A theoretical analysis of an optimal chainring shape to maximize crank power during isokinetic pedaling

Previous studies have sought to improve cycling performance by altering various aspects of the pedaling motion using novel crank–pedal mechanisms and non-circular chainrings. However, most designs have been based on empirical data and very few have provided significant improvements in cycling performance. The purpose of this study was to use a theoretical framework that included a detailed musculoskeletal model driven by individual muscle actuators, forward dynamic simulations and design optimization to determine if cycling performance (i.e., maximal power output) could be improved by optimizing the chainring shape to maximize average crank power during isokinetic pedaling conditions. The optimization identified a consistent non-circular chainring shape at pedaling rates of 60, 90 and 120 rpm with an average eccentricity of 1.29 that increased crank power by an average of 2.9% compared to a conventional circular chainring. The increase in average crank power was the result of the optimal chainrings slowing down the crank velocity during the downstroke (power phase) to allow muscles to generate power longer and produce more external work. The data also showed that chainrings with higher eccentricity increased negative muscle work following the power phase due to muscle activation–deactivation dynamics. Thus, the chainring shape that maximized average crank power balanced these competing demands by providing enough eccentricity to increase the external work generated by muscles during the power phase while minimizing negative work during the subsequent recovery phase.     

Simple criteria for finding (nearly) optimal vaccination strategies

Strategies for best controlling the spread of the diseases with limited vaccine available are explored. I use influenza as a representative disease in point. The model describes the dynamics of influenza spread among multiple groups that have different risks and activity levels. I define a core group consisting of individuals with occupations that brings them in contact with many other people in a day. These occupations may include service industries, teachers, health care, and government workers, to name a few. High-risk individuals are those as typically designated for: children under 5 and adults over 50, people with weakened immune systems as well as emergency and health care personnel. Under certain conditions, shifting vaccination resources away from the high-risk group to the high-activity group will result in improved herd immunity in both the high-risk group and the population as whole. This results in more high-risk people protected even though less of them are being vaccinated, with the obvious implications that current vaccination policies may be far less then optimal. I show that the criteria for the optimal strategy can be derived from simple expressions gleaned from the expression for the basic reproductive number.     

Evaluation of a method to scale muscle strength for gait simulations of children with cerebral palsy

Cerebral palsy (CP) is a neurological disorder that results in life-long mobility impairments. Musculoskeletal models used to investigate mobility deficits for children with CP often lack subject-specific characteristics such as altered muscle strength, despite a high prevalence of muscle weakness in this population. We hypothesized that incorporating subject-specific strength scaling within musculoskeletal models of children with CP would improve accuracy of muscle excitation predictions in walking simulations. Ten children (13.5 ± 3.3 years; GMFCS level II) with spastic CP participated in a gait analysis session where lower-limb kinematics, ground reaction forces, and bilateral electromyography (EMG) of five lower-limb muscles were collected. Isometric strength was measured for each child using handheld dynamometry. Three musculoskeletal models were generated for each child including a ‘Default’ model with the generic musculoskeletal model’s muscle strength, a ‘Uniform’ model with muscle strength scaled allometrically, and a ‘Custom’ model with muscle strength scaled based on handheld dynamometry strength measures. Muscle-driven gait simulations were generated using each model for each child. Simulation accuracy was evaluated by comparing predicted muscle excitations and measured EMG signals, both in the duration of muscle activity and the root-mean-square difference (RMSD) between signals. Improved agreement with EMG were found in both the ‘Custom’ and ‘Uniform’ models compared to the ‘Default’ model indicated by improvement in RMSD summed across all muscles, as well as RMSD and duration of activity for individual muscles. Incorporating strength scaling into musculoskeletal models can improve the accuracy of walking simulations for children with CP.     

