Size Matters: Rethinking Hertz Model Interpretation for Cell Mechanics Using AFM.

Cell mechanics are a biophysical indicator of cell state, such as cancer metastasis, leukocyte activation, and cell cycle progression. Atomic force microscopy (AFM) is a widely used technique to measure cell mechanics, where the Young modulus of a cell is usually derived from the Hertz contact model. However, the Hertz model assumes that the cell is an elastic, isotropic, and homogeneous material and that the indentation is small compared to the cell size. These assumptions neglect the effects of the cytoskeleton, cell size and shape, and cell environment on cell deformation. In this study, we investigated the influence of cell size on the estimated Young's modulus using liposomes as cell models. Liposomes were prepared with different sizes and filled with phosphate buffered saline (PBS) or hyaluronic acid (HA) to mimic the cytoplasm. AFM was used to obtain the force indentation curves and fit them to the Hertz model. We found that the larger the liposome, the lower the estimated Young's modulus for both PBS-filled and HA-filled liposomes. This suggests that the Young modulus obtained from the Hertz model is not only a property of the cell material but also depends on the cell dimensions. Therefore, when comparing or interpreting cell mechanics using the Hertz model, it is essential to account for cell size.

Measuring the viscoelastic relaxation function of cells with a time-dependent interpretation of the Hertz-Sneddon indentation model.

The Hertz-Sneddon elastic indentation model is widely adopted in the biomechanical investigation of living cells and other soft materials using atomic force microscopy despite the explicit viscoelastic nature of these materials. In this work, we demonstrate that an exact analytical viscoelastic force model for power-law materials, can be interpreted as a time-dependent Hertz-Sneddon-like model. Characterizing fibroblasts (L929) and osteoblasts (OFCOLII) demonstrates the model's accuracy. Our results show that the difference between Young's modulus EY obtained by fitting force curves with the Hertz-Sneddon model and the effective Young's modulus derived from the viscoelastic force model is less than 3%, even when cells are probed at large forces where nonlinear deformation effects become significant. We also propose a measurement protocol that involves probing samples at different indentation speeds and forces, enabling the construction of the average viscoelastic relaxation function of samples by conveniently fitting the force curves with the Hertz-Sneddon model.

Estimation of Ground Reaction Forces during Sports Movements by Sensor Fusion from Inertial Measurement Units with 3D Forward Dynamics Model.

Rotational jumps are crucial techniques in sports competitions. Estimating ground reaction forces (GRFs), a constituting component of jumps, through a biomechanical model-based approach allows for analysis, even in environments where force plates or machine learning training data would be impossible. In this study, rotational jump movements involving twists on land were measured using inertial measurement units (IMUs), and GRFs and body loads were estimated using a 3D forward dynamics model. Our forward dynamics and optimization calculation-based estimation method generated and optimized body movements using cost functions defined by motion measurements and internal body loads. To reduce the influence of dynamic acceleration in the optimization calculation, we estimated the 3D orientation using sensor fusion, comprising acceleration and angular velocity data from IMUs and an extended Kalman filter. As a result, by generating cost function-based movements, we could calculate biomechanically valid GRFs while following the measured movements, even if not all joints were covered by IMUs. The estimation approach we developed in this study allows for measurement condition- or training data-independent 3D motion analysis.

Multibody Model with Foot-Deformation Approach for Estimating Ground Reaction Forces and Moments and Joint Torques during Level Walking through Optical Motion Capture without Optimization Techniques.

The biomechanical-model-based approach with a contact model offers advantages in estimating ground reaction forces (GRFs) and ground reaction moments (GRMs), as it does not rely on the need for training data and gait assumptions. However, this approach faces the challenge of long computational times due to the inclusion of optimization processes. To address this challenge, the present study developed a new optical motion capture (OMC)-based method to estimate GRFs, GRMs, and joint torques without prolonged computational times. The proposed approach performs the estimation process by distributing external forces, as determined by a multibody model, between the left and right feet based on foot deformations, thereby predicting the GRFs and GRMs without relying on optimization techniques. In this study, prediction accuracies during level walking were confirmed by comparing a general analysis using a force plate with the estimation results. The comparison revealed excellent or strong correlations between the prediction and the measurements for all GRFs, GRMs, and lower-limb-joint torques. The proposed method, which provides practical estimation with low computational cost, facilitates efficient biomechanical analysis and rapid feedback of analysis results, contributing to its increased applicability in clinical settings.

A new method for determining the ogden parameters of soft materials using indentation experiments.

