Simulating dynamic activities using a five-axis knee simulator

This work describes the design and capabilities of the Purdue Knee Simulator: Mark II and a sagittal-plane model of the machine. This five-axis simulator was designed and constructed to simulate dynamic loading activities on either cadaveric knee specimens or total knee prostheses mounted on fixtures. The purpose of the machine was to provide a consistent, realistic loading of the knee joint, allowing the kinematics and specific loading of the structures of the knee to be determined based on condition, articular geometry, and simulated activity. The sagittal-plane model of the knee simulator was developed both to predict the loading at the knee from arbitrary inputs and to generate the necessary inputs required to duplicate specified joint loading. Measured tibio-femoral compressive force and quadriceps tension were shown to be in good agreement with the predicted loads from the model. A controlled moment about the ankle-flexion axis was also shown to change the loading on the quadriceps.     

Computational modeling of a dynamic knee simulator for reproduction of knee loading

As a first step towards reproducing desired three-dimensional joint loading and motion on a dynamic knee simulator, the goal of this study was to develop and verify a three-dimensional computational model that generated control profiles for the simulator using desired knee loading and motion as model inputs. The developed model was verified by predicting tibio-femoral loading on an instrumented analog knee for given actuator forces and the ability to generate simulator control profiles was demonstrated using a three-dimensional walking profile. The model predicted axial tibia loading for a sagittal-plane dual-limb squat within 1% of measured peak loading. Adding out-of-sagittal-plane forces decreased the accuracy of load prediction. The model generated control profiles to the simulator that produced axial tibia loading within 16% of desired for walking. Discrepancies in predicted and measured quadriceps forces influenced the accuracy of the generated control profiles. Future work will replace the analog knee in both the model and machine with a prosthetic knee.     

The development,calibration and validation of a numerical total knee replacement kinematics simulator considering laxity and unconstrained flexion motions

Kinematics testing is essential during the development of total knee replacement (TKR) designs. Although computational analysis cannot replace physical testing, it offers repeatability and consistency at a much lower cost and shorter time, making it an excellent complement to experiments. Previous numerical models have been limited by several factors: the validity of the models is usually only considered for a single TKR design, friction models are typically overly simplified and the determination of simulation parameters is often inadequate, or tedious and expensive. The objective of this study is to develop, calibrate and validate a TKR kinematics simulation considering multiple TKR geometries, an accurate friction model and simulation parameters determined using a systematic optimisation method. The calibrated model was able to predict TKR kinematics for different TKR geometries, and is ideal for screening new implant designs, reducing the number of experiments required at the design stage.     

The development, calibration and validation of a numerical total knee replacement kinematics simulator considering laxity and unconstrained flexion motions

Kinematics testing is essential during the development of total knee replacement (TKR) designs. Although computational analysis cannot replace physical testing, it offers repeatability and consistency at a much lower cost and shorter time, making it an excellent complement to experiments. Previous numerical models have been limited by several factors: the validity of the models is usually only considered for a single TKR design, friction models are typically overly simplified and the determination of simulation parameters is often inadequate, or tedious and expensive. The objective of this study is to develop, calibrate and validate a TKR kinematics simulation considering multiple TKR geometries, an accurate friction model and simulation parameters determined using a systematic optimisation method. The calibrated model was able to predict TKR kinematics for different TKR geometries, and is ideal for screening new implant designs, reducing the number of experiments required at the design stage.     

A reliable simulator for dynamic flux balance analysis

Dynamic flux balance analysis (DFBA) provides a platform for detailed design, control and optimization of biochemical process technologies. It is a promising modeling framework that combines genome‐scale metabolic network analysis with dynamic simulation of the extracellular environment. Dynamic flux balance analysis assumes that the intracellular species concentrations are in equilibrium with the extracellular environment. The resulting underdetermined stoichiometric model is solved under the assumption of a biochemical objective such as growth rate maximization. The model of the metabolism is coupled with the dynamic mass balance equations of the extracellular environment via expressions for the rates of substrate uptake and product excretion, which imposes additional constraints on the linear program (LP) defined by growth rate maximization of the metabolism. The linear program is embedded into the dynamic model of the bioreactor, and together with the additional constraints this provides an accurate model of the substrate consumption, product secretion, and biomass production during operation. A DFBA model consists of a system of ordinary differential equations for which the evaluation of the right‐hand side requires not only function evaluations, but also the solution of one or more linear programs. The numerical tool presented here accurately and efficiently simulates large‐scale dynamic flux balance models. The main advantages that this approach has over existing implementation are that the integration scheme has a variable step size, that the linear program only has to be solved when qualitative changes in the optimal flux distribution of the metabolic network occur, and that it can reliably simulate behavior near the boundary of the domain where the model is defined. This is illustrated through large‐scale examples taken from the literature. Biotechnol. Bioeng. 2013; 110: 792–802. © 2012 Wiley Periodicals, Inc.     