Intravoxel bone micromechanics for microCT-based finite element simulations

While micro-FE simulations have become a standard tool in computational biomechanics, the choice of appropriate material properties is still a relevant topic, typically involving empirical grey value-to-elastic modulus relations. We here derive the voxel-specific volume fractions of mineral, collagen, and water, from tissue-independent bilinear relations between mineral and collagen content in extracellular bone tissue (J. Theor. Biol. 287: 115, 2011), and from the measured X-ray attenuation information quantified in terms of grey values. The aforementioned volume fractions enter a micromechanics representation of bone tissue, as to deliver voxel-specific stiffness tensors. In order to check the relevance of this strategy, we convert a micro Computer Tomograph of a mouse femur into a regular Finite Element mesh, apply forces related to the dead load of a standing mouse, and then compare simulation results based on voxel-specific heterogeneous elastic properties to results based on homogeneous elastic properties related to the spatial average over the solid bone matrix compartment, of the X-ray attenuation coefficients. The element-specific strain energy density illustrates that use of homogeneous elastic properties implies overestimation of the organ stiffness. Moreover, the simulation reveals large tensile normal stresses throughout the femur neck, which may explain the mouse femur neck's trabecular morphology being quite different from the human case, where the femur neck bears compressive forces and bending moments.     

An improved neutral landscape model for recreating real landscapes and generating landscape series for spatial ecological simulations

Many studies have assessed the effect of landscape patterns on spatial ecological processes by simulating these processes in computer‐generated landscapes with varying composition and configuration. To generate such landscapes, various neutral landscape models have been developed. However, the limited set of landscape‐level pattern variables included in these models is often inadequate to generate landscapes that reflect real landscapes. In order to achieve more flexibility and variability in the generated landscapes patterns, a more complete set of class‐ and patch‐level pattern variables should be implemented in these models. These enhancements have been implemented in Landscape Generator (LG), which is a software that uses optimization algorithms to generate landscapes that match user‐defined target values. Developed for participatory spatial planning at small scale, we enhanced the usability of LG and demonstrated how it can be used for larger scale ecological studies. First, we used LG to recreate landscape patterns from a real landscape (i.e., a mountainous region in Switzerland). Second, we generated landscape series with incrementally changing pattern variables, which could be used in ecological simulation studies. We found that LG was able to recreate landscape patterns that approximate those of real landscapes. Furthermore, we successfully generated landscape series that would not have been possible with traditional neutral landscape models. LG is a promising novel approach for generating neutral landscapes and enables testing of new hypotheses regarding the influence of landscape patterns on ecological processes. LG is freely available online.     

Timely identification of optimal control strategies for emerging infectious diseases

Background

Health authorities must rely on quarantine, isolation, and other non-pharmaceutical interventions to contain outbreaks of newly emerging human diseases.

Methods

We modeled a generic disease caused by a pathogen apparently transmitted by close interpersonal contact, but about which little else is known. In our model, people may be infectious while incubating or during their prodrome or acute illness. We derived an expression for ℜ, the reproduction number, took its partial derivatives with respect to control parameters, and encoded these analytical results in a user-friendly Mathematica™ notebook. With biological parameters for SARS estimated from the initial case series in Hong Kong and infection rates from hospitalizations in Singapore, we determined ℜ's sensitivity to control parameters.

Results

Stage-specific infection rate estimates from cases hospitalized before quarantine began exceed those from the entire outbreak, but are qualitatively similar: infectiousness was negligible until symptom onset, and increased 10-fold from prodrome to acute illness. Given such information, authorities might instead have emphasized a strategy whose efficiency more than compensates for any possible reduction in efficacy.

Conclusions

In future outbreaks of new human diseases transmitted via close interpersonal contact, it should be possible to identify the optimal intervention early enough to facilitate effective decision-making.     

A Model of Human Muscle Energy Expenditure

A model of muscle energy expenditure was developed for predicting thermal, as well as mechanical energy liberation during simulated muscle contractions. The model was designed to yield energy (heat and work) rate predictions appropriate for human skeletal muscle contracting at normal body temperature. The basic form of the present model is similar to many previous models of muscle energy expenditure, but parameter values were based almost entirely on mammalian muscle data, with preference given to human data where possible. Nonlinear phenomena associated with submaximal activation were also incorporated. The muscle energy model was evaluated at varying levels of complexity, ranging from simulated contractions of isolated muscle, to simulations of whole body locomotion. In all cases, acceptable agreement was found between simulated and experimental energy liberation. The present model should be useful in future studies of the energetics of human movement using forward dynamic computer simulation.     

