The influence of model parameters on model validation

The study examined the sensitivity of two musculoskeletal models to the parameters describing each model. Two different models were examined: a phenomenological model of human jumping with parameters based on live subject data, and the second a model of the First Dorsal Interosseous with parameters based on cadaveric measurements. Both models were sensitive to the model parameters, with the use of mean group data not producing model outputs reflective of either the performance of any group member or the mean group performance. These results highlight the value of subject specific model parameters, and the problems associated with model validation.     

Studies on mixing in horizontal rotating tubular bioreactor

In previous investigations on mixing in a horizontal rotating tubular bioreactor (HRTB) the structured “spiral flow” model was developed which contained four adjustable parameters [1, 2]. In order to incorporate the mixing model in a semifundamental scale-up procedure it was necessary to make a relation between the adjustable model parameters and process parameters of the bioreactor expressed as dimensionless numbers. Mathematical equations which relate adjustable model parameters with dimensionless numbers were developed by non-linear and surface regression methods. These equations were applied to develop the prediction systems for adjustable model parameters. In total, nine systems of equations for the prediction of the adjustable model parameters were established and examined by simulation. Three of them (SC-2, SC-6 and SC-9) were selected as adequate to describe the mixing performance of HRTB in a wide range of process conditions.     

Analysing the genetic control of peach fruit quality through an ecophysiological model combined with a QTL approach

Ecophysiological models are increasingly expected to include genetic information via genotype-dependent parameters. These parameters could be considered as quantitative traits and submitted to analysis. A pre-existing ecophysiological model of fruit quality was used and the distribution of the genotypic parameters in a second backcross population derived from a clone of a wild peach (Prunus davidiana) and commercial nectarine varieties (P. persica (L.) Batsch) was analysed. The correlations between the two years of experimentation were higher for the genotypic parameters than for the quality traits commonly studied by breeders. The correlations between the genotypic parameters and the quality traits were low. Quantitative trait loci (QTLs) for the genotypic key parameters of the ecophysiological model were detected by linear regression. Co-locations of QTLs for parameters were observed as well as co-locations of QTLs for parameters and quality traits. The ecophysiological model and the results of the QTL analysis were combined by substituting each parameter in the model by the sum of QTL effects. This combined model can simulate the behaviour of genotypes carrying diverse combinations of alleles. The quality of this combined model was moderately suitable, but had some shortcomings. Improvements are suggested and further use of this combined model as a tool for breeders is discussed.     

Identifyability measures to select the parameters to be estimated in a solid‐state fermentation distributed parameter model

Process modeling can lead to of advantages such as helping in process control, reducing process costs and product quality improvement. This work proposes a solid‐state fermentation distributed parameter model composed by seven differential equations with seventeen parameters to represent the process. Also, parameters estimation with a parameters identifyability analysis (PIA) is performed to build an accurate model with optimum parameters. Statistical tests were made to verify the model accuracy with the estimated parameters considering different assumptions. The results have shown that the model assuming substrate inhibition better represents the process. It was also shown that eight from the seventeen original model parameters were nonidentifiable and better results were obtained with the removal of these parameters from the estimation procedure. Therefore, PIA can be useful to estimation procedure, since it may reduce the number of parameters that can be evaluated. Further, PIA improved the model results, showing to be an important procedure to be taken. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:905–917, 2016     

Sensitivity Analysis of the APEX Model for Assessing Sustainability of Switchgrass Grown for Biofuel Production in Central Texas

Crop simulation models are increasingly being used to understand the feasibility of large-scale cellulosic biofuel production along with the multi-dimensional impacts on environmental sustainability. However, how the uncertainty in model parameters impacts model performance for sustainability is unclear. In this case study, sensitivity analyses were conducted for three switchgrass sustainability metrics: total biomass production, nitrogen loss, and soil carbon change using the APEX (Agricultural Policy/Environmental eXtender) model. Fifteen out of the 45 parameters (25 crop growth (CROP) parameters and 20 additional model parameters (PARM)) were identified as influential for the three sustainability metrics for three lowland genotypes (WBC, AP13, and KAN) across two locations (Temple, TX, and Austin, TX). Our sensitivity results showed that parameter importance was not dependent on the genotypes but depended on the variables of interest, and differed only slightly between locations. Influential belowground-related CROP and PARM parameters were identified for each sustainability metric, indicating that belowground-related parameters are just as important as commonly measured aboveground CROP parameters. Further investigation of the linear or non-linear relationships and the two-way interactions between each of the individual influential parameters with the three sustainability metrics reflected the functions and characteristics within the APEX model and the interrelations among different processes. Strong interactions between the most influential parameters for total biomass, nitrogen loss, and soil carbon change also highlighted the importance of accurately setting these parameters. Identification of influential model parameters for switchgrass sustainability may help guide field measurements and provide further understanding of the interrelated processes in the APEX model. Furthermore, future field experiments can be designed to measure these influential parameters and understand the non-linear relationships identified between influential parameters and response variables. More accurate model parameterization will help improve APEX model performance and our understanding of the possible underlying physiological mechanisms.     

