Sven Zenker

From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement todays evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information.

An adequately robust early TNF-α response is a hallmark of survival following trauma/hemorrhage

Background Trauma/hemorrhagic shock (T/HS) results in cytokine-mediated acute inflammation that is generally considered detrimental. Methodology/Principal Findings Paradoxically, plasma levels of the early inflammatory cytokine TNF-α (but not IL-6, IL-10, or NO2 -/NO3 -) were significantly elevated within 6 h post-admission in 19 human trauma survivors vs. 4 non-survivors. Moreover, plasma TNF-α was inversely correlated with Marshall Score, an index of organ dysfunction, both in the 23 patients taken together and in the survivor cohort. Accordingly, we hypothesized that if an early, robust pro-inflammatory response were to be a marker of an appropriate response to injury, then individuals exhibiting such a response would be predisposed to survive. We tested this hypothesis in swine subjected to various experimental paradigms of T/HS. Twenty-three anesthetized pigs were subjected to T/HS (12 HS-only and 11 HS + Thoracotomy; mean arterial pressure of 30 mmHg for 45–90 min) along with surgery-only controls. Plasma obtained at pre-surgery, baseline post-surgery, beginning of HS, and every 15 min thereafter until 75 min (in the HS only group) or 90 min (in the HS + Thoracotomy group) was assayed for TNF-α, IL-6, IL-10, and NO2 -/NO3 -. Mean post-surgery±HS TNF-α levels were significantly higher in the survivors vs. non-survivors, while non-survivors exhibited no measurable change in TNF-α levels over the same interval. Conclusions/Significance Contrary to the current dogma, survival in the setting of severe, acute T/HS appears to be associated with an immediate increase in serum TNF-α. It is currently unclear if this response was the cause of this protection, a marker of survival, or both. This abstract won a Young Investigator Travel Award at the SHOCK 2008 meeting in Cologne, Germany.

Physiologic responses to severe hemorrhagic shock and the genesis of cardiovascular collapse: can irreversibility be anticipated?

BACKGROUND The causes of cardiovascular collapse (CC) during hemorrhagic shock (HS) are unknown. We hypothesized that vascular tone loss characterizes CC, and that arterial pulse pressure/stroke volume index ratio or vascular tone index (VTI) would identify CC. METHODS Fourteen Yorkshire-Durock pigs were bled to 30 mmHg mean arterial pressure and held there by repetitive bleeding until rendered unable to compensate (CC) or for 90 min (NoCC). They were then resuscitated in equal parts to shed volume and observed for 2 h. CC was defined as a MAP < 30 mmHg for 10 min or <20 mmHg for 10 s. Study variables were recorded at baseline (B0), 30, 60, 90 min after bleeding and at resuscitation (R0), 30, and 60 min afterward. RESULTS Swine were bled to 32% ± 9% of total blood volume. Epinephrine (Epi) and VTI were low and did not change in NoCC after bleeding compared with CC swine, in which both increased (0.97 ± 0.22 to 2.57 ± 1.42 mcg/dL, and 173 ± 181 to 939 ± 474 mmHg/mL, respectively), despite no differences in bled volume. Lactate increase rate (LIR) increased with hemorrhage and was higher at R0 for CC, but did not vary in NoCC. VTI identified CC from NoCC and survivors from non-survivors before CC. A large increase in LIR was coincident with VTI decrement before CC occurred. CONCLUSIONS Vasodilatation immediately prior to CC in severe HS occurs at the same time as an increase in LIR, suggesting loss of tone as the mechanism causing CC, and energy failure as its probable cause.

The inverse problem in mathematical biology.

Biological systems present particular challengers to model for the purposes of formulating predictions of generating biological insight. These systems are typically multi-scale, complex, and empirical observations are often sparse and subject to variability and uncertainty. This manuscript will review some of these specific challenges and introduce current methods used by modelers to construct meaningful solutions, in the context of preserving biological relevance. Opportunities to expand these methods are also discussed.

Peristaltic Pneumatic Compression of the Legs Reduces Fluid Demand and Improves Hemodynamic Stability during Surgery: A Randomized, Prospective Study

Background:Perioperative fluid restriction might be beneficial in specific clinical settings. In this prospective, randomized and blinded study, we assessed whether peristaltic pneumatic compression of the legs can support restrictive fluid management strategies by reducing intraoperative fluid demand and improving hemodynamic stability. Methods:Seventy patients scheduled for minor surgery were randomly assigned to receive either intraoperative peristaltic pneumatic compression or placebo compression. Both groups received fluid therapy according to a goal-directed protocol with a crystalloid base rate of 2 ml · kg−1 · h−1 and bolus infusions of 250 ml crystalloids triggered by hypotension, tachycardia, or high Pleth Variability Index. Results:Patients treated with peristaltic pneumatic compression received less intravenous fluid: median (interquartile range) 286 (499) versus 921 (900) ml (P < 0.001), resulting in a median difference of 693 ml (95% CI, 495–922 ml) and a median difference of 8.4 ml/kg (95% CI, 5.3–11.5 ml; P < 0.001). After the anesthesia induction phase, median overall infusion rates were 12.2 (14.1) ml · kg−1 · h−1 in the control group and 1.9 (0.4) ml · kg−1 · h−1 in the pneumatic peristaltic compression group (P < 0.001). Among patients treated with pneumatic peristaltic compression, the median cumulative time of hypotension was shorter (0 [12.5] vs. 22.6 [22.8] min; P = 0.002), fewer hypotensive events were recorded (39 vs. 137; P = 0.001), and median lowest individual systolic pressure was higher (92 [8] vs. 85 [16] mmHg; P = 0.002). Conclusions:This study demonstrates that peristaltic pneumatic compression of the legs significantly improves hemodynamic stability and reduces fluid demand during minor surgery.

Parallel particle filters for online identification of mechanistic mathematical models of physiology from monitoring data: performance and real-time scalability in simulation scenarios

ObjectiveCombining mechanistic mathematical models of physiology with quantitative observations using probabilistic inference may offer advantages over established approaches to computerized decision support in acute care medicine. Particle filters (PF) can perform such inference successively as data becomes available. The potential of PF for real-time state estimation (SE) for a model of cardiovascular physiology is explored using parallel computers and the ability to achieve joint state and parameter estimation (JSPE) given minimal prior knowledge tested.MethodsA parallelized sequential importance sampling/resampling algorithm was implemented and its scalability for the pure SE problem for a non-linear five-dimensional ODE model of the cardiovascular system evaluated on a Cray XT3™ using up to 1,024 cores. JSPE was implemented using a state augmentation approach with artificial stochastic evolution of the parameters. Its performance when simultaneously estimating the 5 states and 18 unknown parameters when given observations only of arterial pressure, central venous pressure, heart rate, and, optionally, cardiac output, was evaluated in a simulated bleeding/resuscitation scenario.ResultsSE was successful and scaled up to 1,024 cores with appropriate algorithm parametrization, with real-time equivalent performance for up to 10 million particles. JSPE in the described underdetermined scenario achieved excellent reproduction of observables and qualitative tracking of enddiastolic ventricular volumes and sympathetic nervous activity. However, only a subset of the posterior distributions of parameters concentrated around the true values for parts of the estimated trajectories.ConclusionsParallelized PF’s performance makes their application to complex mathematical models of physiology for the purpose of clinical data interpretation, prediction, and therapy optimization appear promising. JSPE in the described extremely underdetermined scenario nevertheless extracted information of potential clinical relevance from the data in this simulation setting. However, fully satisfactory resolution of this problem when minimal prior knowledge about parameter values is available will require further methodological improvements, which are discussed.

Using Mathematical Models to Improve the Utility of Quantitative ICU Data

Intensive care medicine is one of the areas of medicine most closely linked to applied physiology. Furthermore, it has a long tradition of being the forefront of advanced physiologic measurement technologies. The associated volume of quantitative data about a patient’s physiologic status, therapy, together with the output of off-line analyses, creates an information overload that profoundly reduces efficient and effective information processing. To a certain extent, this disconnection is a reason for the slow progress in utilizing such information across patients and hospital systems to improve patient care, perhaps most prominently evidenced by the failure of the physiologically valuable information provided by pulmonary artery catheterization to improve outcome in the critical care setting [1, 2]. In fact, for newer and more advanced monitoring equipment, evaluations of utility and ability to fit into proven treatment protocols is often lacking. Although the difficulty in translating the increased amount of available patient-specific information into patient benefit may in part be due to the lack of adequate therapeutic options, where clear benefit is known, actual translation of this information into practice is a primary barrier to improving patient care.

Robust model-based quantification of global ventricular torsion from spatially sparse three-dimensional time series data by orthogonal distance regression: evaluation in a canine animal model under different pacing regimes.

Background: Quantification of global ventricular rotational deformation, expressed as twist or torsion, and its dynamic changes is important in understanding the pathophysiology of heart disease and its therapy. Various techniques, such as sonomicrometry, allow tracking of specific sites within the myocardium. Quantification of twist from such data requires a longitudinal reference axis of rotation. Current methods require specific positioning and numbers of myocardial markers and assumptions about temporal positional evolution that may be violated during dyssynchronous contraction.

Differential Effects of Left Ventricular Pacing Sites on Regional Contraction Patterns and Global Performance

OBJECTIVE To define the differential effect of site-specific ventricular counterpacing efficacy during cardiac resynchronization therapy (CRT) to identify the most informative imaging views to quantify it. Cross-sectional and long-axis views commonly are used to assess left ventricular (LV) contractility. DESIGN The effects of LV apical (LVa) and free-wall (LVfw) pacing during CRT on long- and short-axis contraction, cardiac output, and stroke work were assessed in an open-chested acute canine model to determine whether LVa and LVfw would induce earlier apical than basilar LV radial contraction and earlier free-wall than septal contraction, respectively. Apical (CRTa) and free-wall (CRTfw) using right ventricular (RV) pacing-induced dyssynchrony also were examined. SETTING University large animal research laboratory. PARTICIPANTS Ten acutely anesthetized and instrumented open-chested purpose-bred dogs. INTERVENTIONS RV pacing served as the model of cardiac dyssynchrony. Selective LVfw and LVa pacing alone or with RV (CRTfw and CRTa, respectively) were studied relative to right atrial pacing (RA) as the control. MEASUREMENTS AND MAIN RESULTS Two pairs of 3 ultrasonic crystals were place along the LV longitudinal axis-apex and mid-to-base pairs along septal and free wall lines. Conductance catheter-defined longitudinal LV segmental volumes and pressure-volume data were collected. RV decreased cardiac output and stroke work compared with RA (2.0±0.3 v 1.4±0.1 L/min; 137±22 v 60±14 mJ; p<0.05, respectively). LVfw but not LVa decreased stroke work (130±35 mJ), and CRTa but not CRTfw improved both (2.1±0.2 L/min; 113±13 mJ; p<0.01 v RV pacing). No difference in time to minimal length free wall-to-septal crystal was seen with pacing. Both LVa and CRTa displayed increased apical-to-basilar shortening delay compared with RA, RV, and LVfw (42±47, 9±105, and 1±46 msec, respectively; p<0.05). No matching regional LV volume changes were seen during LVa. CONCLUSIONS LV functional analysis from only a cross-sectional plane may be insufficient to characterize improved LV contraction synchrony during multisite CRT.

Introduction to the special issue: papers from the Society for Complex Acute Illness (SCAI)

This is the first special issue of articles contributed by members of the Society for Complex Acute Illness (SCAI, http://www. scai-med.org). Since its founding in 2003, SCAI has focused on bringing acute care clinicians, experimentalists, mathematicians, physicists, and engineers together to tackle refractory problems in critical care. The multidisciplinary society emphasizes quantitative scientific approaches for understanding critical illness and translation of these findings into practice. Over time, the mathematical toolbox discussed by the group has broadened and evolved, from primarily nonlinear timeseries analysis techniques and mechanistic mathematical modeling to include emerging tools such as machine learning methods. SCAI members have also addressed developments relevant to the goals of the society such as innovative applications of acute care electronic health records and novel sensor and imaging technology, prompting the society’s recent name change from ‘‘Society for Complexity in Acute Illness’’ to ‘‘Society for Complex Acute Illness’’. The concept for this special issue was hatched at SCAI’s International Conference on Complexity in Acute Illness (ICCAI, http://www.iccai.org) in September 2011 in Bonn, Germany, the 10th SCAI annual meeting. After an open invitation to SCAI members and past ICCAI contributors to submit relevant manuscripts, 20 contributions were subjected to rigorous peer review, of which 12 were finally accepted for publication in this special issue. The accepted articles reflect the society’s goals and scope, covering a broad range of quantitative methodologies and clinical applications across all of acute care medicine. Advanced timeseries analysis techniques are successfully brought to bear on clinical problems in neurocritical care in the original contributions of Kvandal et al. [1], Park et al. [2], and Soehle et al. [3], using input data available in standard clinical settings. Scheff et al. [4] review applications of similar methodologies in the context of clinical endotoxemia. In another contribution applying timeseries analysis, Dorantes Mendez et al. [5] study the effects of propofol anesthesia induction on baroreflex sensitivity. In Csete and Hunt [6], a pathway towards adapting sensor technology not currently used routinely in acute care for clinical applications is outlined, while Hoog Antink et al. [7] describe and evaluate an algorithm that may help to improve the utility of existing imaging technology in acute care. Advanced applications of electronic medical records in the acute care setting are reviewed by Herasevich et al. [8]. Data driven modeling approaches are well-represented by Guiza et al. [9], in a review of predictive data mining approaches to intensive care data, and the original contribution by Engoren et al. [10], which applies different data driven modeling approaches in predicting perioperative readmission rates and compares their performance. Mechanistic mathematical modeling is applied to physiological processes highly relevant to critical illness by Bagci et al. [11] in an in depth theoretical investigation of possible determinants of interindividual variability in response to proand antiapoptotic interventions. Podziemski and _ Zebrowski [12] present a reduced model of the right atrium with possible applications to further understanding arrhythmias. Finally, the editor would like to thank the numerous anonymous reviewers, without whose dedication and expertise this special issue would not have been possible. S. Zenker (&) Applied Mathematical Physiology (AMP) Laboratory, Department of Anesthesiology and Intensive Care Medicine, Universitatsklinikum Bonn, University of Bonn, Bonn, Germany e-mail: Sven.Zenker@ukb.uni-bonn.de