A continuum-atomistic method for incorporating Joule heating into classical molecular dynamics simulations

A hybrid atomistic-continuum method is presented for incorporating Joule heating into large-scale molecular dynamics (MD) simulations. When coupled to a continuum thermostat, the method allows resistive heating and heat transport in metals to be modeled without explicitly including electronic degrees of freedom. Atomic kinetic energies in a MD simulation are coupled via an ad hoc feedback loop to continuum current and heat transfer equations that are solved numerically on a finite difference grid (FDG). For resistive heating, the resistance in each region of the FDG is calculated from the experimental resistivity, atomic density, and average kinetic energy in the MD simulation. A network of resistors is established from which the potential at every FDG region is calculated given an applied voltage. The potential differences and the resistance between connected FDG regions are used to calculate the current between the two points and the heat generated from that current. This information is then added back into the atomic simulation. The method is demonstrated by simulating Joule heating and melting, along with associated changes in current, of single and bundles of metal nanowires, as well as a “pinched” wire under applied strain.     

Homology modeling and molecular dynamics simulations of lymphotactin

We have modeled the structure of human lymphotactin (hLpnt), by homology modeling and molecular dynamics simulations. This chemokine is unique in having a single disulfide bond and a long C-terminal tail. Because other structural classes of chemokines have two pairs of Cys residues, compared to one in Lpnt, and because it has been shown that both disulfide bonds are required for stability and function, the question arises how the Lpnt maintains its structural integrity. The initial structure of hLpnt was constructed by homology modeling. The first 63 residues in the monomer of hLpnt were modeled using the structure of the human CC chemokine, RANTES, whose sequence appeared most similar. The structure of the long C-terminal tail, missing in RANTES, was taken from the human muscle fatty-acid binding protein. In a Protein Data Bank search, this protein was found to contain a sequence that was most homologous to the long tail. Consequently, the modeled hLpnt C-terminal tail consisted of both alpha-helical and beta-motifs. The complete model of the hLpnt monomer consisted of two alpha-helices located above the five-stranded beta-sheet. Molecular dynamics simulations of the solvated initial model have indicated that the stability of the predicted fold is related to the geometry of Pro78. The five-stranded beta-sheet appeared to be preserved only when Pro78 was modeled in the cis conformation. Simulations were also performed both for the C-terminal truncated forms of the hLpnt that contained one or two (CC chemokine-like) disulfide bonds, and for the chicken Lpnt (cLpnt). Our MD simulations indicated that the turn region (T30-G34) in hLpnt is important for the interactions with the receptor, and that the long C-terminal region stabilizes both the turn (T30-G34) and the five-stranded beta-sheet. The major conclusion from our theoretical studies is that the lack of one disulfide bond and the extension of the C-terminus in hLptn are mutually complementary. It is very likely that removal of two Cys residues sufficiently destabilizes the structure of a chemokine molecule, particularly the core beta-sheet, to abolish its biological function. However, this situation is rectified by the long C-terminal segment. The role of this long region is most likely to stabilize the first beta-turn region and alpha-helix H1, explaining how this chemokine can function with a single disulfide bond.     

Design of experiments for predictive microbial modeling

Summary Good predictive microbial models can be built with appropriate data from well-designed experiments. Anyone setting up an experiment should consider the sources of variability, possible screening experiments, optimum spacing between points on a continuous scale, and the most appropriate type of design, e.g. factorial, screening, or central composite.     

