that may have a role in the neurologic disorders observed in the patients. This report describes a rigid image registration-based method to evaluate outcomes of craniosynostosis surgical treatments, local quantification of head growth, and indirect intracranial volume change measurements. The developed semiautomatic analysis method was applied to computed tomography data sets of a 5-month-old boy with sagittal craniosynostosis who underwent expansion of the posterior skull with cranioplasty. Quantification of the local changes between pre- and postoperative images was quantified by mapping the minimum distance of individual points from the preoperative to the postoperative surface meshes, and indirect intracranial volume changes were estimated. The proposed methodology can provide the surgeon a tool for the quantitative evaluation of surgical procedures and detection of abnormalities of the infant skull and its development.
Abstract: The spine is a complex structure that provides motion in three directions: flexion and extension, lateral bending and axial rotation. So far, the investigation of the mechanical and kinematic behavior of the basic unit of the spine, a motion segment, is predominantly a domain of in vitro experiments on spinal loading simulators. Most existing approaches to measure spinal stiffness intraoperatively in an in vivo environment use a distractor. However, these concepts usually assume a planar loading and motion. The objective of our study was to develop and validate an apparatus, that allows to perform intraoperative in vivo measurements to determine both the applied force and the resulting motion in three dimensional space. The proposed setup combines force measurement with an instrumented distractor and motion tracking with an optoelectronic system. As the orientation of the applied force and the three dimensional motion is known, not only force-displacement, but also moment-angle relations could be determined. The validation was performed using three cadaveric lumbar ovine spines. The lateral bending stiffness of two motion segments per specimen was determined with the proposed concept and compared with the stiffness acquired on a spinal loading simulator which was considered to be gold standard. The mean values of the stiffness computed with the proposed concept were within a range of ±15% compared to data obtained with the spinal loading simulator under applied loads of less than 5Nm.
Abstract: Abstract Purpose: To assess if finite element (FE) models can be used to predict deformation of the femoropopliteal segment during knee flexion. Methods: Magnetic resonance angiography (MRA) images were acquired on the lower limbs of 8 healthy volunteers (5 men; mean age 28±4 years). Images were taken in 2 natural positions, with the lower limb fully extended and with the knee bent at ∼40°. Patient-specific FE models were developed and used to simulate the experimental situation. The displacements of the artery during knee bending as predicted by the numerical model were compared to the corresponding positions measured on the MRA images. Results: The numerical predictions showed a good overall agreement between the calculated displacements of the motion measures from MRA images. The average position error comparing the calculated vs. actual displacements of the femoropopliteal intersection measured on the MRA was 8±4 mm. Two of the 8 subjects showed large prediction errors (average 13±5 mm); these 2 volunteers were the tallest subjects involved in the study and had a low body mass index (20.5 kg/m(2)). Conclusion: The present computational model is able to capture the gross mechanical environment of the femoropopliteal intersection during knee bending and provide a better understanding of the complex biomechanical behavior. However, results suggest that patient-specific mechanical properties and detailed muscle modeling are required to provide accurate patient-specific numerical predictions of arterial displacement. Further adaptation of this model is expected to provide an improved ability to predict the multiaxial deformation of this arterial segment during leg movements and to optimize future stent designs.
Abstract: Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.
Abstract: Parkinson's disease (PD) is a chronic neurodegenerative disorder characterized by a selective loss of dopaminergic neurons in the substantia nigra, decreased striatal dopamine levels, and consequent extrapyramidal motor dysfunctions. Several potential early diagnostic markers of PD have been proposed. Since they have not been validated in presymptomatic PD, the diagnosis and monitoring of the disease is based on subjective clinical assessment of cognitive and motor symptoms. In this study, we investigated interjoint coordination synergies in the upper limb of healthy and parkinsonian subjects during the performance of unconstrained linear-periodic movements in a horizontal plane using the mutual information (MI). We found that the MI is a sensitive metric in detecting upper limb motor dysfunction, thus suggesting that this method might be applicable to quantitatively evaluating the effects of the antiparkinsonian medication and to monitoring the disease progression.
