@article{matzuka_mehlsen_tran_olufsen_2015, title={Using Kalman Filtering to Predict Time-Varying Parameters in a Model Predicting Baroreflex Regulation During Head-Up Tilt}, volume={62}, ISSN={0018-9294 1558-2531}, url={http://dx.doi.org/10.1109/TBME.2015.2409211}, DOI={10.1109/tbme.2015.2409211}, abstractNote={The cardiovascular control system is continuously engaged to maintain homeostasis, but it is known to fail in a large cohort of patients suffering from orthostatic intolerance. Numerous clinical studies have been put forward to understand how the system fails, yet noninvasive clinical data are sparse, typical studies only include measurements of heart rate and blood pressure, as a result it is difficult to determine what mechanisms that are impaired. It is known, that blood pressure regulation is mediated by changes in heart rate, vascular resistance, cardiac contractility, and a number of other factors. Given that numerous factors contribute to changing these quantities, it is difficult to devise a physiological model describing how they change in time. One way is to build a model that allows these controlled quantities to change and to compare dynamics between subject groups. To do so, it requires more knowledge of how these quantities change for healthy subjects. This study compares two methods predicting time-varying changes in cardiac contractility and vascular resistance during head-up tilt. Similar to the study by Williams et al.[51], the first method uses piecewise linear splines, while the second uses the ensemble transform Kalman filter (ETKF) [1] , [11], [12], [33]. In addition, we show that the delayed rejection adaptive Metropolis (DRAM) algorithm can be used for predicting parameter uncertainties within the spline methodology, which is compared with the variability obtained with the ETKF. While the spline method is easier to set up, this study shows that the ETKF has a significantly shorter computational time. Moreover, while uncertainty of predictions can be augmented to spline predictions using DRAM, these are readily available with the ETKF.}, number={8}, journal={IEEE Transactions on Biomedical Engineering}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Matzuka, Brett and Mehlsen, Jesper and Tran, Hien and Olufsen, Mette Sofie}, year={2015}, month={Aug}, pages={1992–2000} }
 @article{attarian_batzel_matzuka_tran_2013, title={Application of the Unscented Kalman Filtering to Parameter Estimation}, volume={2064}, ISBN={["978-3-642-32881-7"]}, ISSN={["0075-8434"]}, DOI={10.1007/978-3-642-32882-4_4}, abstractNote={Filtering is a methodology used to combine a set of observations with a model to obtain the optimal state. This technique can be extended to estimate the state of the system as well as the unknown model parameters. Estimating the model parameters given a set of data is often referred to as the inverse problem. Filtering provides many benefits to the inverse problem by providing estimates in real time and allowing model errors to be taken into account. Assuming a linear model and Gaussian noises, the optimal filter is the Kalman filter. However, these assumptions rarely hold for many problems of interest, so a number of extensions have been proposed in the literature to deal with nonlinear dynamics. In this chapter, we illustrate the application of one approach to deal with nonlinear model dynamics, the so-called unscented Kalman filter. In addition, we will also show how some of the tools for model validation discussed in other chapters of this volume can be used to improve the estimation process.}, journal={MATHEMATICAL MODELING AND VALIDATION IN PHYSIOLOGY: APPLICATIONS TO THE CARDIOVASCULAR AND RESPIRATORY SYSTEMS}, author={Attarian, Adam and Batzel, Jerry J. and Matzuka, Brett and Tran, Hien}, year={2013}, pages={75–88} }
 @inproceedings{aoi_matzuka_olufsen_2011, title={Toward online, noninvasive, nonlinear assessment of cerebral autoregulation}, DOI={10.1109/iembs.2011.6090671}, abstractNote={Online estimation of cerebral autoregulation (CA) may be advantageous in neurosurgical and neurointensive care units. Data from transcranial Doppler, and continuous arterial blood pressure are readily available at high temporal resolution and may be used to assess CA. There are currently no methods for nonlinear, noninvasive, online assessment of CA. We frame the assessment of CA as a parameter estimation problem, in which we estimate the parameters of a nonlinear mathematical model of CA using the ensemble Kalman filter (EnKF). In this simulation study, we use the EnKF to estimate the parameters of a model of cerebral hemodynamics which predicts intracranial pressure and cerebral blood flow velocity, generated from real patient arterial blood pressure measurements. We examine the flexibility and appropriateness of the EnKF for CA assessment.}, booktitle={2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)}, author={Aoi, M. C. and Matzuka, B. J. and Olufsen, M. S.}, year={2011}, pages={2410–2413} }