A full understanding of the material properties of skin tissue is crucial for exploring its tribo-mechanical behaviour. It has been widely accepted that the mechanical behaviour of skin tissue for both small and large deformations can be accurately described using a hyperelastic model, such as the one developed by Ogden. However, obtaining these Ogden parameters for in-vivo skin by in-vivo experiments no matter the indentation or suction tests is a significant challenge. The mathematical model used to describe the material behaviour during the test should consider not only the material nonlinearity but also the geometrical confinement of the tissue, the large deformations induced, and the fact that the specimens are relatively thin. A range of contact models is available to describe the contact behaviour during the indentation test. However, none of them can be used for hyperelastic materials with small thickness under large deformations. Simultaneously explaining material nonlinearity and geometric nonlinearity, either through theoretical equations or numerical calculations, poses a significant challenge. In this research, we propose a pragmatic method to obtain Ogden parameters for in-vivo skin tissue by combining experimental indentation results and numerical simulations. The indentation tests were used to obtain the force-indentation depth curves, while the numerical simulations were used to obtain the strain fields. The method assumes the material behaviour of specimens can be linearized in each small deformation increment, and the contact model developed by Hayes can be applied to accommodate each increment. Then, the linear elastic behaviour in each increment can be described by the elastic modulus E which were obtained using Hayes model, and the principal stresses in each increment were subsequently obtained using Hooke's law. By combining all stress fields, overall stress-strain curves can be constructed, from which the hyperelastic Ogden parameters can be obtained. A second numerical simulation of the hyperelastic indentation was then performed using the obtained Ogden parameters, allowing a comparison of the experimental and simulated relationships between force and indentation.

Modeling foot rockers via functional calibration for use in clinical gait analysis.

BACKGROUND: Goal of this work is a quantitative description of Jacquelin Perry's rocker concept by locating the position of the heel rocker and the forefoot rocker within segments of the foot via functional calibration. METHODS: Two functional calibration tasks with the foot in ground contact were performed by ten typical developed adults and foot marker motion was captured. After applying a least-square method for constructing foot segments, their motion relative to the floor was analyzed via a functional algorithm. Resulting reference positions - namely the heel rotation center and the metatarsal rotation axis - were calculated. Further, the repeatability of the method and variability of outcome within the cohort was tested. RESULTS: The heel rotation center is located substantially posterior (25 mm) and slightly more inferior (5 mm). to the midpoint of the two markers placed medially and laterally on the calcaneus. Repeated measures reveal a variation of this location around 5 mm. The forefoot center is slightly more medial to the "toe marker" (DMT2) and substantially more inferior (19 mm). The metatarsal rotation axis is slightly tilted in the frontal and transverse plane against the metatarsal line given between markers on MT1 and MT5 with small variation in repeated measures (1-2°). SIGNIFICANCE: The determination of heel rotation center and the metatarsal rotation axis relative to foot segments can be determined with good repeatability and their location meet the intuitive expectation. Since they have a direct biomechanical meaning in the foot roll-over process in gait, they may be used for a more functionally oriented definition of foot segments potentially improving the calculation of foot kinematics and kinetics in future work.

Variable Time-Step Physics Engine with Continuous Compliance Contact Model for Optimal Robotic Grinding Trajectory Planning.

In the transition from virtual environments to real-world applications, the role of physics engines is crucial for accurately emulating and representing systems. To address the prevalent issue of inaccurate simulations, this paper introduces a novel physics engine uniquely designed with a compliant contact model designed for robotic grinding. It features continuous and variable time-step simulations, emphasizing accurate contact force calculations during object collision. Firstly, the engine derives dynamic equations considering spring stiffness, damping coefficients, coefficients of restitution, and external forces. This facilitates the effective determination of dynamic parameters such as contact force, acceleration, velocity, and position throughout penetration processes continuously. Secondly, the approach utilizes effective inertia in developing the contact model, which is designed for multi-jointed robots through pose transformation. The proposed physics engine effectively captures energy conversion in scenarios with convex contact surface shapes through the application of spring dampers during collisions. Finally, the reliability of the contact solver in the simulation was verified through bouncing ball experiments and robotic grinding experiments under different coefficients of restitution. These experiments effectively recorded the continuous variations in parameters, such as contact force, verifying the integral stability of the system. In summary, this article advances physics engine technology beyond current geometrically constrained contact solutions, enhancing the accuracy of simulations and modeling in virtual environments. This is particularly significant in scenarios wherein there are constant changes in the outside world, such as robotic grinding tasks.

