A general method for biological parameter estimation

Summary A general observer-based estimator method is developed and applied for process modelling and monitoring. This parameter estimation technique was successfully applied to a L-lysine fermentation process. It was a useful tool to detect the effect of major culture conditions on cell growth and product synthesis. It can also be used for the development of adaptive optimal control schemes.     

On parameter estimation in population models

We describe methods for estimating the parameters of Markovian population processes in continuous time, thus increasing their utility in modelling real biological systems. A general approach, applicable to any finite-state continuous-time Markovian model, is presented, and this is specialised to a computationally more efficient method applicable to a class of models called density-dependent Markov population processes. We illustrate the versatility of both approaches by estimating the parameters of the stochastic SIS logistic model from simulated data. This model is also fitted to data from a population of Bay checkerspot butterfly (Euphydryas editha bayensis), allowing us to assess the viability of this population.     

Using mass distribution information to model the human thigh for body segment parameter estimation

Accurate estimations of body segment inertial parameters (BSPs) are required to calculate the kinetics of motion. The purpose of this study was to develop a geometric model of the human thigh segment based on mass distribution properties determined from dual energy x ray absorptiometry (DEXA). One hundred subjects from four populations underwent a DEXA scan and anthropometric measurements were taken. The mass distribution properties of the thigh segment were determined for 20 subjects, a geometric model was developed, and the model was applied to the remaining 80 subjects. The model was validated by comparing to benchmark DEXA measurements. Four other popular models in the literature were also evaluated in the same manner No one set of predictors performed best for a particular group or BSP, however modeling the mass distribution properties of the segment allows the assumption of constant density while still accurately representing the inertial properties of the segment and provides promise for future development of BSP models.     

Body segment inertial parameters and low back load in individuals with central adiposity

There is a paucity of information regarding the impact of central adiposity on the inertial characteristics of body segments. Deriving low back loads during lifting requires accurate estimate of inertial parameters. The purpose was to determine the body segment inertial parameters of people with central adiposity using a photogrammetric technique, and then to evaluate the impact on lumbar spine loading. Five participants with central adiposity (waist:hip ratio>0.9, waist circumference>102 cm) were compared to a normal BMI group. A 3D wireframe model of the surface topography was constructed, partitioned into 8 body segments and then body segment inertial parameters were calculated using volumetric integration assuming uniform segment densities for the segments. Central adiposity dependent increases in body segment parameters ranged from 12 to 400%, varying across segments (greatest for trunk) and parameters. The increase in mass distribution to the trunk was accompanied by an anterior and inferior shift of the centre of mass. A proximal shift in centre of mass was detected for the extremities, along with a reduction in mass distribution to the lower extremity. L5/S1 torques (392 vs 263 Nm) and compressive forces (5918 vs 3986 N) were substantially elevated in comparison to the normal BMI group, as well as in comparison to torques and forces predicted using published BSIP equations. Central adiposity resulted in substantial but non-uniform increases in inertial parameters resulting in task specific increases in torque and compressive loads arising from different inertial and physical components.     

Quantifying physical functional trajectory in hospitalized older adults using body worn inertial sensors

Acute medical illness requiring hospitalization usually is a critical event in the trajectory leading to disability in older adults. Functional decline frequently occurs during hospitalization, resulting in a loss of Independence in activities of daily living after discharge. The aim of the study was to assess the functional decline in different ADLs of hospitalized elderly patients in an Acute Care for Elderly (ACE) unit incorporating a body-worn inertial sensor and accompanying custom algorithms. 38 hospitalized older adults (age ≥ 75) were included. The patients completed different functional tasks, including a balance test, Gait Velocity Test (GVT), verbal and arithmetic dual-task gait, and a sit-to-stand ability test at admission and discharge. Movement-related parameters were acquired from a unique tri-axial inertial sensor unit. Maximal muscle strength and muscle power output endpoints were also assessed. The results indicated that significant improvements (p < 0.05) were found at discharge compared with the admission values for gait variability and spatiotemporal parameters in the 4- and 6-meter GVT. These significant gains were also obtained in the verbal GVT. In contrast, a significant reduction was found in the functional status measured with the Barthel Index scale. Regarding to the sit-to-stand ability, lower peak power was observed in the sit-to-stand phase of the task at discharge. In conclusion, inertial sensor unit and our custom, validated, algorithms represent a feasible tool for measuring and monitoring functional trajectory during hospitalization in older adults and they are sensitive to detect differences in movement pattern parameters in different ADLs such as walking and the ability to stand from a seated position.     

