Comparison of EEGs Before and After Stunning of Cattle Taking Account of Animal-to-Animal Variation

Data are available for the electroencephalograms (EEGs) of cattle before and after they received a mild electric shock. The purpose of the proposed statistical analysis is to extract from the data what differences there an in pre- and post-stun EEGs and possibly restrict attention to a small frequency band where there is a significant change. We study the log periodogram ratios for each animal and propose a stochastic model based method for smoothing these ratios. This method is novel in that it allows (i) for between animal variation, and (ii) the amount of local smoothing to adapt according to the data requirements. The smoothing method is implemented by utilizing a Kalman filter approach and the fixed interval smoothing algorithm, which allows us to obtain point-wise estimates and standard errors for the log periodogram ratio. Common animal effects which are intimated by animal-by-animal plots of log periodogram ratios against frequency are highlighted by this method.     

Filtering noise for synchronised activity in multi-trial electrophysiology data using Wiener and Kalman filters

Novel approaches to effectively reduce noise in data recorded from multi-trial physiology experiments have been investigated using two-dimensional filtering methods, adaptive Wiener filtering and reduced update Kalman filtering. Test data based on signal and noise model consisting of different conditions of signal components mixed with noise have been considered with filtering effects evaluated using analysis of frequency coherence and of time-dependent coherence. Various situations that may affect the filtering results have been explored and reveal that Wiener and Kalman filtering can considerably improve the coherence values between two channels of multi-trial data and suppress uncorrelated components. We have extended our approach to experimental data: multi-electrode array (MEA) local field potential (LFPs) recordings from the inferotemporal cortex of sheep and LFP vs. electromyogram (LFP-EMG) recording data during resting tremor in Parkinson’s disease patients. Finally general procedures for implementation of these filtering techniques are described.     

On the development and application of a continuous-discrete recursive prediction error algorithm

Recursive state and parameter reconstruction is a well-established field in control theory. In the current paper we derive a continuous-discrete version of recursive prediction error algorithm and apply the filter in an environmental and biological setting as a possible alternative to the well-known extended Kalman filter. The framework from which the derivation is started is the so-called 'innovations-format' of the (continuous time) system model, including (discrete time) measurements. After the algorithm has been motivated and derived, it is subsequently applied to hypothetical and 'real-life' case studies including reconstruction of biokinetic parameters and parameters characterizing the dynamics of a river in the United Kingdom. Advantages and characteristics of the method are discussed.     

Quantification of gait parameters with inertial sensors and inverse kinematics

Measuring human gait is important in medicine to obtain outcome parameter for therapy, for instance in Parkinson’s disease. Recently, small inertial sensors became available which allow for the registration of limb-position outside of the limited space of gait laboratories. The computation of gait parameters based on such recordings has been the subject of many scientific papers. We want to add to this knowledge by presenting a 4-segment leg model which is based on inverse kinematic and Kalman filtering of data from inertial sensors. To evaluate the model, data from four leg segments (shanks and thighs) were recorded synchronously with accelerometers and gyroscopes and a 3D motion capture system while subjects (n = 12) walked at three different velocities on a treadmill. Angular position of leg segments was computed from accelerometers and gyroscopes by Kalman filtering and compared to data from the motion capture system. The four-segment leg model takes the stance foot as a pivotal point and computes the position of the remaining segments as a kinematic chain (inverse kinematics). Second, we evaluated the contribution of pelvic movements to the model and evaluated a five segment model (shanks, thighs and pelvis) against ground-truth data from the motion capture system and the path of the treadmill.ResultsWe found the precision of the Kalman filtered angular position is in the range of 2–6° (RMS error). The 4-segment leg model computed stride length and length of gait path with a constant undershoot of 3% for slow and 7% for fast gait. The integration of a 5th segment (pelvis) into the model increased its precision. The advantages of this model and ideas for further improvements are discussed.     

