A visco-hyperelastic model with damage for the knee ligaments under dynamic constraints

The aim of this study was to identify the behaviour laws governing the knee ligaments, accounting for the damage incurred by the structure under dynamic constraints. The model is developed using a thermodynamic formulation based on the coupling between a viscoelastic model and a damage model. Identification is carried out using the results of dynamic traction tests performed on a bone ligament/bone complex to which traction velocities of around 1.98 m/s were applied. The results show the ability of the model to account for the brittle and ductile failure processes occurring in the cruciate and lateral ligaments, respectively.     

Constitutive Laws and Failure Models for Compact Bones Subjected to Dynamic Loading

Many biological tissues, such as bones and ligaments, are fibrous. The geometrical structure of these tissues shows that they exhibit a similar hierarchy in their ultra- and macro-structures. The aim of this work is to develop a model to study the failure of fibrous structures subjected to dynamic loading. The important feature of this model is that it describes failure in terms of the loss of cohesion between fibres. We have developed a model based on the lamellar structure of compact bone with fibres oriented at 0, 45 and 90° to the longitudinal axis of the bone and have studied the influence of the model parameters on the failure process. Bone porosity and joint stress force at failure were found to be the most significant parameters. Using least square resolution, we deduced a phenomenological model of the lamellar structure. Finally, experimental results were found to be comparable with our numerical model.     

A multi-body model for comparative study of cervical traction simulation – development,improvement and validation

A computer simulation model was developed to study the dynamic behavior of the cervical spine during cervical traction therapy in inclined and sitting traction positions. The model improved upon an old model with additional components to represent the behavior of the intervertebral discs and the posterior ligaments. The simulation result of the new model was compared against the cervical traction data from a radiographic experiment in both positions. The simulation results of the old model and new model were compared to illustrate the improvement. Using the new model, we compared the timing response of cervical traction in the inclined and sitting positions.     

A Finite Element Model of the L5-S1 Functional Spinal Unit: Development and Comparison with Biomechanical Tests In Vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro . Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.     

3D finite element modeling of pelvic organ prolapse

Objectives: The purpose of this study is to develop a validated 3D finite element model of the pelvic floor system which can offer insights into the mechanics of anterior vaginal wall prolapse and have the ability to assess biomedical device treatment methods. The finite element results should accurately mimic the clinical findings of prolapse due to intra-abdominal pressure (IAP) and soft tissues impairment conditions. Methods: A 3D model of pelvic system was created in Creo Parametric 2.0 based on MRI Images, which included uterus, cervix, vagina, cardinal ligaments, uterosacral ligaments, and a simplified levator plate and rectum. The geometrical model was imported into ANSYS Workbench 14.5. Mechanical properties of soft tissues were based on experimental data of tensile test results from current literature. Studies were conducted for IAP loadings on the vaginal wall and uterus, increasing from lowest to extreme values. Results: Anterior vaginal wall collapse occurred at an IAP value corresponding to maximal valsalva and showed similar collapsed shape as clinical findings. Prolapse conditions exhibited high sensitivity to vaginal wall stiffness, whereas healthy tissues was found to support the vagina against prolapse. Ligament impairment was found to have only a secondary effect on prolapse.     

Observation de ligaments artificiels de genou après implantation en MEB à pression variable

ObjectivesWe carried out a comparative study between two methods to prepare explanted artificial ligaments samples before their observation in the variable pressure scanning electron microscope (VP-SEM).Materials and methodsPoly(ethylene terephtalate) (PET) artificial ligaments grafted by a bioactive polymer, the poly(sodium styrene sulfonate) were implanted for three months in the knee of four ewes after section of the anterior cruciate ligament (ACL). The qualitative evaluation of the cellular and tissue colonization of the artificial ligaments was carried out on critical point-dried explants (observed by VP-SEM) or not (observed by VP-SEM–Peltier).Results and discussionThe results showed differences in the biointegration of the two types of studied ligaments. Only the MEB-VP–Peltier technique allowed obtaining images of excellent resolution with high magnification. For this reason the MEB-VP–Peltier technique is a promising method for the fast qualitative evaluation of the cellular and tissue integration of the artificial ligaments.     