A simple cardiovascular system simulator: design and performance

A simple simulator has been constructed, evaluated and used for performance studies of prosthetic aortic valves, balloon assist devices and Koroktof sounds and ausculatory cuff blood pressure measurements. A direct drive piston pump is used. Elastic soft rubber tubes with distributed resistances allow modeling of normal and diseased pressure pulse waves. Pressure pulse amplitude amplification is modeled with tube segments of decreasing diameters. Satisfactory proximal pressure pulse shapes are obtained with a soft rubber tube of uniform diameter.     

A dynamic simulator to evaluate distal radio-ulnar joint kinematics

In order to perform cadaveric biomechanical studies of the human forearm and distal radio-ulnar joint, a dynamic simulator has been constructed. The device is based upon a Plexiglas frame, to which the ulna is secured in a vertical orientation and the humerus in a horizontal orientation. The hand is secured in a sliding bar linkage to a stepper-motor that is used to rotate the forearm. The tendons to be loaded are connected to pneumatic actuators that provide agonist and antagonist muscle loading resulting in torque along the forearm axis. The muscle loading profiles and magnitudes are programmable as a function of the pronation-supination position and direction. A magnetic tracking system is used to collect three-dimensional kinematics data of up to four segments, in conjunction with the muscle tendon loads, forearm torque and other prescribed experimental measures. All functions are under PC control using custom software written with LabVIEW (National Instruments, Austin, TX). For the DRUJ testing, the validity of the tendon loading protocol to produce physiologic torque/rotation patterns was verified using in vivo data. The relationship of individual muscle forces to forearm torque was determined by a cadaveric study.     

The use of a force-controlled dynamic knee simulator to quantify the mechanical performance of total knee replacement designs during functional activity

The experimental evaluation of any total knee replacement (TKR) design should include the pre-implantation quantification of its mechanical performance during tests that simulate the common activities of daily living. To date, few dynamic TKR simulation studies have been conducted before implantation. Once in vivo, the accurate and reproducible assessment of TKR design mechanics is exceedingly difficult, with the secondary variables of the patient and the surgical technique hindering research. The current study utilizes a 6-degree-of-freedom force-controlled knee simulator to quantify the effect of TKR design alone on TKR mechanics during a simulated walking cycle. Results show that all eight TKR designs tested elicited statistically different measures of tibial/femoral kinematics, simulated soft tissue loading, and implant geometric restraint loading during an identical simulated gait cycle, and that these differences were a direct result of TKR design alone. Maximum ranges of tibial kinematics over the eight designs tested were from 0.8mm anterior to 6.4mm posterior tibial displacement, and 14.1 degrees internal to 6.0 degrees external tibial rotation during the walking cycle. Soft tissue and implant reaction forces ranged from 106 and 222N anteriorly to 19 and 127N posteriorly, and from 1.6 and 1.8Nm internally to 3.5 and 5.9Nm externally, respectively. These measures provide valuable experimental insight into the effect of TKR design alone on simulated in vivo TKR kinematics, bone interface loading and soft tissue loading. Future studies utilizing this methodology should investigate the effect of experimentally controlled variations in surgical and patient factors on TKR performance during simulated dynamic activity.     

A direct comparison of patient and force-controlled simulator total knee replacement kinematics

The need to critically evaluate the efficacy of current total knee replacement (TKR) wear testing methodologies is great. Proposed international standards for TKR wear simulation have been drafted, yet their methods continue to be debated. The "gold standard" to which all TKR wear testing methodologies should be compared is measured in vivo TKR performance in patients. The current study compared patient TKR kinematics from fluoroscopic analysis and simulator TKR kinematics from force-controlled wear testing to quantify similarities in clinical ranges of motion and contact bearing kinematics and to evaluate the proposed ISO force-controlled wear testing methodology. The treadmill walking kinematics from eight well-functioning, 13 month average post-op patients were compared to the 2 million cycle interval walking cycle kinematics from a force-controlled (Instron/Stanmore Knee Joint Simulator, Instron, Canton, MA) knee simulator using identical implant designs (Natural Knee II, Standard Congruent, Zimmer, Warsaw, IN). The in vivo and simulator data showed good agreement in kinematic patterns and ranges of clinical motion. Tribologically the data sets showed similar contact pathway ranges of motion and wear travel distances per cycle. Surgical and simulator alignments of the implant systems were determined to be a contributing factor in observed kinematic differences. This study's statistical findings offer supporting evidence that the simulation of in vivo walking cycle wear kinematics can be accurately reproduced with a force controlled testing methodology.     