Systematic investigation of allelic regulatory activity of schizophrenia-associated common variants.

Genome-wide association studies (GWASs) have successfully identified 145 genomic regions that contribute to schizophrenia risk, but linkage disequilibrium makes it challenging to discern causal variants. We performed a massively parallel reporter assay (MPRA) on 5,173 fine-mapped schizophrenia GWAS variants in primary human neural progenitors and identified 439 variants with allelic regulatory effects (MPRA-positive variants). Transcription factor binding had modest predictive power, while fine-map posterior probability, enhancer overlap, and evolutionary conservation failed to predict MPRA-positive variants. Furthermore, 64% of MPRA-positive variants did not exhibit expressive quantitative trait loci signature, suggesting that MPRA could identify yet unexplored variants with regulatory potentials. To predict the combinatorial effect of MPRA-positive variants on gene regulation, we propose an accessibility-by-contact model that combines MPRA-measured allelic activity with neuronal chromatin architecture.

[Discrete element simulation study of mixing process of Guizhi Fuling Capsules: parameter calibration].

The mixing process is a critical link in the formation of oral solid preparations of traditional Chinese medicine. This paper took the extract powder of Guizhi Fuling Capsules and Paeonol powder as research objects. The angle of repose, loose packing density, and particle size of the two powders were measured to calibrate discrete element simulation parameters for the mixing process. The discrete element method was used to calibrate the simulated solid density of Paeonol powder and extract powder of Guizhi Fuling Capsules based on the Hertz-Mindlin with JKR V2 contact model and particle scaling. The Plackett-Burman experimental design was used to screen out the critical contact parameters that had a significant effect on the simulation of the angle of repose. The regression model between the critical contact parameters and the simulated angle of repose was established by the Box-Behnken experimental design, and the critical contact parameters of each powder were optimized based on the regression model. The best combination of critical contact parameters of the extract powder of Guizhi Fuling Capsules was found to be 0.51 for particle-particle static friction coefficient, 0.31 for particle-particle rolling friction coefficient, and 0.64 for particle-stainless steel static friction coefficient. For Paeonol powder, the best combination of critical contact parameters was 0.4 for particle-particle static friction coefficient and 0.19 for particle-particle rolling friction coefficient. The best combination of contact parameters between Paeonol powder and extract powder of Guizhi Fuling Capsules was 0.27 for collision recovery coefficient, 0.49 for static friction coefficient, and 0.38 for rolling friction coefficient. The verification results show that the relative error between the simulated value and the measured value of the angle of repose of the two single powders is less than 1%, while the relative error between the simulated value and the measured value of the angle of repose of the mixed powder with a mass ratio of 1∶1 is less than 4%. These research results provide reliable physical property simulation data for the mixed simulation experiment of extract powder of Guizhi Fuling Capsules and Paeonol powder.

A contact model based on the coefficient of restitution for simulations of bio-prosthetic heart valves.

A new general contact model is proposed for preventing inter-leaflet penetration of bio-prosthetic heart valves (BHV) at the end of the systole, which has the advantage of applying kinematic constraints directly and creating smooth free edges. At the end of each time step, the impenetrability constraints and momentum exchange between the impacting bodies are applied separately based on the coefficient of restitution. The contact method is implemented in a rotation-free, large deformation, and thin shell finite-element (FE) framework based on loop's subdivision surfaces. A nonlinear, anisotropic material model for a BHV is employed which uses Fung-elastic constitutive laws for in-plane and bending responses, respectively. The contact model is verified and validated against several benchmark problems. For a BHV-specific validation, the computed strains on different regions of a BHV under constant pressure are compared with experimentally measured data. Finally, dynamic simulations of BHV under physiological pressure waveform are performed for symmetrical and asymmetrical fiber orientations incorporating the new contact model and compared with the penalty contact method. The proposed contact model provides the coaptation area of a functioning BHV during the closing phase for both of the fiber orientations. Our results show that fiber orientation affects the dynamic of leaflets during the opening and closing phases. A swirling motion for the BHV with asymmetrical fiber orientation is observed, similar to experimental data. To include the fluid effects, fluid-structure interaction (FSI) simulation of the BHV is performed and compared to the dynamic results.

Effect of Rolling Resistance Model Parameters on 3D DEM Modeling of Coarse Sand Direct Shear Test.