Bridging the gaps between non-invasive genetic sampling and population parameter estimation

Reliable estimates of population parameters are necessary for effective management and conservation actions. The use of genetic data for capture–recapture (CR) analyses has become an important tool to estimate population parameters for elusive species. Strong emphasis has been placed on the genetic analysis of non-invasive samples, or on the CR analysis; however, little attention has been paid to the simultaneous overview of the full non-invasive genetic CR analysis, and the important insights gained by understanding the interactions between the different parts of the technique. Here, we review the three main steps of the approach: designing the appropriate sampling scheme, conducting the genetic lab analysis, and applying the CR analysis to the genetic results; and present a synthesis of this topic with the aim of discussing the primary limitations and sources of error. We discuss the importance of the integration between these steps, the unique situations which occur with non-invasive studies, the role of ecologists and geneticists throughout the process, the problem of error propagation, and the sources of biases which can be present in the final estimates. We highlight the importance of team collaboration and offer a series of recommendations to wildlife ecologists who are not familiar with this topic yet but may want to use this tool to monitor populations through time.     

A general program for estimation of haplotype frequencies from population diploid data.

The program which is written in FORTRAN estimates haplotype frequencies in two-locus and three-locus genetic systems from population diploid data. It is based on the gene counting method which leads to maximum likelihood estimates, and can be used whenever the possible antigens (one or more) on each chromosome can be specified for each person and for each locus, i.e., ABO-like systems and inclusions are permitted. The number of alleles per locus may be rather large, and both grouped and ungrouped data can be used. Log likelihoods are calculated on the basis of various assumptions, so that likelihood ratio tests can be carried out.     

The estimation of parameters from population data on the general stochastic epidemic

This paper provides a method of using maximum likelihood to estimate the two unknown parameters, the contact rate and the removal rate, in the general stochastic epidemic, using only the observed interremoval times and the total number of cases occurring. A goodness-of-fit test is discussed, and the methods described are illustrated by means of data on an actual smallpox epidemic in a restricted community in southeastern Nigeria.     

The use of magnetic resonance imaging for measuring segment inertial properties

The purpose of the study was to determine whether valid measures of segment inertial properties can be generated from a series of cross-sectional tissue scans using magnetic resonance imaging (MRI). The cross-sectional images for eight baboon cadaver segments (four forearms, two upper arms, and two lower legs) were digitized to yield areas of muscle, bone, and fat tissues. These data, along with tissue density values, were used for calculations of segment volume (V), density (D), mass (M), center of mass location (CM), and moment of inertia (Icm) about a transverse axis through the segment center of mass. Criterion measures of these properties were obtained using standard experimental techniques. Close agreement was found between criterion and MRI values for mean segment CM (44.67 vs. 43.36% from proximal end, respectively) while mean segment D was the same (1.124 g.cm-3) for both methods. MRI procedures tended to overestimate segment V(595.3 vs. 633.4 cm3), M(720.0 vs. 769.9 g), and Icm (3.208 vs. 3.332 x 10(-3) kg.m2). It was concluded that MRI represents a promising technique for generating valid measures of segment inertial characteristics as well as other anatomical features.     

Influence of body segment parameter estimation on calculated ground reaction forces in highly dynamic movements

The effect of body segment parameter estimation (BSP) on the inverse dynamics modelling results has not yet been demonstrated in specific groups during athletic movements with high segment accelerations. Therefore, the purpose of this study was to analyse this effect in ski-jumpers as representatives of a specific group (i.e. low body mass index) by comparing calculated and measured ground reaction forces during ski-jumping imitation jumps. Full body kinematics and vertical ground reaction forces were recorded of 9 ski-jumpers performing three imitation jumps each. BSP were estimated using three previously published, one individually optimized and one ski-jumper group specific model. Vertical ground reaction forces were calculated using the vertical acceleration of the segments as well as the BSP of the single models in a top-down approach. Statistical analysis revealed a main model effect concerning the root mean square error between the calculated and the measured ground reaction force with deviations between the models of 53%. Individual optimization and the application of the ski-jumper group specific model increased the accuracy of the calculated ground reaction forces by 11 and 7%, respectively, compared to the best performing published model. The results of inverse dynamics modelling are very sensitive to the BSP estimation for specific groups like ski-jumpers during movements incorporating high segment accelerations. This emphasizes the importance of selecting adequate BSP estimation models or methods when analysing specific groups in highly dynamic movements in order to increase the accuracy of the inverse dynamics analyses results.     