生态过程模型敏感参数最优取值的时空异质性分析——以BIOME-BGC模型为例

生态过程模型是当前研究陆地生态系统水循环、碳循环有力的工具,但此类模型参数众多,参数的合理取值对模型模拟结果有重要影响.以往研究对模型参数的敏感性以及参数的优化取值有诸多的分析和讨论,但有关参数最优取值的时空异质性关注较少.本文以BIOME-BGC模型为例,在常绿阔叶林、落叶阔叶林、C3草地3种植被类型下,通过构建敏感性判别指数,筛选出模型的敏感参数,并在每种植被类型下选取两个试验站点,使用模拟退火算法结合实测通量数据构建目标函数,获取各站点敏感参数逐月的最优取值,然后构建时间异质性判别指数、空间异质性判别指数和时空异质性判别指数对模型敏感参数最优取值的时空异质性进行定量分析.结果表明:BIOME-BGC模型在3种植被类型下遴选出的敏感参数大部分一致,少数有差异,但参数的敏感性强弱在不同植被类型下的表现不尽相同;BIOME-BGC模型敏感参数的最优取值,大都具有不同程度的时空异质性,但不同植被类型下,敏感参数最优取值的时空异质性表现各异;敏感参数中与植被生理、生态相关的参数,其时空异质性相对较小,而与环境、物候相关的参数,其时空异质性普遍较大;在3种植被类型下,模型敏感参数最优取值的时间异质性与空间异质性表现出显著的线性相关性;依据其最优取值的时空异质性,可对BIOME-BGC模型敏感参数进行类型划分,以便在实践应用中采取不同的参数率定策略.本研究结论有助于加深对生态过程模型参数特性及最优取值的理解,可为实践应用中模型参数的合理取值提供一种思路和参考.     

Modelling and parameter estimation of the enzymatic synthesis of oligosaccharides by β‐galactosidase from Bacillus circulans

The aim of this research is to develop a model to describe oligosaccharide synthesis and simultaneously lactose hydrolysis. Model A (engineering approach) and model B (biochemical approach) were used to describe the data obtained in batch experiments with β‐galactosidase from Bacillus circulans at various initial lactose concentrations (from 0.19 to 0.59 mol·kg⁻¹). A procedure was developed to fit the model parameters and to select the most suitable model. The procedure can also be used for other kinetically controlled reactions. Each experiment was considered as an independent estimation of the model parameters, and consequently, model parameters were fitted to each experiment separately. Estimation of the parameters per experiment preserved the time dependence of the measurements and yielded independent sets of parameters. The next step was to study by ordinary regression methods whether parameters were constant under the altering conditions examined. Throughout all experiments, the parameters of model B did not show a trend upon the initial lactose concentration when inhibition was included. Therefore model B, a galactosyl‐enzyme complex‐based model, was chosen to describe the oligosaccharide synthesis, and one parameter set was determined for various initial lactose concentrations. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 64: 558–567, 1999.     

Projection of climate variables by general circulation and deep learning model for Lahore,Pakistan

Climate change significantly impacts the hydrological cycle and environment. The key parameters driving climate change for densely populated city of Lahore in Pakistan were studied. The projections of these parameters were evaluated using General Circulation Model (GCM) named Community Climate System Model (CCSM4) under two Representative Concentration Pathways (RCP 4.5 and 8.5) scenarios. The outputs of CCSM4 model were bias corrected using quantile mapping using historical data. Additionally, a deep learning model named long short-term memory (LSTM) was developed applying machine learning applications to forecast the climate parameters for the future. LSTM model with two LSTM layers including one fully connected layer was modeled for the projection of climate variables in the region. Total number of parameters were 9888, and the input and forecasted output length was kept as 24 sequential months without overlapping. The conventional projection methods of GCM were compared with LSTM outputs for bridging the gap. The LSTM model was found to be more effective and dependable in forecasting the climate with significant improvement in the statistical parameters for the region. The LSTM model can be applied for projections of climate in comparison to GCM with sufficient precision.     

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.     

Development of a compartmental model of human zinc metabolism: identifiability and multiple studies analyses

A compartmental model of zinc metabolism has been developed from stable isotope tracer studies of five healthy adults. Multiple isotope tracers were administered orally and intravenously, and the resulting enrichment was measured in plasma, erythrocytes, urine, and feces for as long as 3 wk. Data from total zinc measurements and model-independent calculations of various steady-state parameters were also modeled with the kinetic data. A structure comprised of 14 compartments and as many as 25 unknown kinetic parameters was developed to adequately model the data from each of the individual studies. The structural identifiability of the model was established using the GLOBI2 identifiability analysis software. Numerical identifiability of parameter estimates was evaluated using statistical data provided by SAAM. A majority of the model parameters was estimated with sufficient statistical certainty to be considered well determined. After the fitting of the model and data from the individual studies using SAAM/CONSAM, results were submitted to SAAM extended multiple studies analysis for aggregation into a single set of population parameters and statistics. The model was judged to be valid based on criteria described elsewhere.     

A mathematical model of human heart including the effects of heart contractility varying with heart rate changes

Incorporating the intrinsic variability of heart contractility varying with heart rate into the mathematical model of human heart would be useful for addressing the dynamical behaviors of human cardiovascular system, but models with such features were rarely reported. This study focused on the development and evaluation of a mathematical model of the whole heart, including the effects of heart contractility varying with heart rate changes. This model was developed based on a paradigm and model presented by Ottesen and Densielsen, which was used to model ventricular contraction. A piece-wise function together with expressions for time-related parameters were constructed for modeling atrial contraction. Atrial and ventricular parts of the whole heart model were evaluated by comparing with models from literature, and then the whole heart model were assessed through coupling with a simple model of the systemic circulation system and the pulmonary circulation system. The results indicated that both atrial and ventricular parts of the whole heart model could reasonably reflect their contractility varying with heart rate changes, and the whole heart model could exhibit major features of human heart. Results of the parameters variation studies revealed the correlations between the parameters in the whole heart model and performances (including the maximum pressure and the stroke volume) of every chamber. These results would be useful for helping users to adjust parameters in special applications.     

A molecular mechanical analysis of the active site of urease with a special emphasis on determining the binding conformations available to oxygen-bound urea.

In order to model the active site of urease which contains two nickel ions with differing coordination geometries new parameters were derived for the AMBER* force field. These parameters were obtained by structure based optimization and use a single set of parameters with points on a sphere approach to model nickel(II) high-spin in all its coordination geometries. The force field was successfully used to model the active site of urease and to predict that a bridging water between the two nickel ions in urease was missing from the solid state structure of urease. A thorough conformational search was undertaken to find the conformations available to urea within urease. All the low energy conformations found were used to determine a consensus urea binding model.     

Impact of material and morphological parameters on the mechanical response of the lumbar spine – A finite element sensitivity study

Finite element models are frequently used to study lumbar spinal biomechanics. Deterministic models are used to reflect a certain configuration, including the means of geometrical and material properties, while probabilistic models account for the inherent variability in the population. Because model parameters are generally uncertain, their predictive power is frequently questioned. In the present study, we determined the sensitivities of spinal forces and motions to material parameters of intervertebral discs, vertebrae, and ligaments and to lumbar morphology. We performed 1200 model simulations using a generic model of the human lumbar spine loaded under pure moments. Coefficients of determination and of variation were determined for all parameter and response combinations. Material properties of the vertebrae displayed the least impact on results, whereas those of the discs and morphology impacted most. The most affected results were the axial compression forces in the vertebral body and in several ligaments during flexion and the facet-joint forces during extension. Intervertebral rotations were considerably affected only when several parameters were varied simultaneously. Results can be used to decide which model parameters require careful consideration in deterministic models and which parameters might be omitted in probabilistic studies. Findings allow quantitative estimation of a model׳s precision.     

Sensitivity of a Hill-based muscle model to perturbations in model parameters

Musculoskeletal simulations of human movement commonly use Hill muscle models to predict muscle forces, but their sensitivity to model parameter values is not well understood. The purpose of this study was to evaluate muscle model sensitivity to perturbations in 14 Hill muscle model parameters in forward dynamic simulations of running and walking by varying each by +/-50%. Three evaluations of the muscle model were performed based on: (1) calculating the sensitivity of the muscle model only, (2) determining the continuous partial derivatives of the muscle equations with respect to each parameter, and (3) evaluating the effects on the running and walking simulations. Model evaluations were found to be very sensitive (percent change in outputs greater than parameter perturbation) to parameters defining the series elastic component (tendon), force-length curve of the contractile element and maximum isometric force. For some parameters, the range of literature values was larger than the model sensitivity. Model evaluations were insensitive to parameters defining the parallel elastic element, force-velocity curve of the contractile element and muscle activation time constants. The derivative method provided similar results, but also provided a generic, continuous equation that can easily be applied to other motions. The sensitivities of the running and walking simulations were reduced compared to the sensitivity of the muscle model alone. Results demonstrate the importance of evaluating sensitivity of a musculoskeletal simulation in a controlled manner and provide an indication of which parameters must be selected most carefully based on the sensitivity of a given movement.     

基于快鸟影像纹理特性的刺槐林叶面积指数估算

以渭北地区刺槐林为研究对象,通过计算高分辨率影像不同窗口的纹理参数,分别运用一元一次方程、一元二次方程、乘幂模型和指数模型,研究刺槐林野外实测叶面积指数（LAI）与快鸟影像纹理参数间的相关关系,遴选黄土高原地区估算刺槐林LAI最适合的纹理参数以及计算窗口大小.结果表明： 纹理指数对LAI反演精度影响显著,其中角二阶矩阵和熵的估算精度明显高于其他纹理指数;计算窗口的大小显著影响LAI反演精度,非相似度和对比度的反演精度在窗口9×9达到最大,其余纹理指数对于LAI的估算精度随着计算窗口的变大不断降低,在窗口3×3时达到最大;乘幂模型的估算精度低于其他3种方法.     

Passive transverse mechanical properties of skeletal muscle under in vivo compression

The objective of the present study is to determine the passive transverse mechanical properties of skeletal muscle. Compression experiments were performed on four rat tibialis anterior muscles. To assess the stress- and strain-distributions in the muscle during the experiment, a plane stress model of the cross section was developed for each muscle. The incompressible viscoelastic Ogden model was used to describe the passive muscle behaviour. The four material parameters were determined by fitting calculated indentation forces on measured indentation forces. The elastic parameters, mu and alpha, were 15.6+/-5.4 kPa and 21.4+/-5.7, respectively. The viscoelastic parameters, delta and tau, were 0.549+/-0.056 and 6.01+/-0.42 s. When applying the estimated material parameters in a three-dimensional finite element model, the measured behaviour can be accurately simulated.     

General model, based on two mixed weibull distributions of bacterial resistance, for describing various shapes of inactivation curves

Cells of Listeria monocytogenes or Salmonella enterica serovar Typhimurium taken from six characteristic stages of growth were subjected to an acidic stress (pH 3.3). As expected, the bacterial resistance increased from the end of the exponential phase to the late stationary phase. Moreover, the shapes of the survival curves gradually evolved as the physiological states of the cells changed. A new primary model, based on two mixed Weibull distributions of cell resistance, is proposed to describe the survival curves and the change in the pattern with the modifications of resistance of two assumed subpopulations. This model resulted from simplification of the first model proposed. These models were compared to the Whiting's model. The parameters of the proposed model were stable and showed consistent evolution according to the initial physiological state of the bacterial population. Compared to the Whiting's model, the proposed model allowed a better fit and more accurate estimation of the parameters. Finally, the parameters of the simplified model had biological significance, which facilitated their interpretation.     

Application of a bioenergetics growth model for European anchovy (<Emphasis Type="Italic">Engraulis encrasicolus</Emphasis>) linked with a lower trophic level ecosystem model

A bioenergetics model is implemented for European anchovy (Engraulis encrasicolus) and applied to the north-eastern Aegean Sea (eastern Mediterranean Sea). The model reproduces the growth of anchovy in a one-way linked configuration with a lower trophic level (LTL) ecosystem model. The LTL model provides densities for three zooplankton functional groups (heterotrophic flagellates, microzooplankton and mesozooplankton) which serve as available energy via consumption for the anchovy model. Our model follows the basic structure of NEMURO.FISH type models (North Pacific Ecosystem Model for Understanding Regional Oceanography for Including Saury and Herring). Several model parameters were specific for the Mediterranean or the Black Sea anchovy and some others were adopted from related species and NEMURO.FISH due to lack of biological information on E. encrasicolus. Simulation results showed that the fastest growth rate occurs during spring and the slowest growth rate from August to December. Zooplankton abundance during autumn was low implying that decreased prey density lead to a reduction in anchovy weight, especially for the age-3 class. Feeding parameters were adjusted to adequately fit the model growth estimates to available weight-at-age data. A detailed sensitivity analyses is conducted to evaluate the importance of the biological processes (consumption, respiration, egestion, specific dynamic action, excretion and egg production) and their parameters to fish growth. The most sensitive parameters were the intercept and exponent slope of the weight-dependent consumption and respiration process equations. Fish weight was fairly sensitive to temperature-dependent parameters.     

两种败血症休克模型大鼠心肌细胞一氧化氮合酶活性的改变

目的：观察两种败血症休克模型大鼠的血流动力学及心肌细胞一氧化氮合酶活性变化的异同,探讨一氧化氮合酶参与败血症休克性心肌抑制的机制。方法：采用注射脂多糖（LPS）诱导及盲肠结扎穿孔（CLP）致腹膜炎诱导败血症休克模型,测定血流动力学指标以及心肌细胞胞浆一氧化氮合酶（NOS）活性。结果：①CLP模型大鼠的血流动力学指标随时间呈先上升后下降的趋势,LPS模型直接表现为类似于CLP模型晚期的动力学状态。在使用NOS抑制剂N-硝基-L精氨酸甲酯（L-NAME）后,CLP模型晚期及LPS模型的心室动力学指标均有明显改善。②CLP模型大鼠心肌细胞胞浆NOS活性在败血症中期达到最大。与假手术组相比,LPS模型、CLP模型晚期心肌细胞胞浆NOS活性均有明显增加,但是LPS模型与CLP模型晚期两组之间无明显差异。③使用L-NAME后,CLP晚期组与LPS组亚硝基及硝基化合物生成量均明显降低（P〈0.01）。其中,LPS组与CLP晚期组相比,前者固定表达型NOS生成亚硝基及硝基化合物生成量明显高于后者（P〈0．01）。结论：在LPS与CLP诱导的败血症休克模型中,心肌NOS是引起心室动力学变化的主要因素;在两种模型,心肌NOS亚型的表达不同,在LPS模型中主要为iNOS,而在CLP模型中则可能是cNOS和iNOS共同发挥作用。     

Parameter estimation in surface exchange models using nonlinear inversion: how many parameters can we estimate and which measurements are most useful?

Models of mass and energy exchanges between the biosphere and the atmosphere generally contain a nonlinear dependence between fluxes and model parameters, and thus estimation of these parameters from measurements in a heterogeneous landscape depends on the scale of the observations. The scale‐dependence of a typical surface‐exchange model (the CSIRO Biospheric Model, CBM) is examined using the diurnal variation of hourly fluxes of CO₂, latent heat, sensible heat and soil heat. The fluxes were measured using micrometeorological techniques over six sites in a grazing/pasture system in SE Australia during a period of three weeks in 1995. Nonlinear parameter inversion was used to determine model parameters. Analysis of the covariance of the estimates of the parameters and the unexplained residuals of the model showed that a maximum of three or four parameters could be determined independently from the observations for all six sites. Estimates of a key model parameter, j_max, the mean of maximum potential electron transport rate of all leaves within the canopy, was best determined by the measurements of net CO₂ flux at all sites examined. Measurements of ground heat flux provide little information about any of the model parameters in CBM. Because of nonlinearities in the surface exchange model, calculated fluxes will be in error if parameters for the component vegetation types are simply averaged in proportion to their areal fraction. The magnitude of these errors was examined for CBM using a hypothetical land surface consisting of two surface types, each with different parameter values. Predictions of net CO₂, latent heat and ground heat fluxes using a linear combination of model parameters for the two surface types were quite similar with those found using optimal estimates of the parameters for the landscape, but were significantly poorer for sensible heat fluxes.