This paper deals with the micro and macro behaviors of coarse sand inside a direct shear box during a geotechnical test. A 3D discrete element method (DEM) model of the direct shear of sand was performed using sphere particles to explore the ability of the rolling resistance linear contact model to reproduce this commonly used test considering real-size particles. The focus was on the effect of the interaction of the main contact model parameters and particle size on maximum shear stress, residual shear stress, and sand volume change. The performed model was calibrated and validated with experimental data and followed by sensitive analyses. It is shown that the stress path can be reproduced appropriately. For a high coefficient of friction, the peak shear stress and volume change during the shearing process were mainly affected by increasing the rolling resistance coefficient. However, for a low coefficient of friction, shear stress and volume change were marginally affected by the rolling resistance coefficient. As expected, varying the friction and rolling resistance coefficients was found to have less influence on the residual shear stress.

Predicting protein flexibility with AlphaFold.

AlphaFold2 has revolutionized protein structure prediction from amino-acid sequence. In addition to protein structures, high-resolution dynamics information about various protein regions is important for understanding protein function. Although AlphaFold2 has neither been designed nor trained to predict protein dynamics, it is shown here how the information returned by AlphaFold2 can be used to predict dynamic protein regions at the individual residue level. The approach, which is termed cdsAF2, uses the 3D protein structure returned by AlphaFold2 to predict backbone NMR NH S2 order parameters using a local contact model that takes into account the contacts made by each peptide plane along the backbone with its environment. By combining for each residue AlphaFold2's pLDDT confidence score for the structure prediction accuracy with the predicted S2 value using the local contact model, an estimator is obtained that semi-quantitatively captures many of the dynamics features observed in experimental backbone NMR NH S2 order parameter profiles. The method is demonstrated for a set nine proteins of different sizes and variable amounts of dynamics and disorder.

Effectiveness of enhancing contact model on reducing family caregiving burden and improving psychological wellbeing among caregivers of persons with schizophrenia in rural China.

BACKGROUND: It is unclear whether the enhancing contact model (ECM) intervention is effective in reducing family caregiving burden and improving hope and quality of life (QOL) among family caregivers of persons with schizophrenia (FCPWS). METHODS: We conducted a cluster randomized controlled trial in FCPWS in eight rural townships in Xinjin, Chengdu, China. In total, 253 FCPWS were randomly allocated to the ECM, psychoeducational family intervention (PFI), or treatment as usual (TAU) group. FCPWS in three groups were assessed caregiving burden, QOL and state of hope at baseline (T0), post-intervention (T1), 3-month (T2), and 9-month (T3) follow-up, respectively. RESULTS: Compared with participants in the TAU group, participants in the ECM group had statistically significantly lower caregiving burden scores both at T1 and T2 (p = 0.0059 and 0.0257, respectively). Compared with participants in the TAU group, participants in the PFI group had statistically significantly higher QOL scores in T1 (p = 0.0406), while participants in the ECM group had statistically significantly higher QOL scores in T3 (p = 0.0240). Participants in both ECM and PFI groups had statistically significantly higher hope scores than those in the TAU group at T1 (p = 0.0160 and 0.0486, respectively). CONCLUSIONS: This is the first study to explore the effectiveness of ECM on reducing family caregiving burden and improving hope and QOL in rural China. The results indicate the ECM intervention, a comprehensive and multifaceted intervention, is more effective than the PFI in various aspects of mental wellbeing among FCPWS. Future research needs to confirm ECM's effectiveness in various population.

Discrete element simulation study of mixing process of Guizhi Fuling Capsules: parameter calibration / 中国中药杂志

The mixing process is a critical link in the formation of oral solid preparations of traditional Chinese medicine. This paper took the extract powder of Guizhi Fuling Capsules and Paeonol powder as research objects. The angle of repose, loose packing density, and particle size of the two powders were measured to calibrate discrete element simulation parameters for the mixing process. The discrete element method was used to calibrate the simulated solid density of Paeonol powder and extract powder of Guizhi Fuling Capsules based on the Hertz-Mindlin with JKR V2 contact model and particle scaling. The Plackett-Burman experimental design was used to screen out the critical contact parameters that had a significant effect on the simulation of the angle of repose. The regression model between the critical contact parameters and the simulated angle of repose was established by the Box-Behnken experimental design, and the critical contact parameters of each powder were optimized based on the regression model. The best combination of critical contact parameters of the extract powder of Guizhi Fuling Capsules was found to be 0.51 for particle-particle static friction coefficient, 0.31 for particle-particle rolling friction coefficient, and 0.64 for particle-stainless steel static friction coefficient. For Paeonol powder, the best combination of critical contact parameters was 0.4 for particle-particle static friction coefficient and 0.19 for particle-particle rolling friction coefficient. The best combination of contact parameters between Paeonol powder and extract powder of Guizhi Fuling Capsules was 0.27 for collision recovery coefficient, 0.49 for static friction coefficient, and 0.38 for rolling friction coefficient. The verification results show that the relative error between the simulated value and the measured value of the angle of repose of the two single powders is less than 1%, while the relative error between the simulated value and the measured value of the angle of repose of the mixed powder with a mass ratio of 1∶1 is less than 4%. These research results provide reliable physical property simulation data for the mixed simulation experiment of extract powder of Guizhi Fuling Capsules and Paeonol powder.