Abstract: An implantable transducer for monitoring the flow of Cerebrospinal fluid (CSF) for the treatment of hydrocephalus has been developed which is based on measuring the heat dissipation of a local thermal source. The transducer uses passive telemetry at 13.56 MHz for power supply and read out of the measured flow rate. The in vitro performance of the transducer has been characterized using artificial Cerebrospinal Fluid (CSF) with increased protein concentration and artificial CSF with 10% fresh blood. After fresh blood was added to the artificial CSF a reduction of flow rate has been observed in case that the sensitive surface of the flow sensor is close to the sedimented erythrocytes. An increase of flow rate has been observed in case that the sensitive surface is in contact with the remaining plasma/artificial CSF mix above the sediment which can be explained by an asymmetric flow profile caused by the sedimentation of erythrocytes having increased viscosity compared to artificial CSF. After removal of blood from artificial CSF, no drift could be observed in the transducer measurement which could be associated to a deposition of proteins at the sensitive surface walls of the packaged flow transducer. The flow sensor specification requirement of +-10% for a flow range between 2 ml/h and 40 ml/h. could be confirmed at test conditions of 37 degrees C.
Abstract: OBJECTIVES: Despite its importance, implant removal torque can be assessed at present only after implantation. This paper presents a new technique to help clinicians preoperatively evaluate implant stability. STUDY DESIGN: Planning software has been combined with an in-house finite element solver. Once the clinician has chosen the implant position on the planner, a finite element analysis automatically calculates the primary stability. The process was designed to be as simple and fast as possible for clinical use. This paper describes application of the method to the prediction of removal torque. A preliminary validation has been performed in both polyurethane foam and sheep bone. RESULTS: The predicted torque is quantitatively equivalent to experimental values with correlation coefficients of >0.7 in both materials. CONCLUSIONS: This preliminary study is a first step toward the introduction of finite element models in computer-assisted surgery. The fact that the process is fast and automatic makes it suitable for a clinical use.
Abstract: Statistical shape analysis techniques have shown to be efficient tools to build population specific models of anatomical variability. Their use is commonplace as prior models for segmentation, in which case the instance from the shape model that best fits the image data is sought. In certain cases, however, it is not just the most likely instance that must be searched, but rather the whole set of shape instances that meet certain criterion. In this paper we develop a method for the assessment of specific anatomical/morphological criteria across the shape variability found in a population. The method is based on a level set segmentation approach, and used on the parametric space of the statistical shape model of the target population, solved via a multi-level narrow-band approach for computational efficiency. Based on this technique, we develop a framework for evidence-based orthopaedic implant design. To date, implants are commonly designed and validated by evaluating implant bone fitting on a limited set of cadaver bones, which not necessarily span the whole variability in the population. Based on our framework, we can virtually fit a proposed implant design to samples drawn from the statistical model, and assess which range of the population is suitable for the implant. The method highlights which patterns of bone variability are more important for implant fitting, allowing and easing implant design improvements, as to fit a maximum of the target population. Results are presented for the optimisation of implant design of proximal human tibia, used for internal fracture fixation.
Abstract: Knowledge about segmental flexibility in adolescent idiopathic scoliosis is crucial for a better biomechanical understanding, particularly for the development of fusionless, growth-guiding techniques. Currently, there is lack of data in this field. The objective of this study was, therefore, to compute segmental flexibility indices (standing angle minus corrected angle/standing angle). We compared segmental disc angles in 76 preoperative sets of standing and fulcrum-bending radiographs of thoracic curves (paired, two-tailed t tests, p < 0.05). The mean standing Cobb angle was 59.7 degrees (range 41.3 degrees -95 degrees ) and the flexibility index of the curve was 48.6% (range 16.6-78.8%). The disc angles showed symmetric periapical distribution with significant decrease (all p values <0.0001) for every cephalad (+) and caudad (-) level change. The periapical levels +1 and -1 wedged at 8.3 degrees and 8.7 degrees (range 3.5 degrees -14.8 degrees ), respectively. All angles were significantly smaller on the-bending views (p values <0.0001). We noted mean periapical flexibility indices of 46% (+1), 49% (-1), 57% (+2) and 81% (-2), which were significantly less (p < 0.001) than for the group of remote levels 105% (+3), 149% (-3), 231% (+4) and 300% (-4). The discal and bony wedging was 60 and 40%, respectively, and mean values 35 degrees and 24 degrees (p < 0.0001). Their relationship with the Cobb angle showed a moderate correlation (r = 0.56 and 0.45). Functional, radiographic analysis of idiopathic thoracic scoliosis revealed significant, homogenous segmental tethering confined to four periapical levels. Future research will aim at in vivo segmental measurements in three planes under defined load to provide in-depth data for novel therapeutic strategies.
Abstract: Greenstick fractures suffered during growth have a high risk for refracture and posttraumatic deformity, particularly at the forearm diaphysis. The use of a preemptive completion of the fracture by manipulation of the concave cortex is controversial and data supporting this approach are few.
