Rainald M. Ehrig

The SCoRE residual: a quality index to assess the accuracy of joint estimations.

The determination of an accurate centre of rotation (CoR) from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis. Despite the many functional approaches to estimate CoRs, no non-invasive analytical determination of the error in the reconstructed joint location is currently available. The purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation (SCoRE) as a reliable indirect measure of the error of the computed joint centre. To evaluate the SCoRE residual, numerical simulations were performed to evaluate CoR estimations at different ranges of joint motion. A statistical model was developed and used to determine the theoretical relationships among the SCoRE residual, the magnitude of the skin marker artefact, the corrections to the marker positions, and the error of the CoR estimations to the known centre of rotation. We found that the equation err=0.5r(s) provides a reliable relationship among the CoR error, err, and the scaled SCoRE residual, r(s), providing that any skin marker artefact is first minimised using the optimal common shape technique (OCST). Measurements on six healthy volunteers showed a reduction of SCoRE residual from 11 to below 6mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data. This study also demonstrates the significant benefit of the OCST for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis. For the first time, this understanding of the SCoRE residual allows a measure of error in the non-invasive assessment of joint centres. This measure now enables a rapid assessment of the accuracy of the CoR as well as an estimation of the reproducibility and repeatability of skeletal motion patterns.

The weighted optimal common shape technique improves identification of the hip joint center of rotation in vivo.

Functional methods present a promising approach for the identification of skeletal kinematics, but their accuracy is limited by soft tissue artifacts (STAs). We hypothesized that consideration of the nonuniform distribution of STAs across the segment can lead to a significant improvement in the determination of the center of rotation at the hip. Twenty‐four total hip arthroplasty (THA) patients performed repetitions of a star‐arc movement. The location of the hip centers of rotation (CoRs) were estimated from the motion data using the Symmetrical Center of Rotation Estimation (SCoRE), both with and without procedures to minimize the effect of STAs. The precision of the CoR estimations was evaluated using the SCoRE residual, a measure of joint precision. Application of the newly developed weighted Optimal Common Shape Technique (wOCST) achieved the best CoR estimations with a precision of better than 3 mm, while the precision using raw data alone was up to seven times worse. Furthermore, consideration of the nonuniform distribution of STA across the surface of the skin using the wOCST produced an improvement of ∼24% over kinematics data processed using the standard OCST. Functional determination of the CoR at the hip using the newly developed wOCST can now identify the joint CoR with a precision of millimeters. Such approaches therefore offer improved precision in the assessment of skeletal kinematics and may aid in evaluating clinical treatment success and differentiating between therapy outcomes.

Aerosol formation in gas-liquid contact devices: Nucleation, growth and particle dynamics

Abstract In gas–liquid contact devices like absorbers, scrubbers, quench coolers or condensers, aerosols can be formed by spontaneous phase transitions, initiated by homogeneous or heterogeneous nucleation, if special process operation conditions lead to a metastable, i.e. a supersaturated state in the gas phase. Aerosol formation can impact severely the mass separation efficiency of gas–liquid contactors. This is demonstrated by experiments performed in semi-technical plants. The paper is aimed to identify strategies for understanding and describing the complex aerosol behaviour in gas–liquid contact devices. Operation conditions are identified under which supersaturation can arise, and the fundamentals of modelling aerosol formation and growth in gas–liquid contactors are discussed. The SENECA code developed by the authors allows to simulate aerosol formation and behaviour in contact devices as well as in multistage gas cleaning processes. Experimental results show that most of all important features of aerosol behaviour in flue gas cleaning and in condensation processes can be predicted with good accuracy by SENECA.

Modelling and Simulation of Aerosol Formation by Heterogeneous Nucleation in Gas-Liquid Contact Devices

Abstract This paper describes a new simulation tool for the prediction of aerosol formation and behaviour in gas–liquid contact devices such as absorbers, scrubbers, quench coolers, and condensers as well as multistage gas cleaning processes, respectively. Aerosol formation can impact severely the separation efficiency of gas cleaning processes. Aerosol or fog formation can arise by spontaneous condensation or desublimation in supersaturated gas phases. The rigorous description of the mass and energy transfer between the gas phase, the liquid phase, and the growing aerosol droplets leads to a system of partial differential and algebraic equations. For the solution of these systems, we have developed the plant simulation tool AerCoDe. This programme bases upon the linearly-implicit Euler discretization, which in combination with extrapolation permits an adaptive step size and order control. Typical simulation results of a multistage industrial flue gas scrubbing process are presented. It is shown, that experimental data can be confirmed if the number concentration of condensation nuclei as an input parameter is roughly known.

Massively Parallel Linearly-Implicit Extrapolation Algorithms as a Powerful Tool in Process Simulation*

We study the parallelization of linearly-implicit extrapolation codes for the solution of large scale PDE systems and differential algebraic equations on distributed memory machines. The main advantage of these algorithms is that they enable adapativity both in time and space. Additive Krylov-Schwarz methods yield high parallel perfomance for extrapolation methods. Our approach combines a slightly overlapping domain decomposition together with a polynomial block Neumann preconditioner and a reduced system technique. A further speedup we got by the explicit computation of the matrix-products of the preconditioner and the matrix of the linear system. The parallel algorithms exhibit scalability up to 64 processors already for medium-sized test problems. We show that the codes are really efficient in large application systems for chemical engineering problems.