Evaluating diagnostic and management agreement between audiology and ENT: a prospective inter-rater agreement study in a paediatric primary contact clinic.

BACKGROUND: Ear, Nose and Throat (ENT) primary contact models of care use audiologists as the first triage point for children referred to ENT for middle ear and hearing concerns; and have shown reduced waiting time, improved ENT surgical conversion rates and increased service capacity. This study aimed to investigate 'safety and quality' of the model by looking at agreement between audiologists' and an ENT's clinical decisions.  METHODS: We performed an inter-rater agreement study on diagnosis and management decisions made by audiologists and an ENT for 50 children seen in an Australian hospital's ENT primary contact service, and examined the nature and patterns of disagreements. RESULTS: Professionals agreed on at least one site-of-lesion diagnosis for all children (100%) and on the primary management for 74% (Gwet's AC1 = 0.67). Management disagreements clustered around i) providing 'watchful waiting' versus sooner medical opinion (18%), and ii) providing monitoring versus discharge for children with no current symptoms (8%). There were no cases where the audiologist recommended discharge when the ENT recommended further medical opinion. CONCLUSIONS: Our novel research provides further evidence that Audiologist-led primary contact models for children with middle ear and hearing concerns are safe as well as efficient.

Effectiveness of enhancing contact model on reducing stigma of mental illness among family caregivers of persons with schizophrenia in rural China: A cluster randomized controlled trial.

Background: Contact-based intervention has been documented and proved effective on reducing stigma of mental illness in high-income countries, but it is still unclear about the effectiveness of the contact-based intervention among family caregivers of persons with schizophrenia (FCPWS) in low- and middle-income countries including rural China. Methods: We conducted a cluster randomized controlled trial in FCPWS in eight rural townships in Xinjin district of Chengdu city in Southwest China. The FCPWS in these townships were randomly allocated to the Enhancing Contact Model (ECM), Psychoeducational Family Intervention (PFI), or Treatment as Usual (TAU) group. FCPWS in three groups were provided specific interventions and follow-ups. By using a mixed-effect model, our goal was to examine the differences in affiliate self-stigma scale (ASSS) scores among three groups with the data collected at baseline (T0), post-intervention (T1), 3-month (T2), and 9-month (T3) follow-up timepoints, respectively. This trial is registered with ChiCTR, number ChiCTR2000039133. Findings: In April 2019, 253 FCPWS from 8 townships were randomly assigned to receive either ECM (cluster=3, n=90), PFI (cluster=2, n=81), or TAU (cluster=3, n=82). Compared with participants in the TAU group, participants in the ECM group had statistically significantly lower ASSS scores at 9-month follow-up (estimated parameter [EP]= -5.51, 95% CI -10.27 to -0.74, p=0.02). There were no statistically significantly different ASSS scores at 9-month follow up between ECM and PFI groups. Compared with participants in the PFI group, younger (<60 years old), with higher monthly income and other caregiver (e.g., parent, sibling, child) participants in the ECM group had statistically significantly lower ASSS scores in the 3-month follow-up (EP = -5.66, 95% CI -10.13 to -1.19, p<0.01; EP = -7.82, 95% CI -11.87 to -3.78, p<0.001; EP = -6.79, 95% CI -10.69 to -2.90, p<0.001, respectively). Interpretation: This first trial in rural China shows that ECM intervention, a new anti-stigma intervention model, is a promising method for reducing affiliate stigma among FCPWS. The ECM intervention is more effective and stable than the PFI on reducing affiliate stigma among FCPWS. Further research needs to explore whether a long-term intervention could produce a more positive anti-stigma outcome trajectory. Funding: General Research Fund, University Grants Committee, Hong Kong SAR (GRF, Grant No. 17605618, 2018-2021, PI: Dr. M.S. Ran).