Mathematical modeling of elution curves for a protein mixture in ion exchange chromatography and for the optimal selection of operational conditions

Elution curves in ionic exchange chromatography (IEC) for a three-protein mixture (alpha-lactoalbumin, ovalbumin, and beta-lactoglobulin), carried out under different flow rates and ionic strength conditions, were simulated using two different mathematical models. These models were the Plate Model and the more fundamentally based Rate Model. Relatively low protein concentrations were used to avoid protein-protein interactions. Simulated elution curves were compared with experimental data not used for parameter identification. Deviation between experimental data and the simulated curves using the Plate Model was less than 0.0189 (absorbance units); a slightly higher deviation [0.0252 (absorbance units)] was obtained when the Rate Model was used. A cost function was built that included the effect of the different production stages, namely fermentation, purification, and concentration. These considered the effect on the performance of IEC; yield, purity, concentration and the time needed to accomplish the separation. Operational conditions in the IEC such as flow rate, ionic strength gradient and the operational time can be selected using this model in order to find the minimum cost for the protein production process depending on the characteristics of the final product desired such as purity and yield. This cost function was successfully used for the selection of the operational conditions as well as the fraction of the product to be collected (peak cutting) in IEC. It can be used for protein products with different characteristics and qualities, such as purity and yield, by choosing the appropriate parameters.     

A new generation of predictive models: The added value of hybrid models for manufacturing processes of therapeutic proteins

Due to the lack of complete understanding of metabolic networks and reaction pathways, establishing a universal mechanistic model for mammalian cell culture processes remains a challenge. Contrarily, data-driven approaches for modeling these processes lack extrapolation capabilities. Hybrid modeling is a technique that exploits the synergy between the two modeling methods. Although mammalian cell cultures are among the most relevant processes in biotechnology and indeed looks ideal for hybrid modeling, their application has only been proposed but never developed in the literature. This study provides a quantitative assessment of the improvement brought by hybrid models with respect to the state-of-the-art statistical predictive models in the context of therapeutic protein production. This is illustrated using a dataset obtained from a 3.5 L fed-batch experiment. With the goal to robustly define the process design space, hybrid models reveal a superior capability to predict the time evolution of different process variables using only the initial and process conditions in comparison to the statistical models. Hybrid models not only feature more accurate prediction results but also demonstrate better robustness and extrapolation capabilities. For the future application, this study highlights the added value of hybrid modeling for model-based process optimization and design of experiments.     

权衡城市扩张、耕地保护与生态效益的京津冀城市群土地利用优化配置情景分析

京津冀城市群作为影响我国经济发展的重要区域,具有多重战略意义。然而,快速的城市扩张在提高社会、经济水平的同时,伴随着资源供求矛盾加深、耕地被侵占、生态退化,以及水、大气环境污染等众多突出问题,如何优化调整城市空间结构与布局,实现社会、经济发展与生态环境保护等多目标的协同优化是京津冀规划管理与决策的关键。从土地覆盖/利用数量和空间布局两个重点方面出发,通过多目标优化模型和CLUE-S模型的构建,提出了多目标权衡下的土地扩张优化情景预案,以期为京津冀城市群扩张布局与土地利用优化配置规划与管理提供科学参考。结果表明:一方面,利用多目标遗传算法(MOGA)可以很好地实现对京津冀土地利用结构优化配置及其与社会、经济及生态效益等多目标的定量化求解,为决策人提供满足不同权衡目标的多种选择,并通过与CLUE-S模型相结合,实现京津冀城市群土地利用格局的空间优化配置情景模拟;另一方面,研究结果表明,综合考虑了社会、经济和生态效益的优化方案中,林地的增加可以相对满足政策要求,增幅较大,耕地较未优化方案减幅放缓,符合耕地保有量的要求,同时,也从空间上减少了对重要生态用地的侵占。本研究的方法与结果可为京津冀城市群土地利用规划与生态安全格局建设提供理论与应用参考。     

Setting up and running molecular dynamics simulations of membrane proteins

Molecular dynamics simulations have become a popular and powerful technique to study lipids and membrane proteins. We present some general questions and issues that should be considered prior to embarking on molecular dynamics simulation studies of membrane proteins and review common simulation methods. We suggest a practical approach to setting up and running simulations of membrane proteins, and introduce two new (related) methods to embed a protein in a lipid bilayer. Both methods rely on placing lipids and the protein(s) on a widely spaced grid and then 'shrinking' the grid until the bilayer with the protein has the desired density, with lipids neatly packed around the protein. When starting from a grid based on a single lipid structure, or several potentially different lipid structures (method 1), the bilayer will start well-packed but requires more equilibration. When starting from a pre-equilibrated bilayer, either pure or mixed, most of the structure of the bilayer stays intact, reducing equilibration time (method 2). The main advantages of these methods are that they minimize equilibration time and can be almost completely automated, nearly eliminating one time consuming step in MD simulations of membrane proteins.     

