A Lumped-Parameter Subject-Specific Model of Blood Volume Response to Fluid Infusion

Abstract

This paper presents a lumped-parameter model that can reproduce blood volume response to fluid infusion. The model represents the fluid shift between the intravascular and interstitial compartments as the output of a hypothetical feedback controller that regulates the ratio between the volume changes in the intravascular and interstitial fluid at a target value (called “target volume ratio”). The model is characterized by only three parameters: the target volume ratio, feedback gain (specifying the speed of fluid shift), and initial blood volume. This model can obviate the need to incorporate complex mechanisms involved in the fluid shift in reproducing blood volume response to fluid infusion. The ability of the model to reproduce real-world blood volume response to fluid infusion was evaluated by fitting it to a series of data reported in the literature. The model reproduced the data accurately with average error and root-mean-squared error (RMSE) of 0.6 and 9.5% across crystalloid and colloid fluids when normalized by the underlying responses. Further, the parameters derived for the model showed physiologically plausible behaviors. It was concluded that this simple model may accurately reproduce a variety of blood volume responses to fluid infusion throughout different physiological states by fitting three parameters to a given dataset. This offers a tool that can quantify the fluid shift in a dataset given the measured fractional blood volumes.

Control-oriented physiological modeling of hemodynamic responses to blood volume perturbation

“…In the context of critical care, the gain or loss of fluid occurs primarily in the intravascular compartment in the form of hemorrhage, UO, fluid infusion etc., but the perturbation in the intravascular fluid volume thus occurred is dynamically distributed across all 3 major compartments via the inter-compartmental fluid shift (Guyton et al, 1975). In our prior work, a control-theoretic model of BV response to fluid infusion was developed (Bighamian, Reisner, & Hahn, 2016). The basic idea was to formalize established physiological principles underlying fluid volume distribution (that fluid infused into the intravascular compartment is distributed in the intravascular and extravascular compartments to regulate the ratio between their volumetric changes (Guyton et al, 1975)) into a mathematical model by abstracting myriads of complex microscopic fluid shift mechanisms into macroscopic feedback control actions.…”

“…The above limitations naturally suggest the desire for autonomy in fluid resuscitation. In fact, published reports document that autonomous closed-loop control systems for fluid resuscitation may alleviate the caregiver workload while still maintaining the quality of care by reducing the laps and errors associated with therapy adjustments (Michard, 2013; Rinehart, Liu, Alexander, & Cannesson, 2012; Rinehart, 2014; Bighamian, Kim, Reisner, & Hahn, 2016). However, existing work on closed-loop fluid resuscitation is not abundant, if not rare, both in terms of design and evaluation.…”

Closed-Loop Control for Fluid Resuscitation: Recent Advances and Future Challenges

“…This is due to the complexities inherent in system physiology, wherein mathematical models capturing complex physiological mechanisms of action are not readily developed. Although there has been considerable progress in understanding the pharmacokinetics and pharmacodynamics of drug distribution and drug effect using compartmental models in pharmacology ( 9 ), the distribution of fluids using compartmental and volume kinetic models ( 10 – 12 ), and lumped parameter models of blood volume response to fluid infusion ( 13 ), such models are approximations to the actual patient physiology. The gap between system modeling and the actual system physiology has been the main limiting factor in the use of rigorous control design frameworks that have been widely used in, for example, the aerospace industry.…”

“…In a recent work, authors in ( 34 ) investigate a model-based controller design predicated on a lumped parameter model of blood volume response involving three parameters ( 13 ). Specifically, this closed-loop control framework involves a two-step process: a “calibration” phase involving administering an initial fluid bolus and observing the patient's response followed by using a model reference adaptive control architecture to guide fluid infusion.…”

Accuracy assessment methods for physiological model selection toward evaluation of closed-loop controlled medical devices

“…Therefore, as a case study, we examine the adequacy of lumped-parameter mathematical models of patient physiology developed for evaluating PCLC fluid resuscitation devices. We build a refined physiological model of blood volume (BV) response by expanding an original model we developed in our prior research [ 19 , 20 ]. We use the experimental data collected from sheep subjects undergoing hemorrhage and fluid resuscitation.…”