A task-specific validation of homogeneous non-linear optimisation approaches

In biomechanics, musculoskeletal models are typically redundant. This situation is referred to as the distribution problem. Often, static, non-linear optimisation methods of the form “min: φ(f) subject to mechanical and muscular constraints” have been used to extract a unique set of muscle forces. Here, we present a method for validating this class of non-linear optimisation approaches where the homogeneous cost function, φ(f), is used to solve the distribution problem. We show that the predicted muscle forces for different loading conditions are scaled versions of each other if the joint loading conditions are just scaled versions. Therefore, we can calculate the theoretical muscle forces for different experimental conditions based on the measured muscle forces and joint loadings taken from one experimental condition and assuming that all input into the optimisation (e.g., moment arms, muscle attachment sites, size, fibre type distribution) and the optimisation approach are perfectly correct. Thus predictions of muscle force for other experimental conditions are accurate if the optimisation approach is appropriate, independent of the musculoskeletal geometry and other input required for the optimisation procedure. By comparing the muscle forces predicted in this way to the actual muscle forces obtained experimentally, we conclude that convex homogeneous non-linear optimisation approaches cannot predict individual muscle forces properly, as force-sharing among synergistic muscles obtained experimentally are not just scaled versions of joint loading, not even in a first approximation.     

Comparison of physics-based and data-driven modelling techniques for dynamic optimisation of fed-batch bioprocesses

The development of digital bioprocessing technologies is critical to operate modern industrial bioprocesses. This study conducted the first investigation on the efficiency of using physics-based and data-driven models for the dynamic optimisation of long-term bioprocess. More specifically, this study exploits a predictive kinetic model and a cutting-edge data-driven model to compute open-loop optimisation strategies for the production of microalgal lutein during a fed-batch operation. Light intensity and nitrate inflow rate are used as control variables given their key impact on biomass growth and lutein synthesis. By employing different optimisation algorithms, several optimal control sequences were computed. Due to the distinct model construction principles and sophisticated process mechanisms, the physics-based and the data-driven models yielded contradictory optimisation strategies. The experimental verification confirms that the data-driven model predicted a closer result to the experiments than the physics-based model. Both models succeeded in improving lutein intracellular content by over 40% compared to the highest previous record; however, the data-driven model outperformed the kinetic model when optimising total lutein production and achieved an increase of 40–50%. This indicates the possible advantages of using data-driven modelling for optimisation and prediction of complex dynamic bioprocesses, and its potential in industrial bio-manufacturing systems.     

Successful Application of Evolutionary Algorithms in Engineering Design

Evolutionary or bionic strategies have proven to be powerful tools in many optimisation studies. Starting with some parent generations, producing sets of children, selecting the best children to be new parents yields impressive improvements of the objective when used with some experience and sufficient equipment. During some years of research the parameters of evolutionary optimisation have been investigated. Many successful applications showed where and how to use it. Especially in the case of objective functions with some or many local maxima, evolutionary approaches may propose solutions which gradient based optimisation would hardly find.When used with a large number of optimisation parameters, evolutionary methods seem to be superior to other strategies, as the chances to find good proposals within an acceptable number of trials and within affordable time are much higher.Nevertheless, evolutionary approaches like all optimisation methods require large numbers of studies of individual solutions. The computer power necessary to apply these strategies should not be underestimated. Even with today low cost and high availability of computers, the time to solve problems may be surprisingly long. So all ways of parallel processing, using single computers with many processors or clusters of many computers may speed up the time to do the optimisation.The basic terms of the method are outlined, some problems discussed, some examples given and some proposals made, how to use evolutionary methods in engineering optimisation. Finally some warnings are given trying to prevent potential users from non-realistic expectations. Optimisation is a difficult and consuming process. This holds for evolutionary optimisation as well.     

The application of a Pareto optimisation method in the design of an integrated bioprocess

A rapid method for designing integrated bioprocesses, using a combination of a windows of operation and a Pareto optimisation approach, is described in this paper. Within bioprocesses, multiple objectives are common, and achieving a satisfactory trade-off amongst the design objectives is crucial. Conventional optimisation results in the identification of the best operating policy for a given desired performance but gives little insight into how the process performance changes in the vicinity of the solution. In this paper, we explore the use of a Pareto optimisation technique to locate the optimal conditions for an integrated bioprocessing sequence and the benefits of first reducing the feasible space by the development of a series of windows of operation to provide a smaller search area for the optimisation. The final results are then presented in performance trade-off graphs and look-up tables, which give the design engineer an easily manageable solution set to work with. In this way, the decision-making procedure for design is made faster and more transparent. Two case studies illustrate the results from this integrated design methodology, some of which are counter-intuitive compared with the general design experience.     