Probabilistic finite element prediction of knee wear simulator mechanics

Computational models have recently been developed to replicate experimental conditions present in the Stanmore knee wear simulator. These finite element (FE) models, which provide a virtual platform to evaluate total knee replacement (TKR) mechanics, were validated through comparisons with experimental data for a specific implant. As with any experiment, a small amount of variability is inherently present in component alignment, loading, and environmental conditions, but this variability has not been previously incorporated in the computational models. The objectives of the current research were to assess the impact of experimental variability on predicted TKR mechanics by determining the potential envelope of joint kinematics and contact mechanics present during wear simulator loading, and to evaluate the sensitivity of the joint mechanics to the experimental parameters. In this study, 8 component alignment and 4 experimental parameters were represented as distributions and used with probabilistic methods to assess the response of the system, including interaction effects. The probabilistic FE model evaluated two levels of parameter variability (with standard deviations of component alignment parameters up to 0.5mm and 1 degrees ) and predicted a variability of up to 226% (3.44mm) in resulting anterior-posterior (AP) translation, up to 169% (4.30 degrees ) in internal-external (IE) rotation, but less than 10% (1.66MPa) in peak contact pressure. The critical alignment parameters were the tilt of the tibial insert and the IE rotational alignment of the femoral component. The observed variability in kinematics and, to a lesser extent, contact pressure, has the potential to impact wear observed experimentally.     

A simple model of dynamic receptor pattern generation

A dynamic pattern generating automaton has been constructed. The rules controlling its function furnish the non-random generation of sub-patterns in consecutive cycles, within a large plane area, covered by four different classes of units of constant mean frequency in each class (standard system). The stabilization of certain specific sub-patterns over 100 subsequent cycles of pattern generation (modified systems) resulted in the modification of the frequency and frequency distribution of the sub-patterns relative to the standard system. Some new types of sub-patterns, not encountered in the standard system, also made appearance in the modified systems. The functioning of the standard and modified systems was analyzed and compared by the methods of mathematical statistics. The automaton was used to model certain features of the cytoplasmic membrane. The latter was regarded as a device by which the cell collects information about its environment. The dynamic generation of sub-patterns was taken as the cell's manner of asking questions, and the complementary chemical structures present in the environment were treated as possible answers to these. The irreversible question-answer interactions were regarded as signals and were modelled by the stabilization of specific sub-patterns. It was found that in a dynamic system like the model presented, it is not necessary to code each possible sub-pattern individually. Precise coding of the relative frequency of units per class and of their possible interactions is sufficient to furnish statistically constant mean frequencies for a given range of sub-patterns. In a dynamic system, the actual range of sub-patterns arisen in a population of identical individuals depends only on the size of the population. If the latter is appropriately large, all possible sub-patterns may be simultaneously present at any time at the average frequencies characteristic of each. Stabilized sub-patterns (signals) seem to modify specifically the frequencies of the other sub-patterns generated by the normal automaton. Some sub-patterns may disappear permanently, while others (new ones) may turn up and persist at given frequencies. Missense signals may definitively put the automaton out of order, i.e. result in the cell's complete misorientation in respect of its relations to the normal tissue structure.Reader of publications in physics, Gondolat Publishing House, Budapest, Hungary     

Modeling biological systems using Dynetica--a simulator of dynamic networks

We present Dynetica, a user-friendly simulator of dynamic networks for constructing, visualizing, and analyzing kinetic models of biological systems. In addition to generic reaction networks, Dynetica facilitates construction of models of genetic networks, where many reactions are gene expression and interactions among gene products. Further, it integrates the capability of conducting both deterministic and stochastic simulations. AVAILABILITY AND SUPPLEMENTARY INFORMATION: Dynetica 1.0, example models, and the user's guide are available at http://www.its.caltech.edu/~you/Dynetica/Dynetica_page.htm     

A simple tide simulator for maintenance of marine (intertidal) algal and lichen cultures