Optimal control for micro‐algae on a raceway model

We apply numerical optimal control methods to an existing algae growth model with the aim to determine the best performance of the model under known conditions using a variety of decision variables. We transform the system of differential algebraic equations in the existing model to a system of ordinary differential equations which introduces dynamics for average light intensity and chlorophyll. In addition, we allow for variable nitrogen concentration of the inflow as well as variable initial nitrogen concentration of the raceway. Our main focus is on optimizing of the production of lipids. We calculate both open and closed loop optimal controllers and test their robustness. Finally, we also consider raceway depth as a decision variable. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 34:107–119, 2018     

Local versus global optimal sports techniques in a group of athletes

Various optimization algorithms have been used to achieve optimal control of sports movements. Nevertheless, no local or global optimization algorithm could be the most effective for solving all optimal control problems. This study aims at comparing local and global optimal solutions in a multistart gradient-based optimization by considering actual repetitive performances of a group of athletes performing a transition move on the uneven bars. Twenty-four trials by eight national-level female gymnasts were recorded using a motion capture system, and then multistart sequential quadratic programming optimizations were performed to obtain global optimal, local optimal and suboptimal solutions. The multistart approach combined with a gradient-based algorithm did not often find the local solution to be the best and proposed several other solutions including global optimal and suboptimal techniques. The qualitative change between actual and optimal techniques provided three directions for training: to increase hip flexion–abduction, to transfer leg and arm angular momentum to the trunk and to straighten hand path to the bar.     

Assessing the accuracy of subject-specific,muscle-model parameters determined by optimizing to match isometric strength

Biomechanical models are sensitive to the choice of model parameters. Therefore, determination of accurate subject specific model parameters is important. One approach to generate these parameters is to optimize the values such that the model output will match experimentally measured strength curves. This approach is attractive as it is inexpensive and should provide an excellent match to experimentally measured strength. However, given the problem of muscle redundancy, it is not clear that this approach generates accurate individual muscle forces. The purpose of this investigation is to evaluate this approach using simulated data to enable a direct comparison. It is hypothesized that the optimization approach will be able to recreate accurate muscle model parameters when information from measurable parameters is given. A model of isometric knee extension was developed to simulate a strength curve across a range of knee angles. In order to realistically recreate experimentally measured strength, random noise was added to the modeled strength. Parameters were solved for using a genetic search algorithm. When noise was added to the measurements the strength curve was reasonably recreated. However, the individual muscle model parameters and force curves were far less accurate. Based upon this examination, it is clear that very different sets of model parameters can recreate similar strength curves. Therefore, experimental variation in strength measurements has a significant influence on the results. Given the difficulty in accurately recreating individual muscle parameters, it may be more appropriate to perform simulations with lumped actuators representing similar muscles.     

A metabolic energy expenditure model with a continuous first derivative and its application to predictive simulations of gait

Whether humans minimize metabolic energy in gait is unknown. Gradient-based optimization could be used to predict gait without using walking data but requires a twice differentiable metabolic energy model. Therefore, the metabolic energy model of Umberger et al. (2003 Umberger BR, Gerritsen KG, Martin PE. 2003. A model of human muscle energy expenditure. Comput Methods Biomech Biomed Eng. 6(2):99–111.[Taylor &; Francis Online] , [Google Scholar]) was adapted to be twice differentiable. Predictive simulations of a reaching task and gait were solved using this continuous model and by minimizing effort. The reaching task simulation showed that energy minimization predicts unrealistic movements when compared to effort minimization. The predictive gait simulations showed that objectives other than metabolic energy are also important in gait.