Identifiability and online estimation of diagnostic parameters with in the glucose insulin homeostasis

Today, diagnostic decisions about pre-diabetes or diabetes are made using static threshold rules for the measured plasma glucose. In order to develop an alternative diagnostic approach, dynamic models as the Minimal Model may be deployed. We present a novel method to analyze the identifiability of model parameters based on the interpretation of the empirical observability Gramian. This allows a unifying view of both, the observability of the system's states (with dynamics) and the identifiability of the system's parameters (without dynamics). We give an iterative algorithm, in order to find an optimized set of states and parameters to be estimated. For this set, estimation results using an Unscented Kalman Filter (UKF) are presented. Two parameters are of special interest for diagnostic purposes: the glucose effectiveness S(G) characterizes the ability of plasma glucose clearance, and the insulin sensitivity S(I) quantifies the impact from the plasma insulin to the interstitial insulin subsystem. Applying the identifiability analysis to the trajectories of the insulin glucose system during an intravenous glucose tolerance test (IVGTT) shows the following result: (1) if only plasma glucose G(t) is measured, plasma insulin I(t) and S(G) can be estimated, but not S(I). (2) If plasma insulin I(t) is captured additionally, identifiability is improved significantly such that up to four model parameters can be estimated including S(I). (3) The situation of the first case can be improved, if a controlled external dosage of insulin is applied. Then, parameters of the insulin subsystem can be identified approximately from measurement of plasma glucose G(t) only.     

Filtering and interpreting location errors in satellite telemetry of marine animals

Argos telemetry offers a powerful means of tracking wild animals in their habitat, yet the delivered locations are subject to complex errors and random coverage. Bayesian filters and statistical models allow for objective trajectory estimates and inference on movement rates. As an alternative to Monte-Carlo methods, we investigate here how classic time series technique, such as the Kalman Filter, can be made robust to uncover patterns in the data. Our approach relies on a composite measurement model to account for outliers, and makes use of all the Location Classes to smooth observations and regularize the track to a regular time grid. Two application examples are presented. Using data from freely-swimming leatherback turtles, we confirm that locations of class A (LCA) are more accurate on average than class 0, and we recommend their use in tracking studies. We further show how measurement errors (and their geometry) interact with the assumed movement model, further modulating the final location error and the discriminating ability of the filter. The choice of the movement model appears important, since a model with no velocity constraint may fit observational errors at the expense of trajectory smoothness, while a speed-based model is better behaved but less forgiving for data fitting and outlier identification. Varying sea surface temperatures also appear to degrade the quality of locations and increase the occurrence of outliers, possibly in relation to thermal stratification and depth behavior. These results have important implications when inferring changes in behavior from long-term movements.     

Time series modelling and trophic interactions: rainfall,vegetation and ungulate dynamics

Time series analysis is a tool that is now commonly used when analysing the states of natural populations. This is a particularly complicated task for ungulates, since the data involved usually contain large observation errors and span short periods of time relative to the species’ life expectancies. Here we develop a method that expands on previous analyses, combining statistical state space modelling with biological mechanistic modelling. This enables biological interpretability of the statistical parameters. We used this method to analyse African ungulate census data, and it revealed some clarifying patterns. The dynamics of one group of species were generally independent of density and strongly affected by rainfall, while the other species were governed by a delayed density dependence and were relatively unaffected by rainfall variability. Dry season rainfall was more influential than wet season rainfall, which can be interpreted as indicating that adult survival is more important than recruitment in governing ungulate dynamics.     

Joint kinematics estimation using a multi-body kinematics optimisation and an extended Kalman filter,and embedding a soft tissue artefact model

To reduce the impact of the soft tissue artefact (STA) on the estimate of skeletal movement using stereophotogrammetric and skin-marker data, multi-body kinematics optimisation (MKO) and extended Kalman filters (EKF) have been proposed. This paper assessed the feasibility and efficiency of these methods when they embed a mathematical model of the STA and simultaneously estimate the ankle, knee and hip joint kinematics and the model parameters. A STA model was used that provides an estimate of the STA affecting the marker-cluster located on a body segment as a function of the kinematics of the adjacent joints. The MKO and the EKF were implemented with and without the STA model. To assess these methods, intra-cortical pin and skin markers located on the thigh, shank, and foot of three subjects and tracked during the stance phase of running were used. Embedding the STA model in MKO and EKF reduced the average RMS of marker tracking from 12.6 to 1.6 mm and from 4.3 to 1.9 mm, respectively, showing that a STA model trial-specific calibration is feasible. Nevertheless, with the STA model embedded in MKO, the RMS difference between the estimated and the reference joint kinematics determined from the pin markers slightly increased (from 2.0 to 2.1 deg) On the contrary, when the STA model was embedded in the EKF, this RMS difference was slightly reduced (from 2.0 to 1.7 deg) thus showing a better potentiality of this method to attenuate STA effects and improve the accuracy of joint kinematics estimate.     