A calibrated EMG-informed neuromusculoskeletal model can appropriately account for muscle co-contraction in the estimation of hip joint contact forces in people with hip osteoarthritis

Abnormal hip joint contact forces (HJCF) are considered a primary mechanical contributor to the progression of hip osteoarthritis (OA). Compared to healthy controls, people with hip OA often present with altered muscle activation patterns and greater muscle co-contraction, both of which can influence HJCF. Neuromusculoskeletal (NMS) modelling is non-invasive approach to estimating HJCF, whereby different neural control solutions can be used to estimate muscle forces. Static optimisation, available within the popular NMS modelling software OpenSim, is a commonly used neural control solution, but may not account for an individual’s unique muscle activation patterns and/or co-contraction that are often evident in pathological population. Alternatively, electromyography (EMG)-assisted neural control solutions, available within CEINMS software, have been shown to account for individual activation patterns in healthy people. Nonetheless, their application in people with hip OA, with conceivably greater levels of co-contraction, is yet to be explored. The aim of this study was to compare HJCF estimations using static optimisation (in OpenSim) and EMG-assisted (in CEINMS) neural control solutions during walking in people with hip OA. EMG-assisted neural control solution was more consistent with both EMG and joint moment data than static optimisation, and also predicted significantly higher HJCF peaks (p < 0.001). The EMG-assisted neural control solution also accounted for more muscle co-contraction than static optimisation (p = 0.03), which probably contributed to these higher HJCF peaks. Findings suggest that the EMG-assisted neural control solution may estimate more physiologically plausible HJCF than static optimisation in a population with high levels of co-contraction, such as hip OA.     

Automated pelvic anatomical coordinate system is reproducible for determination of anterior pelvic plane

Most of computer-assisted planning systems need to determine the anatomical axis based on the anterior pelvic plane (APP). We analysed that our new system is more reproducible for determination of APP than previous methods. A pelvic model bone and two subjects suffering from hip osteoarthritis were evaluated. Multidetector-row computed tomography (MDCT) images were scanned with various rotations by MDCT scanner. The pelvic rotation was calibrated using silhouette images. APP was determined by an optimisation technique. The values of variation of APP caused by pelvic rotation were analysed with statistical analysis. APP determination with calibration and optimisation was most reproducible.The values of variance of APP were within 0.05° in model bone and 0.2° even in patient pelvis. Furthermore, the values of variance of APP with calibration/optimisation were significantly lower in comparison without calibration/optimisation. Both calibration and optimisation are actually required for determination of APP. This system could contribute to the evaluation of hip joint kinematics and computer-assisted surgery.     

Three-dimensional design optimisation of patient-specific femoral plates as a means of bone remodelling reduction

Previous investigations into the optimisation of internal plates have mostly focused on the material properties of the implant. In this work, we optimise the shape, size and placement of the plate for successfully minimising bone remodelling around the implant. A design optimisation algorithm based on strain energy density criterion, combined with the finite element analysis, has been used in this study. The main optimisation goal was to reduce this change and keep it close to the conditions of an intact femur. The results suggest that the anterolateral side of the bone would be the optimum location for the plate, as for the geometry, the optimum moves towards having a thick, wide and short plate. These important results could be directly applicable to orthopaedic surgeons treating a femur fracture with internal plates. Since the optimisation algorithm remains the same for any patient, this advancement provides the surgeon with a tool to minimise the post surgery remodelling by trying to maintain the natural structure of the bone.     

Central composite design for the rapid optimisation of ruggedness and chiral separation of amlodipine in capillary electrophoresis

Systematic optimisation with central composite design offers an efficient route for rapid optimisation of resolution with multiple interacting parameters in chiral CE. This is illustrated by separations of amlodipine with α-CD as chiral selector in the running buffer, for which the predicted performance of central composite design is assessed. The utility of response surface methodology for locating optimum ruggedness in CE is also described. © 1995 Wiley-Liss, Inc.     

Muscle forces during running predicted by gradient-based and random search static optimisation algorithms

Muscle forces during locomotion are often predicted using static optimisation and SQP. SQP has been criticised for over-estimating force magnitudes and under-estimating co-contraction. These problems may be related to SQP's difficulty in locating the global minimum to complex optimisation problems. Algorithms designed to locate the global minimum may be useful in addressing these problems. Muscle forces for 18 flexors and extensors of the lower extremity were predicted for 10 subjects during the stance phase of running. Static optimisation using SQP and two random search (RS) algorithms (a genetic algorithm and simulated annealing) estimated muscle forces by minimising the sum of cubed muscle stresses. The RS algorithms predicted smaller peak forces (42% smaller on average) and smaller muscle impulses (46% smaller on average) than SQP, and located solutions with smaller cost function scores. Results suggest that RS may be a more effective tool than SQP for minimising the sum of cubed muscle stresses in static optimisation.     

Muscle forces during running predicted by gradient-based and random search static optimisation algorithms

Muscle forces during locomotion are often predicted using static optimisation and SQP. SQP has been criticised for over-estimating force magnitudes and under-estimating co-contraction. These problems may be related to SQP's difficulty in locating the global minimum to complex optimisation problems. Algorithms designed to locate the global minimum may be useful in addressing these problems. Muscle forces for 18 flexors and extensors of the lower extremity were predicted for 10 subjects during the stance phase of running. Static optimisation using SQP and two random search (RS) algorithms (a genetic algorithm and simulated annealing) estimated muscle forces by minimising the sum of cubed muscle stresses. The RS algorithms predicted smaller peak forces (42% smaller on average) and smaller muscle impulses (46% smaller on average) than SQP, and located solutions with smaller cost function scores. Results suggest that RS may be a more effective tool than SQP for minimising the sum of cubed muscle stresses in static optimisation.