Abstract: The optical characteristics of the human cornea depends on the mechanical balance between the intra-ocular pressure and intrinsic tissue stiffness. A wide range of ophthalmic surgical procedures alter corneal biomechanics to induce local or global curvature changes for the correction of visual acuity. Due to the large number of surgical interventions performed every day, a deeper understanding of corneal biomechanics is needed to improve the safety of these procedures and medical devices. The aim of this study is to propose a biomechanical model of the human cornea, based on stromal microstructure. The constitutive mechanical law includes collagen fiber distribution based on X-ray scattering analysis, collagen cross-linking, and fiber uncrimping. Our results showed that the proposed model reproduced inflation and extensiometry experimental data [Elsheikh et al., Curr. Eye Res., 2007; Elsheikh et al., Exp. Eye Res., 2008] successfully. The mechanical properties obtained for different age groups demonstrated an increase in collagen cross-linking for older specimens. In future work such a model could be used to simulate non-symmetric interventions, and provide better surgical planning.
Abstract: Resonance frequency analysis (RFA) offers the opportunity to monitor the osseointegration of an implant in a simple, noninvasive way. A better comprehension of the relationship between RFA and parameters related to bone quality would therefore help clinicians improve diagnoses. In this study, a bone analog made from polyurethane foam was used to isolate the influences of bone density and cortical thickness in RFA.
Abstract: Oxygen diffusivity and consumption in the human cornea have not been directly measured yet; current models rely on properties measured in vitro in rabbit corneas. The aim of this study was to present a mathematical model of time-dependent oxygen diffusion that permits the estimation of corneal consumption and diffusivity.
Abstract: The goal of this study was to propose a general numerical analysis methodology to evaluate the magnetic resonance imaging (MRI)-safety of active implants. Numerical models based on the finite element (FE) technique were used to estimate if the normal operation of an active device was altered during MRI imaging. An active implanted pump was chosen to illustrate the method. A set of controlled experiments were proposed and performed to validate the numerical model. The calculated induced voltages in the important electronic components of the device showed dependence with the MRI field strength. For the MRI radiofrequency fields, significant induced voltages of up to 20 V were calculated for a 0.3T field-strength MRI. For the 1.5 and 3.0OT MRIs, the calculated voltages were insignificant. On the other hand, induced voltages up to 11 V were calculated in the critical electronic components for the 3.0T MRI due to the gradient fields. Values obtained in this work reflect to the worst case situation which is virtually impossible to achieve in normal scanning situations. Since the calculated voltages may be removed by appropriate protection circuits, no critical problems affecting the normal operation of the pump were identified. This study showed that the proposed methodology helps the identification of the possible incompatibilities between active implants and MR imaging, and can be used to aid the design of critical electronic systems to ensure MRI-safety.
Abstract: Insertion of an implant in the cornea to achieve corneal multifocality has been suggested as a solution for presbyopia. However, unresolved issues related to nutrient transport need to be resolved. Our aim was to find the best lens position and influence lens transport properties in order to optimize nutrient supply to corneal cells.
Abstract: Glenohumeral conformity has been reported to be one of the most critical implant-related features that may affect the occurrence of glenoid loosening. This study evaluated the mechanical effects of this parameter with a 3-dimensional finite element model of a prosthetic shoulder, which included the scapula, the humerus, and the rotator cuff muscles. Aequalis humeral and glenoid components were implanted numerically according to manufacturer’s recommendations for 2 different orientations of the glenoid component (0 degrees and 15 degrees of retroversion). Different values of glenohumeral conformity (1-15 mm of radial mismatch) were tested by a progressive flattening of the glenoid surface. Free and countered rotation movements were simulated. Glenohumeral contact pressure, cement stress, shear stress, and micromotions at the bone-cement interface were calculated. At 0 degrees of retroversion, conformity had only a slight effect, whereas at 15 degrees of retroversion, all quantities increased by more than 200% and exceeded critical values above 10 mm of mismatch.
Abstract: Osteoarthritis of the shoulder is frequently associated with posterior glenoid wear, which may be difficult to correct during shoulder arthroplasty. This study was designed to evaluate the risks that a prosthetic glenoid implanted in retroversion will loosen. The scapula, the humerus, the rotator cuff, and a total shoulder prosthesis were reconstructed with a 3-dimensional finite element model. The glenoid was placed in 5 different angles of retroversion (0 degrees , 5 degrees , 10 degrees , 15 degrees , and 20 degrees ). Location of the glenohumeral contact point, articular pressure, bone and cement stress, and micromotion around the glenoid implant were calculated during internal and external rotation. Glenoid retroversion induced a posterior displacement of the glenohumeral contact point during internal and external rotation, inducing a significant increase of stress within the cement mantel (+326%) and within the glenoid bone (+162%). Furthermore, a major increase of micromotion was measured at the bone-cement interface (+706%). According to this study, glenoid retroversion exceeding 10 degrees should be corrected during total shoulder arthroplasty. If the correction is impossible, not replacing the glenoid should be considered.
Abstract: BACKGROUND: Although shoulder arthroplasty is an accepted treatment for osteoarthritis, loosening of the glenoid component, which mainly occurs at the bone-cement interface, remains a major concern. Presently, the mechanical effect of the cement mantel thickness on the bone-cement interface is still unclear. METHODS: Finite element analysis of a prosthetic scapula was used to evaluate the effect of cement thickness on stresses and micromotions at the bone-cement interface. The glenoid component was all-polyethylene, keeled and flat back. Cement mantel thickness was gradually increased from 0.5 to 2.0 mm. Two glenohumeral contact forces were applied: concentric and eccentric. Two extreme cases were considered for the bone-cement interface: bonded and debonded. FINDINGS: Within cement, stress increased as cement thickness decreased, reaching the fatigue limit below 1.0 mm. Bone stress was below its ultimate strength and was minimum between 1.0 and 1.5mm. Interface stress was close to the interface strength, and also minimum between 1.0 and 1.5 mm. Both the decentring of the load and the debonding of the interface increased the stress. INTERPRETATION: A cement thinning weakens the cement, but also the bone-cement interface, along the back-keel edges. Conversely, a cement thickening rigidifies the cemented implant, consequently increasing interfacial stresses and micromotions. To avoid both excessive cement fatigue and interface failure, an ideal cement thickness has been identified between 1.0 and 1.5 mm.
Abstract: OBJECTIVE: To study the influence of the shape of the prosthetic humeral head on shoulder biomechanics and then to evaluate the benefits of an anatomical reconstruction of the humeral head after shoulder arthroplasty. DESIGN: A 3D numerical model of a healthy shoulder was reconstructed. The model included the proximal humerus, the scapula and, for stability purposes, the subscapularis, infraspinatus and supraspinatus rotator cuff muscles. BACKGROUND: Shoulder prostheses used nowadays, called third generation, allow for a better adaptation of the implant to the anatomy of the proximal humerus than previously used implants. However, no biomechanical study has shown the benefits of this anatomical reconstruction of the humeral head. METHODS: The model was used to compare the biomechanics of a shoulder without implant with the biomechanics of the same shoulder after humeral hemiarthroplasty. Two humeral components were tested: a second-generation prosthesis and an implant with an anatomically reconstructed humeral head. RESULTS: The anatomical reconstruction of the humeral head restored the physiological motions and limited eccentric loading of the glenoid. Conversely, the second-generation implant produced contact forces in the superior extremity of the glenoid surface leading to bone stresses up to 8 times higher than for the intact shoulder. CONCLUSIONS: This analysis provided insights into the mechanical effects of different reconstructions of the humeral head and highlighted the advantages of anatomical reconstructions of the humeral head during shoulder arthroplasty.
Abstract: A model of tissue differentiation at the bone-implant interface is proposed. The basic hypothesis of the model is that the mechanical environment determines the tissue differentiation. The stimulus chosen is related to the bone-implant micromotions. Equations governing the evolution of the interfacial tissue are proposed and combined with a finite element code to determine the evolution of the fibrous tissue around prostheses. The model is applied to the case of an idealized hip prosthesis.
Abstract: New trends of numerical models of human joints require more and more computation of both large amplitude joint motions and fine bone stress distribution. Together, these problems are difficult to solve and very CPU time consuming. The goal of this study is to develop a new method to diminish the calculation time for this kind of problems which include calculation of large amplitude motions and infinitesimal strains. Based on the Principle of Virtual Power, the present method decouples the problem into two parts. First, rigid body motion is calculated. The bone micro-deformations are then calculated in a second part by using the results of rigid body motions as boundary conditions. A finite element model of the shoulder was used to test this decoupling technique. The model was designed to determine the influence of humeral head shape on stress distribution in the scapula for different physiological motions of the joint. Two versions of the model were developed: a first version completely deformable and a second version based on the developed decoupling method. It was shown that biomechanical variables, as mean pressure and von Mises stress, calculated with the two versions were sensibly the same. On the other hand, CPU time needed for calculating with the new decoupled technique was more than 6 times less than with the completely deformable model.
Abstract: OBJECTIVE: The objective of the present study was to develop a numerical model of the shoulder able to quantify the influence of the shape of the humeral head on the stress distribution in the scapula. The subsequent objective was to apply the model to the comparison of the biomechanics of a normal shoulder (free of pathologies) and an osteoarthritic shoulder presenting primary degenerative disease that changes its bone shape. DESIGN: Since the stability of the glenohumeral joint is mainly provided by soft tissues, the model includes the major rotator cuff muscles in addition to the bones. BACKGROUND: No existing numerical model of the shoulder is able to determine the modification of the stress distribution in the scapula due to a change of the shape of the humeral head or to a modification of the glenoid contact shape and orientation. METHODS: The finite element method was used. The model includes the three-dimensional computed tomography-reconstructed bone geometry and three-dimensional rotator cuff muscles. Large sliding contacts between the reconstructed muscles and the bone surfaces, which provide the joint stability, were considered. A non-homogenous constitutive law was used for the bone as well as non-linear hyperelastic laws for the muscles and for the cartilage. Muscles were considered as passive structures. Internal and external rotations of the shoulders were achieved by a displacement of the muscle active during the specific rotation (subscapularis for internal and infrapinatus for external rotation). RESULTS: The numerical model proposed is able to describe the biomechanics of the shoulder during rotations. The comparison of normal vs. osteoarthritic joints showed a posterior subluxation of the humeral head during external rotation for the osteoarthritic shoulder but no subluxation for the normal shoulder. This leads to important von Mises stress in the posterior part of the glenoid region of the pathologic shoulder while the stress distribution in the normal shoulder is fairly homogeneous. CONCLUSION: This study shows that the posterior subluxation observed in clinical situations for osteoarthritic shoulders may also be cause by the altered geometry of the pathological shoulder and not only by a rigidification of the subscapularis muscle as often postulated. This result is only possible with a model including the soft tissues provided stability of the shoulder. RELEVANCE: One possible cause of the glenoid loosening is the eccentric loading of the glenoid component due to the translation of the humeral head. The proposed model would be a useful tool for designing new shapes for a humeral head prosthesis that optimizes the glenoid loading, the bone stress around the implant, and the bone/implant micromotions in a way that limits the risks of loosening.
Abstract: Many methodologies dealing with prediction or simulation of soft tissue deformations on medical image data require preprocessing of the data in order to produce a different shape representation that complies with standard methodologies, such as Mass-spring networks, Finite Element Methods (FEM), etc. On the other hand, methodologies working directly on the image space normally do not take into account mechanical behavior of tissues and tend to lack physics foundations driving soft tissue deformations. This paper presents a method to simulate soft tissue deformations based on coupled concepts from image analysis and mechanics theory. The proposed methodology is based on a robust stochastic approach that takes into account material properties retrieved directly from the image, concepts from continuum mechanics and FEM. The optimization framework is solved within a Hierarchical Markov-Random Field (HMRF) which is implemented on the Graphics Processor Unit (GPU).
Abstract: Statistical shape models (SSMs) have been used widely as a basis for segmenting and interpreting complex anatomical structures. The robustness of these models are sensitive to the registration procedures, i.e., establishment of a dense correspondence across a training data set. In this work, two SSMs based on the same training data set of scoliotic vertebrae, and registration procedures were compared. The first model was constructed based on the original binary masks without applying any image pre- and post-processing, and the second was obtained by means of a feature preserving smoothing method applied to the original training data set, followed by a standard rasterization algorithm. The accuracies of the correspondences were assessed quantitatively by means of the maximum of the mean minimum distance (MMMD) and Hausdorf distance (H(D)). Anatomical validity of the models were quantified by means of three different criteria, i.e., compactness, specificity, and model generalization ability. The objective of this study was to compare quasi-identical models based on standard metrics. Preliminary results suggest that the MMMD distance and eigenvalues are not sensitive metrics for evaluating the performance and robustness of SSMs.
Abstract: Craniosynostosis consists of a premature fusion of the sutures in an infant skull, which restricts the skull and brain growth. During the last decades there has been a rapid increase of fundamentally diverse surgical treatment methods. At present, the surgical outcome has been assessed using global variables such as cephalic index, head circumerence and intracranial volume. However, the variables have failed in describing the local deformations and morphological changes, which are proposed to more likely induce neurological disorders.
Abstract: The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.