Anterior Cruciate Ligament–Deficient Patients With Passive Knee Joint Laxity Have a Decreased Range of Anterior-Posterior Motion During Active Movements

Background: Although instability of the knee joint is known to modify gait patterns, the amount that patients compensate for joint laxity during active movements remains unknown. Purpose: By developing a novel technique to allow the assessment of tibiofemoral kinematics, this study aimed to elucidate the role of passive joint laxity on active tibiofemoral kinematics during walking. Study Design: Controlled laboratory study. Methods: Using motion capture, together with combinations of advanced techniques for assessing skeletal kinematics (including the symmetrical axis of rotation approach [SARA], symmetrical center of rotation estimation [SCoRE], and optimal common shape technique [OCST]), a novel noninvasive approach to evaluate dynamic tibiofemoral motion was demonstrated as both reproducible and repeatable. Passive and active anterior-posterior translations of the tibiofemoral joint were then examined in 13 patients with anterior cruciate ligament (ACL) ruptures that were confirmed by magnetic resonance imaging and compared with those in their healthy contralateral limbs. Results: Passive tibial anterior translation was significantly greater in the ACL-ruptured knees than in the contralateral healthy controls. However, the femora of the ACL-ruptured knees generally remained more posterior (~3 mm) relative to the tibia within a gait cycle of walking compared with the healthy limbs. Surprisingly, the mean range of tibiofemoral anterior-posterior translation over an entire gait cycle was significantly lower in ACL-ruptured knees than in the healthy joints (P = .026). A positive correlation was detected between passive laxity and active joint mobility, but with a consistent reduction in the range of tibiofemoral anterior-posterior translation of approximately 3 mm in the ACL-deficient knees. Conclusion: It seems that either active stabilization of tibiofemoral kinematics or anterior subluxation of the tibia reduces joint translation in lax knees. This implies that either a muscular overcompensation mechanism or a physical limitation due to secondary passive stabilizers occurs within the joint and thus produces a situation that has a reduced range of active motion compared with knees with physiological stability. Clinical Relevance: The reduced range of active tibiofemoral translation suggests overloading of the passive structures in passively lax knees, either through excessive muscular action or joint subluxation, and could provide a plausible mechanism for explaining posttraumatic degeneration of cartilage in the joint.

Effective marker placement for functional identification of the centre of rotation at the hip

The accuracy and precision of quantifying musculoskeletal kinematics, and particularly determining the centre of rotation (CoR) at the hip joint, using skin marker based motion analysis is limited by soft tissue artefact (STA). We posed the question of whether the contribution of individual markers towards improving the precision of the functional joint centre using marker based methods could be assessed, and then utilised to allow effective marker placement for determination of the CoR at the hip. Sixty-three retro-reflective skin markers were placed to encompass the thighs of seven healthy subjects, together with a set of sixteen markers on the pelvis. The weighted optimal common shape technique (wOCST) was then applied to determine the weighting, or importance, of each marker for identifying the centre of rotation at the hip. The markers with the highest weightings over all subjects and measurements were determined that identified the HJC with the highest precision. The use of six markers in selected regions (two anterior, two lateral and two posterior) allowed the HJC to be determined with a similar precision to the complete set of 63 markers, with the determined regions predominantly distant from the hip joint, excluding areas associated with the bellies of large muscles and therefore large motion artefact from muscle activity. The novel approach presented here allows an understanding of each markers contribution towards a precise joint determination, and therefore enables the targeted placement of markers for reliable assessment of musculoskeletal kinematics.

The medial–lateral force distribution in the ovine stifle joint during walking

Knowledge of the load distribution in the knee is essential for understanding the interaction between mechanics and biology in both the healthy and diseased joint. While the sheep stifle joint is a predominant model for better understanding regeneration after injury, little is known about the compartmental force distribution between the medial and lateral condyles. By including sheep specific anatomy and gait analyses, we used computational musculoskeletal analyses to estimate the medial–lateral joint contact force distribution in ovine stifle joints during walking by simplifying the system of equations into a 2D problem that was solved directly. Gait analysis was conducted using bone markers in three female Merino‐mix sheep. Joint contact forces were computed with respect to the specific anatomy of the ovine tibia, resulting in low (<0.13 bodyweight) mean anteroposterior shear forces throughout the gait cycle, with mean peak contact forces perpendicular to the tibial plateau of 2.2 times bodyweight. The medial–lateral compartmental load distribution across the tibial condyles was determined and revealed loading predominantly on the medial condyle, bearing approximately 75% of the total load during phases of peak loading. By considering the anatomical characteristics of the ovine stifle joint, together with the dynamic forces during gait, this study provides evidence for predominantly medial loading in sheep, somewhat similar to the distribution reported in man. However, the exact conditions under which the loading in the ovine stifle joint is representative of the human situation will need to be elucidated in further studies.

Frontal plane alignment: An imageless method to predict the mechanical femoral–tibial angle (mFTA) based on functional determination of joint centres and axes

Lower limb alignment is important for the internal loading conditions in the knee. In this study, we aimed to evaluate a new imageless, non-invasive method for quantifying frontal plane alignment by direct comparison against CT. To determine the mechanical femoral-tibial angle (mFTA), functional posture analysis was performed in 15 limbs (13 individuals) using previously published methods for the minimisation of skin marker artefact together with the functional identification of joints, and compared against a published regression method. Whilst the average Functional-mFTA (1.3 + or - 2.3) was not significantly different (p > 0.25) from the CT-mFTA (1.5 + or - 2.1), the Regression-mFTA (4.7 + or - 5.6) showed a significant error (p < 0.01). The Functional-mFTA correlated significantly (R = 0.91; p < 0.0001), with a small bias (0.3 degrees) and agreed better with the CT-mFTA than the Regression-mFTA (R = 0.76; p < 0.001), which had a bias of 3.4 degrees. The results demonstrate that the mFTA can be quantified accurately using an imageless, non-invasive functional approach, which also offers greater accuracy over regression methods.These new techniques could provide an accurate, non-invasive approach for quantifying frontal plane alignment, particularly in cases where X-rays may not be available.

Parameter Identification in a Tuberculosis Model for Cameroon

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.