Strumpshaw Broad is a medieval man-made lake, excavated about 500 years ago in valley peat deposits. Evidence from diatom fossils, and other remains (filamentous algae, Chrysophycean cysts, sponge spicules, snail shells) indicates a series of changes since the eighteenth century probably related to development of the city of Norwich and sophistications of its sewerage system. Progressive nutrient-enrichment led to replacement around 1912 of low-growing macrophytes (Chara) and sparse plankton populations by tall-growing vascular aquatic macrophytes, with increased epiphytic diatom numbers. A blanketing phase of filamentous algae (probably Vaucheria) was associated with the transition between 1795 and 1903. Around 1950, after a phase of increasing plankton populations and declining epiphyte and macrophyte numbers, the macrophyte-epiphyte complex disappeared altogether, to be replaced by dense plankton populations for a few years. These changes and the progressive decrease in volume of the lake owing to increased build up of sediment throughout the period covered by the core, led to alterations in hydrology which now prevent even plankton development. All data are expressed on absolute bases (amount sedimented per unit area per year) and the necessity for this, as opposed to relative measures (percentage representation, concentration per unit weight) in valid interpretation of palaeolimnological data is emphasized.     

A rolling-gliding wear simulator for the investigation of tribological material pairings for application in total knee arthroplasty

Background  

Material wear testing is an important technique in the development and evaluation of materials for use in implant for total knee arthroplasty. Since a knee joint induces a complex rolling-gliding movement, standardised material wear testing devices such as Pin-on-Disc or Ring-on-Disc testers are suitable to only a limited extent because they generate pure gliding motion only.     

A cis-regulatory logic simulator

Background  

A major goal of computational studies of gene regulation is to accurately predict the expression of genes based on the cis-regulatory content of their promoters. The development of computational methods to decode the interactions among cis-regulatory elements has been slow, in part, because it is difficult to know, without extensive experimental validation, whether a particular method identifies the correct cis-regulatory interactions that underlie a given set of expression data. There is an urgent need for test expression data in which the interactions among cis-regulatory sites that produce the data are known. The ability to rapidly generate such data sets would facilitate the development and comparison of computational methods that predict gene expression patterns from promoter sequence.     

A phase dynamic model of systematic error in simple copying tasks

A crucial insight into handwriting dynamics is embodied in the idea that stable, robust handwriting movements correspond to attractors of an oscillatory dynamical system. We present a phase dynamic model of visuomotor performance involved in copying simple oriented lines. Our studies on human performance in copying oriented lines revealed a systematic error pattern in orientation of drawn lines, i.e., lines at certain orientation are drawn more accurately than at other values. Furthermore, human subjects exhibit “flips” in direction at certain characteristic orientations. It is argued that this flipping behavior has its roots in the fact that copying process is inherently ambiguous—a line of given orientation may be drawn in two different (mutually opposite) directions producing the same end result. The systematic error patterns seen in human copying performance is probably a result of the attempt of our visuomotor system to cope with this ambiguity and still be able to produce accurate copying movements. The proposed nonlinear phase-dynamic model explains the experimentally observed copying error pattern and also the flipping behavior with remarkable accuracy.     

A simple Markov model of sodium channels with a dynamic threshold

Characteristics of action potential generation are important to understanding brain functioning and, thus, must be understood and modeled. It is still an open question what model can describe concurrently the phenomena of sharp spike shape, the spike threshold variability, and the divisive effect of shunting on the gain of frequency-current dependence. We reproduced these three effects experimentally by patch-clamp recordings in cortical slices, but we failed to simulate them by any of 11 known neuron models, including one- and multi-compartment, with Hodgkin-Huxley and Markov equation-based sodium channel approximations, and those taking into account sodium channel subtype heterogeneity. Basing on our voltage-clamp data characterizing the dependence of sodium channel activation threshold on history of depolarization, we propose a 3-state Markov model with a closed-to-open state transition threshold dependent on slow inactivation. This model reproduces the all three phenomena. As a reduction of this model, a leaky integrate-and-fire model with a dynamic threshold also shows the effect of gain reduction by shunt. These results argue for the mechanism of gain reduction through threshold dynamics determined by the slow inactivation of sodium channels.     

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.     

Two-dimensional dynamic modelling of human knee joint

A mathematical dynamic model of the two-dimensional representation of the knee joint is presented. The profiles of the joint surfaces are determined from X-ray films and they are represented by polynomials. The joint ligaments are modelled as nonlinear elastic springs of realistic stiffness properties. Nonlinear equations of motion coupled with nonlinear constraint conditions are solved numerically. Time derivatives are approximated by Newmark difference formulae and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads are applied to the center of mass of the tibia and the ensuing motion is investigated. Numerical results on ligament forces, contact point locations between femur and tibia, and the orientation of tibia relative to femur are presented. The results are shown to be consistent with the anatomy of the knee joint.