Ann E. Rundell

A sliding mode observer and controller for stabilization of rotational motion of a vertical shaft magnetic bearing

In this paper we present the development of (1) a sliding mode controller for stabilization of the rotational dynamics of a vertical shaft magnetic bearing in addition to providing tracking capabilities, and (2) a sliding mode observer for state and disturbance estimation. Rotor imbalance causes sinusoidal disturbances which necessitates robustness inherent in sliding mode observers and controllers. The sliding mode control design includes (1) the definition of an equilibrium manifold upon which the magnetic bearing has the desired stability and tracking properties, and (2) the control selection from one of several potential control strategies for driving the system to this manifold and maintaining it there. A sliding mode observer strategy is proposed to estimate derivatives of measured signals in the presence of unmatched disturbances by filtering discontinuous approximations of the derivatives. Simulation results demonstrate the utility and robustness of a sliding mode controller and observer for stabilizing the rotational dynamics of a magnetic bearing.

SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool

BackgroundIt has long been recognized that sensitivity analysis plays a key role in modeling and analyzing cellular and biochemical processes. Systems biology markup language (SBML) has become a well-known platform for coding and sharing mathematical models of such processes. However, current SBML compatible software tools are limited in their ability to perform global sensitivity analyses of these models.ResultsThis work introduces a freely downloadable, software package, SBML-SAT, which implements algorithms for simulation, steady state analysis, robustness analysis and local and global sensitivity analysis for SBML models. This software tool extends current capabilities through its execution of global sensitivity analyses using multi-parametric sensitivity analysis, partial rank correlation coefficient, SOBOLs method, and weighted average of local sensitivity analyses in addition to its ability to handle systems with discontinuous events and intuitive graphical user interface.ConclusionSBML-SAT provides the community of systems biologists a new tool for the analysis of their SBML models of biochemical and cellular processes.

Modeling Mitochondrial Bioenergetics with Integrated Volume Dynamics

Mathematical models of mitochondrial bioenergetics provide powerful analytical tools to help interpret experimental data and facilitate experimental design for elucidating the supporting biochemical and physical processes. As a next step towards constructing a complete physiologically faithful mitochondrial bioenergetics model, a mathematical model was developed targeting the cardiac mitochondrial bioenergetic based upon previous efforts, and corroborated using both transient and steady state data. The model consists of several modified rate functions of mitochondrial bioenergetics, integrated calcium dynamics and a detailed description of the K+-cycle and its effect on mitochondrial bioenergetics and matrix volume regulation. Model simulations were used to fit 42 adjustable parameters to four independent experimental data sets consisting of 32 data curves. During the model development, a certain network topology had to be in place and some assumptions about uncertain or unobserved experimental factors and conditions were explicitly constrained in order to faithfully reproduce all the data sets. These realizations are discussed, and their necessity helps contribute to the collective understanding of the mitochondrial bioenergetics.

Using adaptive model predictive control to customize maintenance therapy chemotherapeutic dosing for childhood acute lymphoblastic leukemia

Acute lymphoblastic leukemia (ALL) is a common childhood cancer in which nearly one-quarter of patients experience a disease relapse. However, it has been shown that individualizing therapy for childhood ALL patients by adjusting doses based on the blood concentration of active drug metabolite could significantly improve treatment outcome. An adaptive model predictive control (MPC) strategy is presented in which maintenance therapy for childhood ALL is personalized using routine patient measurements of red blood cell mean corpuscular volume as a surrogate for the active drug metabolite concentration. A clinically relevant mathematical model is developed and used to describe the patient response to the chemotherapeutic drug 6-mercaptopurine, with some model parameters being patient-specific. During the course of treatment, the patient-specific parameters are adaptively identified using recurrent complete blood count measurements, which sufficiently constrain the patient parameter uncertainty to support customized adjustments of the drug dose. While this work represents only a first step toward a quantitative tool for clinical use, the simulated treatment results indicate that the proposed mathematical model and adaptive MPC approach could serve as valuable resources to the oncologist toward creating a personalized treatment strategy that is both safe and effective.