Development of Mixed Anxiety/Depression-Like State as a Consequence of Chronic Anxiety: Review of Experimental Data.

The review presents experimental data considered from the point of view of dynamic changes in the brain neurochemistry, physiology, and behavior of animals during the development of mixed anxiety/depression-like disorder caused by chronic social stress from norm to severe psychopathology. Evidences are presented to support the hypothesis that chronic anxiety rather than social defeat stress is an etiological factor in depression. The consequences of chronic anxiety for human health and social life are discussed.

Computational Fluid-Structure Interaction Study of a New Wave Membrane Blood Pump.

PURPOSE: Wave membrane blood pumps (WMBP) are novel pump designs in which blood is propelled by means of wave propagation by an undulating membrane. In this paper, we computationally studied the performance of a new WMBP design (J-shaped) for different working conditions, in view of potential applications in human patients. METHODS: Fluid-structure interaction (FSI) simulations were conducted in 3D pump geometries and numerically discretized by means of the extended finite element method (XFEM). A contact model was introduced to capture membrane-wall collisions in the pump head. Mean flow rate and membrane envelope were determined to evaluate hydraulic performance. A preliminary hemocompatibility analysis was performed via calculation of fluid shear stress. RESULTS: Numerical results, validated against in vitro experimental data, showed that the hydraulic output increases when either the frequency or the amplitude of membrane oscillations were higher, with limited increase in the fluid stresses, suggesting good hemocompatibility properties. Also, we showed better performance in terms of hydraulic power with respect to a previous design of the pump. We finally studied an operating point which achieves physiologic flow rate target at diastolic head pressure of 80 mmHg. CONCLUSION: A new design of WMBP was computationally studied. The proposed FSI model with contact was employed to predict the new pump hydraulic performance and it could help to properly select an operating point for the upcoming first-in-human trials.

A Computationally Efficient Lower Limb Finite Element Musculoskeletal Framework Directly Driven Solely by Inertial Measurement Unit Sensors.

Finite element musculoskeletal (FEMS) approaches using concurrent musculoskeletal (MS) and finite element (FE) models driven by motion data such as marker-based motion trajectory can provide insight into the interactions between the knee joint secondary kinematics, contact mechanics, and muscle forces in subject-specific biomechanical investigations. However, these data-driven FEMS systems have two major disadvantages that make them challenging to apply in clinical environments: they are computationally expensive and they require expensive and inconvenient equipment for data acquisition. In this study, we developed an FEMS model of the lower limb, driven solely by inertial measurement unit (IMU) sensors, that includes the tissue geometries of the intact knee joint and combines muscle modeling and elastic foundation (EF) theory-based contact analysis of a knee into a single framework. The model requires only the angular velocities and accelerations measured by the sensors as input, and the target outputs (knee contact mechanics, secondary kinematics, and muscle forces) are predicted from the convergence results of iterative calculations of muscle force optimization and knee contact mechanics. To evaluate its accuracy, the model was compared with in vivo experimental data during gait. The maximum contact pressure (12.6 MPa) in the rigid body contact analysis occurred on the medial side of the cartilage at the maximum loading response. The proposed computationally efficient framework drastically reduced the computational time (97.5% reduction) in comparison with the conventional deformable FE analysis. The developed framework combines measurement convenience and computational efficiency and shows promise for clinical applications aimed at understanding subject-specific interactions between the knee joint secondary kinematics, contact mechanics, and muscle forces.

Extended Kalman filter for online soft tissue characterization based on Hunt-Crossley contact model.

Real-time soft tissue characterization is significant to robotic assisted minimally invasive surgery for achieving precise haptic control of robotic surgical tasks and providing realistic force feedback to the operator. This paper presents a nonlinear methodology for online soft tissue characterization. An extended Kalman filter (EKF) is developed based on dynamic linearization of the nonlinear H-C contact model in terms of system state for online characterization of soft tissue parameters. To handle the resultant linearization modelling error, an innovation orthogonal EKF is further developed by incorporating an adaptive factor in the EKF filtering to adaptively adjust the innovation covariance according to the principle of innovation orthogonality. Simulation and experimental results as well as comparison analysis demonstrate that the proposed methodology can effectively characterize soft tissue parameters, leading to dramatically improved accuracy comparing to recursive least square estimation. Further, the proposed methodology also requires a smaller computational load and can achieve the real-time performance for soft tissue characterization.