Computational approaches for RNA energy parameter estimation

Methods for efficient and accurate prediction of RNA structure are increasingly valuable, given the current rapid advances in understanding the diverse functions of RNA molecules in the cell. To enhance the accuracy of secondary structure predictions, we developed and refined optimization techniques for the estimation of energy parameters. We build on two previous approaches to RNA free-energy parameter estimation: (1) the Constraint Generation (CG) method, which iteratively generates constraints that enforce known structures to have energies lower than other structures for the same molecule; and (2) the Boltzmann Likelihood (BL) method, which infers a set of RNA free-energy parameters that maximize the conditional likelihood of a set of reference RNA structures. Here, we extend these approaches in two main ways: We propose (1) a max-margin extension of CG, and (2) a novel linear Gaussian Bayesian network that models feature relationships, which effectively makes use of sparse data by sharing statistical strength between parameters. We obtain significant improvements in the accuracy of RNA minimum free-energy pseudoknot-free secondary structure prediction when measured on a comprehensive set of 2518 RNA molecules with reference structures. Our parameters can be used in conjunction with software that predicts RNA secondary structures, RNA hybridization, or ensembles of structures. Our data, software, results, and parameter sets in various formats are freely available at http://www.cs.ubc.ca/labs/beta/Projects/RNA-Params.     

Analysis of body segment parameter differences between four human populations and the estimation errors of four popular mathematical models

Calculating the kinetics of motion using inverse or forward dynamics methods requires the use of accurate body segment inertial parameters. The methods available for calculating these body segment parameters (BSPs) have several limitations and a main concern is the applicability of predictive equations to several different populations. This study examined the differences in BSPs between 4 human populations using dual energy x-ray absorptiometry (DEXA), developed linear regression equations to predict mass, center of mass location (CM) and radius of gyration (K) in the frontal plane on 5 body segments and examined the errors produced by using several BSP sources in the literature. Significant population differences were seen in all segments for all populations and all BSPs except hand mass, indicating that population specific BSP predictors are needed. The linear regression equations developed performed best overall when compared to the other sources, yet no one set of predictors performed best for all segments, populations or BSPs. Large errors were seen with all models which were attributed to large individual differences within groups. Equations which account for these differences, including measurements of limb circumferences and breadths may provide better estimations. Geometric models use these parameters, however the models examined in this study did not perform well, possibly due to the assumption of constant density or the use of an overly simple shape. Creating solids which account for density changes or which mimic the mass distribution characteristics of the segment may solve this problem. Otherwise, regression equations specific for populations according to age, gender, race, and morphology may be required to provide accurate estimations of BSPs for use in kinetic equations of motion.     

On parameter estimation in population models III: time-inhomogeneous processes and observation error

Essential to applying a mathematical model to a real-world application is calibrating the model to data. Methods for calibrating population models often become computationally infeasible when the population size (more generally the size of the state space) becomes large, or other complexities such as time-dependent transition rates, or sampling error, are present. Continuing previous work in this series on the use of diffusion approximations for efficient calibration of continuous-time Markov chains, I present efficient techniques for time-inhomogeneous chains and accounting for observation error. Observation error (partial observability) is accounted for by joint estimation using a scaled unscented Kalman filter for state-space models. The methodology will be illustrated with respect to models of disease dynamics incorporating seasonal transmission rate and in the presence of observation error, including application to two influenza outbreaks and measles in London in the pre-vaccination era.     

On parameter estimation in population models II: Multi-dimensional processes and transient dynamics

Recently, a computationally-efficient method was presented for calibrating a wide-class of Markov processes from discrete-sampled abundance data. The method was illustrated with respect to one-dimensional processes and required the assumption of stationarity. Here we demonstrate that the approach may be directly extended to multi-dimensional processes, and two analogous computationally-efficient methods for non-stationary processes are developed. These methods are illustrated with respect to disease and population models, including application to infectious count data from an outbreak of “Russian influenza” (A/USSR/1977 H1N1) in an educational institution. The methodology is also shown to provide an efficient, simple and yet rigorous approach to calibrating disease processes with gamma-distributed infectious period.     

The relation between limb segment coordination during walking and fall history in community-dwelling older adults

Control of the swing foot during walking is important to prevent falls. The trajectories of the swing foot are adjusted by coordination of the lower limbs, which is evaluated with uncontrolled manifold (UCM) analysis. A previous study that applied this analysis to walking revealed that older adults with fall history had compensatorily great segment coordination to stabilize the swing foot during normal walking. However, it is unknown whether the increase in segment coordination helps for preventing incident falls in the future. At baseline measurement, 30 older adults walked for 20 times at a comfortable speed. UCM analysis was performed to evaluate how the segment configuration in the lower limbs contributes to the swing foot stability. One year after the baseline visit, we asked the subjects if there were incident falls through a questionnaire. The univariate and multivariable logistic regression analyses were performed to assess the association between the index of segment coordination and incident falls with and without adjustment for gait velocity. Twenty-eight older adults who responded to the questionnaire were classified into older adults (n = 12) who had the incident fall and those (n = 16) who did not have falls. It was revealed that older adults who increased the segment coordination associated with swing foot stability tended to experience at least one fall within one year of measurement. The index of the UCM analysis can be a sensitive predictor of incident falls.