Rhythmic abdominal compression CPR ventilates without supplemental breaths and provides effective blood circulation

OBJECTIVES Standard chest-compression CPR has an out-of-hospital resuscitation rate of less than 10% and can result in rib fractures or mouth-to-mouth transfer of infection. Recently, we introduced a new CPR method that utilizes only rhythmic abdominal compressions (OAC-CPR). The present study compares ventilation and hemodynamics produced by chest and abdominal compression CPR. METHODS Twelve swine (29-34kg) were anesthetized, intubated and allowed to breathe spontaneously. Physiologic dead space, resting tidal volume, compression-induced lung air flow, and blood pressures were recorded. Ventricular fibrillation (VF) was electrically induced and subjects were treated with either standard CPR or OAC-CPR at various force and rate settings. Minute alveolar ventilation (MAV) and mean coronary perfusion pressure (CPP) were compared. RESULTS For OAC-CPR, ventilation per compression tended to increase with increasing force and decreasing rate. Chest only compressions produced no MAV, while OAC-CPR at 80cycles/min or less, matched the MAV for spontaneous respiration. For all rates, abdominal compressions met, or exceeded, the CPP of chest compressions performed at 100lbs. CONCLUSIONS OAC-CPR generated ventilatory volumes significantly greater than the dead space and produced equivalent, or larger, CPP than with chest compressions. Thus, OAC-CPR ventilates a subject, eliminating the need for mouth-to-mouth breathing, and effectively circulates blood during VF without breaking ribs. Furthermore, this technique is simple to perform, can be administered by a single rescuer, and should reduce bystander reluctance to administer CPR.

A Global Parallel Model Based Design of Experiments Method to Minimize Model Output Uncertainty

Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the estimated experimental noise. The method is based upon computationally efficient sparse grids and requires only a bounded uncertain parameter space; it does not rely upon initial parameter estimates. The design sequence emerges through the use of scenario trees with experimental design points chosen to minimize the uncertainty in the predicted dynamics of the measurable responses of the system. The algorithm was illustrated herein using a T cell activation model for three problems that ranged in dimension from 2D to 19D. The results demonstrate that it is possible to extract useful information from a mathematical model where traditional model-based design of experiments approaches most certainly fail. The experiments designed via this method fully constrain the model output dynamics to within experimentally resolvable limits. The method is effective for highly uncertain biological systems characterized by deterministic mathematical models with limited data sets. Also, it is highly modular and can be modified to include a variety of methodologies such as input design and model discrimination.

Experiment design through dynamical characterisation of non-linear systems biology models utilising sparse grids

The sparse grid-based experiment design algorithm sequentially selects an experimental design point to discriminate between hypotheses for given experimental conditions. Sparse grids efficiently screen the global uncertain parameter space to identify acceptable parameter subspaces. Clustering the located acceptable parameter vectors by the similarity of the simulated model trajectories characterises the data-compatible model dynamics. The experiment design algorithm capitalizes on the diversity of the experimentally distinguishable system output dynamics to select the design point that best discerns between competing model-structure and parameter-encoded hypotheses. As opposed to designing the experiments to explicitly reduce uncertainty in the model parameters, this approach selects design points to differentiate between dynamical behaviours. This approach further differs from other experimental design methods in that it simultaneously addresses both parameter- and structural-based uncertainty that is applicable to some ill-posed problems where the number of uncertain parameters exceeds the amount of data, places very few requirements on the model type, available data and a priori parameter estimates, and is performed over the global uncertain parameter space. The experiment design algorithm is demonstrated on a mitogen-activated protein kinase cascade model. The results show that system dynamics are highly uncertain with limited experimental data. Nevertheless, the algorithm requires only three additional experimental data points to simultaneously discriminate between possible model structures and acceptable parameter values. This sparse grid-based experiment design process provides a systematic and computationally efficient exploration over the entire uncertain parameter space of potential model structures to resolve the uncertainty in the non-linear systems biology model dynamics.

Optimal chemotherapy for leukemia: a model-based strategy for individualized treatment.

Acute Lymphoblastic Leukemia, commonly known as ALL, is a predominant form of cancer during childhood. With the advent of modern healthcare support, the 5-year survival rate has been impressive in the recent past. However, long-term ALL survivors embattle several treatment-related medical and socio-economic complications due to excessive and inordinate chemotherapy doses received during treatment. In this work, we present a model-based approach to personalize 6-Mercaptopurine (6-MP) treatment for childhood ALL with a provision for incorporating the pharmacogenomic variations among patients. Semi-mechanistic mathematical models were developed and validated for i) 6-MP metabolism, ii) red blood cell mean corpuscular volume (MCV) dynamics, a surrogate marker for treatment efficacy, and iii) leukopenia, a major side-effect. With the constraint of getting limited data from clinics, a global sensitivity analysis based model reduction technique was employed to reduce the parameter space arising from semi-mechanistic models. The reduced, sensitive parameters were used to individualize the average patient model to a specific patient so as to minimize the model uncertainty. Models fit the data well and mimic diverse behavior observed among patients with minimum parameters. The model was validated with real patient data obtained from literature and Riley Hospital for Children in Indianapolis. Patient models were used to optimize the dose for an individual patient through nonlinear model predictive control. The implementation of our approach in clinical practice is realizable with routinely measured complete blood counts (CBC) and a few additional metabolite measurements. The proposed approach promises to achieve model-based individualized treatment to a specific patient, as opposed to a standard-dose-for-all, and to prescribe an optimal dose for a desired outcome with minimum side-effects.

Model-based design of experiments for cellular processes

Model‐based design of experiments (MBDOE) assists in the planning of highly effective and efficient experiments. Although the foundations of this field are well‐established, the application of these techniques to understand cellular processes is a fertile and rapidly advancing area as the community seeks to understand ever more complex cellular processes and systems. This review discusses the MBDOE paradigm along with applications and challenges within the context of cellular processes and systems. It also provides a brief tutorial on Fisher information matrix (FIM)‐based and Bayesian experiment design methods along with an overview of existing software packages and computational advances that support MBDOE application and adoption within the Systems Biology community. As cell‐based products and biologics progress into the commercial sector, it is anticipated that MBDOE will become an essential practice for design, quality control, and production. WIREs Syst Biol Med 2013, 5:181–203. doi: 10.1002/wsbm.1204

Analysis of gap gene regulation in a 3D organism-scale model of the Drosophila melanogaster embryo.

The axial bodyplan of Drosophila melanogaster is determined during a process called morphogenesis. Shortly after fertilization, maternal bicoid mRNA is translated into Bicoid (Bcd). This protein establishes a spatially graded morphogen distribution along the anterior-posterior (AP) axis of the embryo. Bcd initiates AP axis determination by triggering expression of gap genes that subsequently regulate each others expression to form a precisely controlled spatial distribution of gene products. Reaction-diffusion models of gap gene expression on a 1D domain have previously been used to infer complex genetic regulatory network (GRN) interactions by optimizing model parameters with respect to 1D gap gene expression data. Here we construct a finite element reaction-diffusion model with a realistic 3D geometry fit to full 3D gap gene expression data. Though gap gene products exhibit dorsal-ventral asymmetries, we discover that previously inferred gap GRNs yield qualitatively correct AP distributions on the 3D domain only when DV-symmetric initial conditions are employed. Model patterning loses qualitative agreement with experimental data when we incorporate a realistic DV-asymmetric distribution of Bcd. Further, we find that geometry alone is insufficient to account for DV-asymmetries in the final gap gene distribution. Additional GRN optimization confirms that the 3D model remains sensitive to GRN parameter perturbations. Finally, we find that incorporation of 3D data in simulation and optimization does not constrain the search space or improve optimization results.