Real‐time model based process monitoring of enzymatic biodiesel production

In this contribution we extend our modelling work on the enzymatic production of biodiesel where we demonstrate the application of a Continuous‐Discrete Extended Kalman Filter (a state estimator). The state estimator is used to correct for mismatch between the process data and the process model for Fed‐batch production of biodiesel. For the three process runs investigated, using a single tuning parameter, q_x = 2 × 10^?2 which represents the uncertainty in the process model, it was possible over the entire course of the reaction to reduce the overall mean and standard deviation of the error between the model and the process data for all of the five measured components (triglycerides, diglycerides, monoglycerides, fatty acid methyl esters, and free fatty acid). The most significant reduction for the three process runs, were for the monoglyceride and free fatty acid concentration. For those components, there was over a ten‐fold decrease in the overall mean error for the state estimator prediction compared with the predictions from the pure model simulations. It is also shown that the state estimator can be used as a tool for detection of outliers in the measurement data. For the enzymatic biodiesel process, given the infrequent and sometimes uncertain measurements obtained we see the use of the Continuous‐Discrete Extended Kalman Filter as a viable tool for real time process monitoring. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:585–595, 2015     

Optimal spatio‐temporal hybrid sampling designs for ecological monitoring

Question: Static sampling designs for collecting spatial data efficiently are being readily utilized by ecologists, however, most ecological systems involve a multivariate spatial process that evolves dynamically over time. Efficient monitoring of such spatio‐temporal systems can be achieved by modeling the dynamic system and reducing the uncertainty associated with the effect of design choice at future observation times. However, can we combine traditional techniques with dynamic methods to find optimal dynamic sampling designs for monitoring the succession of a herbaceous community? Location: Lower Hamburg Bend Conservation Area, Missouri, USA (40°34′42″ lat. 95°45′38″ long.). Methods: The dynamic nature of the system under study is modeled in such a way that uncertainty in the measurements and temporal process can both be accounted for. Both fixed and roving monitoring locations were used in conjunction with a spatio‐temporal statistical model to efficiently determine optimal locations of roving monitors over time based on the reduction of uncertainty in predictions. Results: During the first 3 years of the study, roving monitors where held at fixed locations to allow for statistical parameter estimation from which to make predictions. Optimal monitoring locations for the remaining 2 years were selected based on the overall reduction in prediction uncertainty. Conclusions: The dynamic and adaptive vegetation monitoring scheme allowed for the efficient collection of data that will be utilized for many future ecological studies. By optimally placing an additional set of monitoring locations, we were able to utilize information about the system dynamics when informing the data collection process.     

Parameter estimation and change-point detection from Dynamic Contrast Enhanced MRI data using stochastic differential equations

Dynamic Contrast Enhanced imaging (DCE-imaging) following a contrast agent bolus allows the extraction of information on tissue micro-vascularization. The dynamic signals obtained from DCE-imaging are modeled by pharmacokinetic compartmental models which integrate the Arterial Input Function. These models use ordinary differential equations (ODEs) to describe the exchanges between the arterial and capillary plasma and the extravascular-extracellular space. Their least squares fitting takes into account measurement noises but fails to deal with unpredictable fluctuations due to external/internal sources of variations (patients’ anxiety, time-varying parameters, measurement errors in the input function, etc.). Adding Brownian components to the ODEs leads to stochastic differential equations (SDEs). In DCE-imaging, SDEs are discretely observed with an additional measurement noise. We propose to estimate the parameters of these noisy SDEs by maximum likelihood, using the Kalman filter. In DCE-imaging, the contrast agent injected in vein arrives in plasma with an unknown time delay. The delay parameter induces a change-point in the drift of the SDE and ODE models, which is estimated also. Estimations based on the SDE and ODE pharmacokinetic models are compared to real DCE-MRI data. They show that the use of SDE provides robustness in the estimation results. A simulation study confirms these results.     

Software sensors for the monitoring of perfusion cultures: Evaluation of the hybridoma density and the medium composition from glucose concentration measurements

New software sensors based on the Extended Kalman Filter technique have been developed for the monitoring of animal cell perfusion cultures. They use a kinetic model describing the growth, death and metabolism of hybridoma cells as a function of the medium composition. The model was initially validated on a batch culture and found to correctly predict the continuous perfusion culture kinetics, except for the production of ammonia and lactate. Using the measurement of a single component in the culture medium, in this case glucose, the Extended Kalman Filter provides an excellent evaluation of the time variation of the concentrations of living and dead cells, of glutamine and antibodies, during the whole perfusion culture for a retained cell density rising from 1 to 11×10⁶ cells.ml^–1 inside the reactor.     

A constrained extended Kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise

This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4 mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9 N and 10 N m) were much lower than obtained using a classical inverse dynamics approach (22 N and 30 N m). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated.