Mikhail Skliar

Itô–Volterra Optimal State Estimation With Continuous, Multirate, Randomly Sampled, and Delayed Measurements

The optimal filter for continuous, linear, stochastic, time-varying systems described by the Itocirc-Volterra equations with discontinuous measure is derived. With an appropriately selected measure, the result is applicable to a wide range of observation processes, including the hybrid case of observations formed by an arbitrary combination of continuous and discrete measurements, which may be sampled with a priori unknown, changing, and, possibly, random rates and delays. The simultaneous presence of continuous and sampled measurements causes impulsive discontinuity in the inputs of the optimal filter equations, which leads to a discontinuous change in state estimates every time a sampled measurement becomes available. Using the theory of vibrosolutions, the explicit and unique expressions for the jumps in state estimates and estimation error covariance are derived. Several examples illustrate the procedure of modeling hybrid measurement systems by selecting an appropriate discontinuous measure. We further show that the Itocirc-Volterra model and the main result of the paper can be specialized to several important cases, including state space systems, for which we recover several known state estimation results, and derive a novel optimal filter for continuous LTV systems with an arbitrary combination of continuous and delayed sampled measurements. This optimal filter updates the state estimates for incoming measurements as soon as they become available and does not require prior knowledge of sampling instants and delays, which makes it applicable when deterministic and random changes in sampling and delays are present. Several computational examples demonstrate the implementation of the developed filter and compare its performance to the traditional alternatives using Monte-Carlo simulations

Modeling and control of a brushless DC axial flow ventricular assist device.

This article presents an integrated model of the human circulatory system that incorporates circulatory support by a brushless DC axial flow ventricular assist device (VAD), and a feedback VAD controller designed to maintain physiologically sufficient perfusion. The developed integrated model combines a network type model of the circulatory system with a nonlinear dynamic model of the brushless DC pump. We show that maintaining a reference differential pressure between the left ventricle and aorta leads to adequate perfusion for different pathologic cases, ranging from normal heart to left heart asystole, and widely varying physical activity scenarios from rest to exercise.

Model-predictive control of hyperthermia treatments

A model-predictive controller (MPC) of the thermal dose in hyperthermia cancer treatments has been developed and evaluated using simulations with one-point and one-dimensional models of a tumor. The developed controller is the first effort in: 1) the application of feedback control to pulsed, high-temperature hyperthermia treatments; 2) the direct control of the treatment thermal dose rather than the treatment temperatures; and 3) the application of MPC to hyperthermia. treatments. Simulations were performed with different blood flow rates in the tumor and constraints on temperatures in normal tissues. The results demonstrate that 1) thermal dose can be controlled in the presence of plant-model mismatch and 2) constraints on the maximum allowable temperatures in normal tissue and/or the pulsed power magnitude can be directly incorporated into MPC and met while delivering the desired thermal dose to the tumor. For relatively high blood flow rates and low transducer surface intensities-factors that limit the range of temperature variations in the tumor, the linear MPC, obtained by piece-wise linearization of the dose-temperature relationship, provides an adequate performance. For large temperature variations, the development of nonlinear MPC is necessary.

Direct thermal dose control of constrained focused ultrasound treatments: phantom and in vivo evaluation

The first treatment control system that explicitly and automatically balances the efficacy and safety goals of noninvasive thermal therapies is described, and its performance is evaluated in phantoms and in vivo using ultrasound heating with a fixed, focused transducer. The treatment efficacy is quantified in terms of thermal dose delivered to the target. The developed feedback thermal dose controller has a cascade structure with the main nonlinear dose controller continuously generating the reference temperature trajectory for the secondary, constrained, model predictive temperature controller. The control system ensures thermal safety of the normal tissue by automatically complying with user-specified constraints on the maximum allowable normal tissue temperatures. To reflect hardware limitations and to prevent cavitation, constraints on the maximum transducer power can also be imposed. It is shown that the developed controller can be used to achieve the minimum-time delivery of the desired thermal dose to the target without violating safety constraints, which is a novel and clinically desirable feature. The developed controller is model based, and requires patient- and site-specific models for its operation. These models were obtained during pre-treatment identification experiments. In our implementation, predictive models, internally used by the automatic treatment controller, are dynamically updated each time new temperature measurements become available. The adaptability of internal models safeguards against adverse effects of modelling errors, and ensures robust performance of the control system in the presence of a priori unknown treatment disturbances. The successful validation with two experimental models of considerably different thermal and ultrasound properties suggests the applicability of the developed treatment control system to different anatomical sites.

Physiologic control of rotary blood pumps: An in vitro study

Rotary blood pumps (RBPs) are currently being used as a bridge to transplantation as well as for myocardial recovery and destination therapy for patients with heart failure. Physiologic control systems for RBPs that can automatically and autonomously adjust the pump flow to match the physiologic requirement of the patient are needed to reduce human intervention and error, while improving the quality of life. Physiologic control systems for RBPs should ensure adequate perfusion while avoiding inflow occlusion via left ventricular (LV) suction for varying clinical and physical activity conditions. For RBPs used as left ventricular assist devices (LVADs), we hypothesize that maintaining a constant average pressure difference between the pulmonary vein and the aorta (ΔPa) would give rise to a physiologically adequate perfusion while avoiding LV suction. Using a mock circulatory system, we tested the performance of the control strategy of maintaining a constant average ΔPa and compared it with the results obtained when a constant average pump pressure head (ΔP) and constant rpm are maintained. The comparison was made for normal, failing, and asystolic left heart during rest and at light exercise. The ΔPa was maintained at 95 ± l mm Hg for all the scenarios. The results indicate that the ΔPa control strategy maintained or restored the total flow rate to that of the physiologically normal heart during rest (3.8 L/m) and light exercise (5.4 L/m) conditions. The ΔPa approach adapted to changing exercise and clinical conditions better than the constant rpm and constant ΔP control strategies. The ΔPa control strategy requires the implantation of two pressure sensors, which may not be clinically feasible. Sensorless RBP control using the ΔPa algorithm, which can eliminate the failure prone pressure sensors, is being currently investigated.

Optimal filtering for polynomial system states with polynomial multiplicative noise

In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman-Bucy filter.

Size and shape characterization of hydrated and desiccated exosomes

Exosomes are stable nanovesicles secreted by cells into the circulation. Their reported sizes differ substantially, which likely reflects the difference in the isolation techniques used, the cells that secreted them, and the methods used in their characterization. We analyzed the influence of the last factor on the measured sizes and shapes of hydrated and desiccated exosomes isolated from the serum of a pancreatic cancer patient and a healthy control. We found that hydrated exosomes are close-to-spherical nanoparticles with a hydrodynamic radius that is substantially larger than the geometric size. For desiccated exosomes, we found that the desiccated shape and sizing are influenced by the manner in which drying occurred. Isotropic desiccation in aerosol preserves the near-spherical shape of the exosomes, whereas drying on a surface likely distorts their shapes and influences the sizing results obtained by techniques that require surface fixation prior to analysis.

MR thermometry-based feedback control of efficacy and safety in minimum-time thermal therapies: Phantom and in-vivo evaluations

The experimental validation of a model-based, thermal therapy control system which automatically and simultaneously achieves the specified efficacy and safety objectives of the treatment is reported. MR-thermometry measurements are used in real-time to control the power of a stationary, focused ultrasound transducer in order to achieve the desired treatment outcome in minimum time without violating the imposed safety constraints. Treatment efficacy is quantified in terms of the thermal dose delivered to the target. Normal tissue safety is ensured by automatically maintaining normal tissue temperature below the imposed limit in the user-specified locations. To reflect hardware limitations, constraints on the maximum applied power are also imposed. At the pretreatment stage, MR imaging and thermometry are used to localize the treatment target and identify thermal and actuation models. The results of phantom and canine experiments demonstrate that spatially-distributed, real-time MR temperature measurements enhance ones ability to robustly achieve the desired treatment outcome in minimum time without violating safety constraints. Post-treatment evaluation of the outcome using T2-weighted images of canine muscle showed good spatial correlation between the sonicated area and thermally damaged tissue.

Optimal and robust integral sliding mode filter design for systems with continuous and delayed measurements

In this paper, the optimal filtering problem for a linear system over observations with a fixed delay is treated, proceeding from the general expression for the stochastic Ito differential of the optimal estimate and its variance. As a result, the optimal filtering equations similar to the traditional Kalman-Bucy filter are obtained in the form dual to the Smith predictor, commonly used control structure for model-based time delay compensation. The paper then presents a robustification algorithm for the obtained optimal filter based on sliding mode compensation of disturbances. As a result, the sliding mode control of observations leading to suppression of the disturbances in a finite time is designed. This control algorithm also guarantees finite-time convergence of the estimate based on the corrupted observations to the optimal estimate satisfying the obtained optimal filtering equations over delayed observations.

Optimal filtering for partially measured polynomial system states

In this paper, the optimal filtering problem for polynomial systems with partially measured linear part over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with partially measured linear part over linear observations with delay is then established, which yields the explicit closed form of the filtering equations in the particular case of a bilinear system state. In the example, performance of the designed optimal filter is verified for a quadratic-linear state with unmeasured linear part over linear observations against the conventionally designed extended Kalman-Bucy filter.