External approach to in vivo force measurement on mitral valve traction suture

BackgroundForce measurements on the mitral valve apparatus have been reported from in vivo and in vitro studies. Recent reparative techniques for ischemic mitral valve insufficiency call for papillary muscle relocation. This study describes a device to measure forces generated on traction sutures utilized for this purpose.MethodsThe transducer design was based on a modified caliper with strain gauges attached. Finite element computer simulation was employed to optimize the signal output. The system was designed to facilitate investigation of the effects of shortening GoreTex traction suture that was extended from near the fibrous trigones of the mitral valve through the papillary muscles. The suture was exteriorized out through the left ventricle in a porcine setup (n=11) and attached to the dedicated device for simultaneous papillary muscle relocation and traction suture force measurement.ResultsThe transducer demonstrated excellent signal strength, linearity, and durability. Peak force was seen at the onset of the systolic isovolumic contraction (p<0.001). Initial results indicated that this external approach can document force magnitudes comparable to previous internally measured forces in the mitral valve apparatus.ConclusionsIt has been proven feasible to measure forces in the mitral valve papillary muscle relocation sutures with an external device. The results from using this equipment will provide insight into the biomechanical requirements of relocation traction sutures and other devices utilized for papillary muscle relocation.     

Bone remodelling around the tibia due to total ankle replacement: effects of implant material and implant–bone interfacial conditions

Abstract

One of the major causes of implant loosening is due to excessive bone resorption surrounding the implant due to bone remodelling. The objective of the study is to investigate the effects of implant material and implant–bone interface conditions on bone remodelling around tibia bone due to total ankle replacement. Finite element models of intact and implanted ankles were developed using CT scan data sets. Bone remodelling algorithm was used in combination with FE analysis to predict the bone density changes around the ankle joint. Dorsiflexion, neutral, and plantar flexion positions were considered, along with muscle force and ligaments. Implant–bone interfacial conditions were assumed as debonded and bonded to represent non-osseointegration and fully osseointegration at the porous coated surface of the implant. To investigate the effect of implant material, three finite element models having different material combinations of the implant were developed. For model 1, tibial and talar components were made of Co–Cr–Mo, and meniscal bearing was made of UHMWPE. For model 2, tibial and talar components were made of ceramic and meniscal bearing was made of UHMWPE. For model 3, tibial and talar components were made of ceramic and meniscal bearing was made of CFR-PEEK. Changes in implant material showed no significant changes in bone density due to bone remodelling. Therefore, ceramic appears to be a viable alternative to metal and CFR-PEEK can be used in place of UHMWPE. This study also indicates that proper bonding between implant and bone is essential for long-term survival of the prosthetic components.     

Performance evaluation of a novel conceptual bioprocess for clinically-required mass production of hematopoietic cells

Objective

The novel engineered bioprocess, which was designed and modeled to provide the clinically relevant cell numbers for different therapies in our previous work (Kaleybar et al. Food Bioprod Process 122:254–268, https://doi.org/10.1016/j.fbp.2020.04.012, 2020), was evaluated by using U937 as hematopoietic model cells.

Results

The culture system showed a 30-fold expansion of U937 cells in one-step during a 10-day culture period. The cell growth profile, the substrate and oxygen consumptions, and byproduct formations were all in agreement with the model predications during 7 days. The cell proliferation decrease after 7 days was attributed to optional oxygen limiting condition in the last days of culture. The bioreactor culture system revealed also a slight enhancement of lactate dehydrogenase (LDH) production as compared to the 2D conventional culture system, indicating the low impact of shear stress on cellular damage in the dynamic system.

Conclusions

The results demonstrated that the conceptual bioprocess for suspended stem cell production has a great potential in practice although additional experiments are required to improve the system.

     

人工半骨盆假体置换联合腰椎椎弓根螺钉固定术后生物力学的有限元分析

目的:建立人工半骨盆假体置换与联合腰椎椎弓根螺钉固定后的三维有限元模型,评价腰骶段生物力学改变后半骨盆假体力学结构的特点。方法:采用CT薄层扫描采集原始数据,分别建立正常骨盆、半骨盆假体置换术后以及半骨盆假体置换联合腰椎椎弓根螺钉固定术后骨盆的三维有限元模型,分别在第4腰椎上终板平面施以500 N的垂直纵向载荷,分析不同骨盆模型的应力分布特点。结果:与正常骨盆有限元模型相比,半骨盆假体置换术后健侧骨盆应力分布以骶髂关节、髋臼窝及耻骨为主,置换侧半骨盆假体以耻骨连接棒、髋臼杯及髂骨座为主,最大应力出现在耻骨连接棒,应力峰值为65.62 MPa。联合腰椎椎弓根螺钉固定后健侧应力相对减小,置换侧髂骨固定座与骶骨固定处应力相对减小,应力分布以腰椎椎弓根钉棒、耻骨连接棒及髋臼杯为主,最大应力出现在椎弓根螺钉,应力峰值为107 MPa。结论:半骨盆假体置换联合腰椎椎弓根螺钉固定后钉棒分担了半骨盆置换后健侧骨盆及置换侧髂骨固定座与骶骨固定处附近的部分应力,缓解应力集中现象,降低术后骨盆破坏风险,一定程度上增加了半骨盆置换后骨盆的稳定性。     

A real-time computational model for estimating kinematics of ankle ligaments

Background: An accurate assessment of ankle ligament kinematics is crucial in understanding the injury mechanisms and can help to improve the treatment of an injured ankle, especially when used in conjunction with robot-assisted therapy. A number of computational models have been developed and validated for assessing the kinematics of ankle ligaments. However, few of them can do real-time assessment to allow for an input into robotic rehabilitation programs. Method: An ankle computational model was proposed and validated to quantify the kinematics of ankle ligaments as the foot moves in real-time. This model consists of three bone segments with three rotational degrees of freedom (DOFs) and 12 ankle ligaments. This model uses inputs for three position variables that can be measured from sensors in many ankle robotic devices that detect postures within the foot–ankle environment and outputs the kinematics of ankle ligaments. Validation of this model in terms of ligament length and strain was conducted by comparing it with published data on cadaver anatomy and magnetic resonance imaging. Results: The model based on ligament lengths and strains is in concurrence with those from the published studies but is sensitive to ligament attachment positions. Conclusions: This ankle computational model has the potential to be used in robot-assisted therapy for real-time assessment of ligament kinematics. The results provide information regarding the quantification of kinematics associated with ankle ligaments related to the disability level and can be used for optimizing the robotic training trajectory.     

Extract and fraction of Musa paradisiaca flower have osteogenic effect and prevent ovariectomy induced osteopenia

BackgroundOsteoporosis is an asymptomatic bone disorder leading to altered bone microarchitecture, mineralization and strength. Musa paradisiaca has been reported to have antioxidant and anti-inflammatory effects in various diseases. Its impact on postmenopausal osteoporosis has not been investigated yet.PurposeThe intention of the current study was to evaluate the bone regeneration and osteoprotective potential of extract and fraction of M. paradisiaca flower in ovariectomized (Ovx) Sprague Dawley (SD) rats, a model of post-menopausal bone loss. The study also aims to identify osteogenic compounds from active fraction.MethodsEthanolic extract (MFE) and butanolic fraction (MFE-Bu) from flower of M. paradisiaca were prepared and their efficacy was tested in rat femur osteotomy model at different doses. Effective dose from both extract (250 mg/kg) and fraction (50 mg/kg) were taken for study in osteopenic bone loss model. PTH was taken as reference standard (20 µg/kg/twice a week). Bones were harvested at autopsy for dynamic and static histomorphometry. Serum was collected for ELISA. Pure compounds were isolated from butanolic fraction (MFE-Bu), and were assessed for their osteogenic effect.ResultsMFE and MFE-Bu were observed for their potential in bone healing and prevention of bone loss. Both MFE and MFE-Bu promoted new bone regeneration at injury site as assessed by microCT and calcein dye labeling studies. These also led to restoration of bone microarchitecture deteriorated as a result of osteopenia and improved bone biomechanical properties. Extract as well as the fraction exhibited dual bone anabolic and anti-resorptive properties where they elevated serum procollagen type I N-terminal propeptide (P1NP), a bone formation marker and suppressed serum C-telopeptide of type I collagen (CTX-1), a bone resorption marker. As many as four osteogenic compounds were isolated from MFE-Bu. Oleracein-E was found to be the most potent osteogenic agent based on osteoblast differentiation, mineralization assays, qPCR and protein expression studies.ConclusionOur studies demonstrates that ethanolic extract from the flower of M. paradisiaca and its butanolic fraction exhibit dual osteogenic and anti-resorptive potential, and have an advantage over PTH which though promotes bone formation but is also bone catabolic in nature.     

The inhibitory effects of a RANKL-binding peptide on articular and periarticular bone loss in a murine model of collagen-induced arthritis: a bone histomorphometric study

IntroductionWe designed OP3-4 (YCEIEFCYLIR), a cyclic peptide, to mimic the soluble osteoprotegerin (OPG), and was proven to bind to RANKL (receptor activator of NF-κB ligand), thereby inhibiting osteoclastogenesis. We recently found that another RANKL binding peptide, W9, could accelerate bone formation by affecting RANKL signaling in osteoblasts. We herein demonstrate the effects of OP3-4 on bone formation and bone loss in a murine model of rheumatoid arthritis.MethodsTwenty-four seven-week-old male DBA/1J mice were used to generate a murine model of collagen-induced arthritis (CIA). Then, vehicle or OP3-4 (9 mg/kg/day or 18 mg/kg/day) was subcutaneously infused using infusion pumps for three weeks beginning seven days after the second immunization. The arthritis score was assessed, and the mice were sacrificed on day 49. Thereafter, radiographic, histological and biochemical analyses were performed.ResultsThe OP3-4 treatment did not significantly inhibit the CIA-induced arthritis, but limited bone loss. Micro-CT images and quantitative measurements of the bone mineral density revealed that 18 mg/kg/day OP3-4 prevented the CIA-induced bone loss at both articular and periarticular sites of tibiae. As expected, OP3-4 significantly reduced the CIA-induced serum CTX levels, a marker of bone resorption. Interestingly, the bone histomorphometric analyses using undecalcified sections showed that OP3-4 prevented the CIA-induced reduction of bone formation-related parameters at the periarticular sites.ConclusionThe peptide that mimicked OPG prevented inflammatory bone loss by inhibiting bone resorption and stimulating bone formation. It could therefore be a useful template for the development of small molecule drugs for inflammatory bone loss.

Electronic supplementary material

The online version of this article (doi:10.1186/s13075-015-0753-8) contains supplementary material, which is available to authorized users.     

Preliminary simulation model toward the study of the effects caused by different mandibular advancement devices in OSAS treatment

Abstract

The paper aims to evaluate the effects caused by a Mandibular Advancement Device (MAD) for Obstructive Sleep Apnoea Syndrome (OSAS) treatment. This study is based on Finite Element Method (FEM) for evaluating the load distribution on temporomandibular joint, especially on the mandibular condyle and disc, and on periodontal ligaments. The stress values on condyle and periodontal ligaments lead authors to consider MAD a safe procedure even for a long period. The obtained results also show the relationship between MAD material and load distribution at the periodontal ligaments. The paper is a step toward future analyses for studying and comparing the effects of MAD features, such as material, shape and dimensions, in order to allow the clinician prescribing the most fitting device.     

Investigation of impact loading rate effects on the ligamentous cervical spinal load-partitioning using finite element model of functional spinal unit C2–C3

The cervical spine functions as a complex mechanism that responds to sudden loading in a unique manner, due to intricate structural features and kinematics. The spinal load-sharing under pure compression and sagittal flexion/extension at two different impact rates were compared using a bio-fidelic finite element (FE) model of the ligamentous cervical functional spinal unit (FSU) C2–C3. This model was developed using a comprehensive and realistic geometry of spinal components and material laws that include strain rate dependency, bone fracture, and ligament failure. The range of motion, contact pressure in facet joints, failure forces in ligaments were compared to experimental findings. The model demonstrated that resistance of spinal components to impact load is dependent on loading rate and direction. For the loads applied, stress increased with loading rate in all spinal components, and was concentrated in the outer intervertebral disc (IVD), regions of ligaments to bone attachment, and in the cancellous bone of the facet joints. The highest stress in ligaments was found in capsular ligament (CL) in all cases. Intradiscal pressure (IDP) in the nucleus was affected by loading rate change. It increased under compression/flexion but decreased under extension. Contact pressure in the facet joints showed less variation under compression, but increased significantly under flexion/extension particularly under extension. Cancellous bone of the facet joints region was the only component fractured and fracture occurred under extension at both rates. The cervical ligaments were the primary load-bearing component followed by the IVD, endplates and cancellous bone; however, the latter was the most vulnerable to extension as it fractured at low energy impact.     

