Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen

Abstract

The inflammatory response aims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen. In cases of acute systemic inflammation, the possibility of collateral tissue damage arises, which leads to a necessary down-regulation of the response. A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. That system contains multiple positive and negative feedback loops and is a highly coupled and nonlinear ODE. The implementation of nonlinear model predictive control (NMPC) as a methodology for determining proper therapeutic intervention for in silico patients displaying complex inflammatory states was initially explored in [5]. Since direct measurements of the bacterial population and the magnitude of tissue damage/dysfunction are not readily available or biologically feasible, the need for robust state estimation was evident. In this present work, we present results on the nonlinear reachability of the underlying model, and then focus our attention on improving the predictability of the underlying model by coupling the NMPC with a particle filter. The results, though comparable to the initial exploratory study, show that robust state estimation of this highly nonlinear model can provide an alternative to prior updating strategies used when only partial access to the unmeasurable states of the system are available.

Inflammation and disease: Modelling and modulation of the inflammatory response to alleviate critical illness

“…The model-based control methodology of Model Predictive Control (MPC) was used to determine appropriate therapeutic inputs to correct dysfunctional immune responses in an in silico clinical trial of sepsis using heterogeneous virtual patients defined from an ODE model [22, 24], and in simulations with an ODE model of endotoxemia in rats [23]. In addition to control-theory based analysis, increased computational capabilities offered by advances in high performance computing (HPC) have now made feasible the application of simulation-based optimization and control discovery.…”

“…In this way, the framework seeks to realize an optimized reprograming of dynamic inflammation networks in vivo . The MPC methodology utilized in [22–24] provides the model-based control architecture that can more robustly tune and implement the immunomodulatory device on a patient-to-patient basis. Additionally, the framework allows for a closer integration of the modelling work with the data, promoting the necessary iterative process described above and providing an enhanced understanding of the acute inflammatory response in Gram-negative sepsis.…”

Immune therapeutic strategies using optimal controls with L 1 and L 2 type objectives

“…In particular, applying automatic control for biomedical therapeutic intervention has recently gained interest in such areas as glucose control for diabetes or in critically ill patients and for anesthesia depth control, as seen for example, in [5], [6], [7], [8], and the references therein. The use of optimal control theory for biomedical applications can be seen in [9], [10], and [11] for example; and, more recently, the use of model predictive control (MPC) in [12] and [13] which used the same mathematical model as used herein. MPC was also used in [14] and [15] for diabetes treatment strategies and [16] for an application to a multi-compartment respiratory system.…”

“…As in our prior work ( [17], [18], [12], [13]), we utilize a phenomenological ordinary differential equations model of the system inflammatory response to pathogenic infection developed in [19] (see also [20]). This model provides a dynamical system with rich behavior that is ideal for testing various theoretical control strategies.…”

“…The necessary inclusion here of N and Ca in the objective function differs from that used in our previous studies using MPC([12],[13]). …”