MicroCT image based simulation to design heating protocols in magnetic nanoparticle hyperthermia for cancer treatment

ObjectivesThe objective is to design heating protocols to completely damage PC3 tumors after a single magnetic nanoparticle hyperthermia session with minimal collateral thermal damage, based on microCT image generated tumor and mouse models.MethodsTumor geometries and volumetric heat generation rate distributions that are generated from microCT scans in our previous study are imported into COMSOL 4.3® multiphysics for heat transfer simulations and heating protocol design using the Arrhenius damage model. Then, parametric studies are performed to evaluate how significantly the infusion rate affects the protocol design and its resulted collateral thermal damage.ResultsThe simulated temperature field in the generated tumor geometry and volumetric heat generation rate distribution are reasonable and correlates well with the amount of the total thermal energy deposited into the tumors. The time needed for complete thermal damage is determined to be approximately 12 min or 25 min if one uses the Arrhenius integral Ω equal to 1 or 4 as the damage threshold, when the infusion rate is 3 μL/min. The heating time increases 26% or 91% in the higher infusion rate groups of 4 or 5 μL/min, respectively. Collateral thermal damage to the surrounding tissue is also assessed. Although the two larger infusion rate groups can still cause thermal damage to the entire tumor, the collateral thermal damage would have exceeded the design criterion of 5%, while the assessment criterion is acceptable only in the infusion rate group of 3 μL/min. Based on the results of this study, we identify an injection strategy and heating protocols to be implemented in future animal experiments to evaluate treatment efficacy for model validation.     

Adoptive transfer of mesenchymal stromal cells accelerates intestinal epithelium recovery of irradiated mice in an interleukin-6-dependent manner

Background aimsApoptosis of radiosensitive cells in the bone marrow and gut is a serious, at times life-threatening, complication arising from radiation exposure.MethodsWe investigated whether adoptive transfer of allogeneic bone marrow-derived mesenchymal stromal cells (MSC) could exert cytoprotective and life-sparing effects in a mouse model of sublethal total body irradiation (TBI).ResultsWe demonstrated that a single intraperitoneal injection of C57Bl/6 MSC given to major histocompatibility complex (MHC)-mismatched Balb/c mice within 24 h of sublethal TBI significantly reduced mortality in a dose-dependent manner. Histologic analysis and Ki67 immunostaining of jejunum sections collected 3 and 6 days post-TBI indicated that MSC protected the gastrointestinal epithelium from TBI-induced damage and significantly accelerated recovery of the gut by stimulating proliferation of the crypt cell pool. Using interleukin-6^–/– (IL-6) MSC, we demonstrated that IL-6 expressed by MSC played a role in gastrointestinal epithelium regeneration.ConclusionsOur results suggest that allogeneic MHC-mismatched MSC may be exploited to reduce gastrointestinal complications and mortality arising from ionizing radiation exposure.     

Kinetics of gene expression and bone remodelling in the clinical phase of collagen-induced arthritis

IntroductionPathological bone changes differ considerably between inflammatory arthritic diseases and most studies have focused on bone erosion. Collagen-induced arthritis (CIA) is a model for rheumatoid arthritis, which, in addition to bone erosion, demonstrates bone formation at the time of clinical manifestations. The objective of this study was to use this model to characterise the histological and molecular changes in bone remodelling, and relate these to the clinical disease development.MethodsA histological and gene expression profiling time-course study on bone remodelling in CIA was linked to onset of clinical symptoms. Global gene expression was studied with a gene chip array system.ResultsThe main histopathological changes in bone structure and inflammation occurred during the first two weeks following the onset of clinical symptoms in the joint. Hereafter, the inflammation declined and remodelling of formed bone dominated.Global gene expression profiling showed simultaneous upregulation of genes related to bone changes and inflammation in week 0 to 2 after onset of clinical disease. Furthermore, we observed time-dependent expression of genes involved in early and late osteoblast differentiation and function, which mirrored the histopathological bone changes. The differentially expressed genes belong to the bone morphogenetic pathway (BMP) and, in addition, include the osteoblast markers integrin-binding sialoprotein (Ibsp), bone gamma-carboxyglutamate protein (Bglap1), and secreted phosphoprotein 1 (Spp1). Pregnancy-associated protein A (Pappa) and periostin (Postn), differentially expressed in the early disease phase, are proposed to participate in bone formation, and we suggest that they play a role in early bone formation in the CIA model. Comparison to human genome-wide association studies (GWAS) revealed differential expression of several genes associated with human arthritis.ConclusionsIn the CIA model, bone formation in the joint starts shortly after onset of clinical symptoms, which results in bony fusion within one to two weeks. This makes it a candidate model for investigating the relationship between inflammation and bone formation in inflammatory arthritis.

Electronic supplementary material

The online version of this article (doi:10.1186/s13075-015-0531-7) contains supplementary material, which is available to authorized users.     

Modélisation mathématique du traitement par laser endoveineux (LEV)

Background and ObjectivesEndovenous laser treatment (ELT) has been recently proposed as an alternative in the treatment of reflux of the great saphenous vein (GSV) and small saphenous vein (SSV). Successful ELT depends on the selection of optimal parameters required to achieve an optimal vein damage while avoiding side effects. Mathematical modeling of ELT could provide a better understanding of the ELT process and could determine the optimal dosage as a function of vein diameter.Study design–materials and methodsThe model is based on calculations describing the light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma Inc., Arlington, MA, USA). Damage to the vein wall for CW and single shot energy was calculated for one vein diameter (3 mm). In pulsed mode, the pullback distance (3, 5 and 7 mm) was considered. For CW mode simulation, the pullback speed (1, 2, 3 mm/s) was the variable. The total dose was expressed as joules per centimeter in order to perform comparison to results already reported in clinical studies.ResultsIn pulsed mode, for a 3 mm vein diameter, irrespective of the pullback distance (2, 5 or 7 mm), a minimum fluence of 15 J/cm is required to obtain a permanent damage of the intima. In continuous mode, for a 3 mm vein diameter, 65 J/cm are required to obtain a permanent damage of the vessel wall. Finally, the use of different wavelengths (810 or 980 nm) played only a minor influence on these results.Discussion and conclusionThe parameters determined by mathematical modeling are in keeping with those used in clinical practice. They confirm that thermal damage of the inner vein wall is required to obtain a permanent occlusion. However, in order to obtain a high rate of success, without adverse events, the knowledge of the vein diameter after tumescent anesthesia is required. When performing ELT, the pulsed mode should be preferred for 2 reasons: 1) it requires less energy since the vein is only damaged sequentially and not continuously, 2) it reduces the risk of too high an energy inside the vein when pullback speed is not controlled. So, the pulsed mode requires a very precise positioning of the fiber after each pullback and the time of treatment is longer but it has been prove that this technique is reproducible, safe and efficient [29].This model should be a very useful tool to simulate ELT.     

Numerical Models for the Simulation of Flexible Artificial Heart Valves: Part I - Computational Methods

Abstract

A numerical model of the coupled motion of a flexing surface in a high Reynolds number flow is presented for the simulation of flexible polyurethane heart valves in the aortic position. This is achieved by matching a Lagrangian dynamic leaflet model with a panel method based flow solver. The two models are coupled via the time-dependent pressure field using the unsteady Bernoulli equation.

Incorporation of sub-cycling in the dynamic model equations and fast pre conditioning techniques in the panel method solver yields efficient convergence and near real-time simulations of valve motion. The generality of dynamic model allows different material properties and/or geometries to be studied easily and interactively. This interactivity is realized by embedding the models within a design environment created using the software IRIS Explorer ^TM.

Two flow domains are developed, an infinite domain and an internal domain using conformal mapping theory. In addition bending stress on the valve is computed using a simple stress model based on spline and circle equation techniques.