Nervous Methodology

Overview

Abstract

The BioGears Nervous System is a preliminary system representing the central nervous system (CNS) and peripheral nervous system (PNS). Currently, the system includes baroreceptor and chemoreceptor feedback models that are used to regulate arterial pressure and blood-gas levels. Additionally, the Nervous System provides for tracking of parameters related to traumatic brain injury events, pain stimulus response, and drug effects. In the future, other feedback mechanisms will be added for improved modeling of homeostatic and crisis states.

Introduction

The Nervous System in the human body is comprised of the central nervous system (CNS) and the the peripheral nervous system (PNS). The CNS contains the brain and the spinal cord, while the PNS is subdivided into the somatic, autonomic, and enteric nervous systems. The somatic system controls voluntary movement. The autonomic nervous system is further subdivided into the parasympathetic and sympathetic nervous system. The sympathetic nervous system is activated in times of stress and crisis, commonly referred to as the "flight or fight" behaviors. The parasympathetic nervous system controls homeostasis functions during the relaxed state. The enteric nervous system controls the gastrointestinal system. Many of these behaviors are tightly connected to the Endocrine System. In many cases, the Nervous System receptors trigger hormone releases that cause systemic changes, such as dilation and constriction of vessels, heart contractility changes, and respiration changes [121].

BioGears will focus on a select few mechanisms within the Nervous System to provide feedback for both homeostasis and crisis behavior in the body. The list is shown below:

  • Baroreceptors
  • Chemoreceptors
  • Local autoregulation
  • Temperature Effects
  • Generic parasympathetic and sympathetic effects
  • Pain stimulus

Additionally, BioGears will model the following features related to brain function:

  • Simple model of traumatic brain injury (TBI)
  • Intracranial pressure
  • Pupillary response to drugs and TBI

System Design

Background and Scope

The BioGears Nervous System began as a low-fidelity model that tracked metrics associated with brain injury. Over time, feedback models local to other BioGears systems (i.e. baroreceptors, chemoreceptors) were relocated to the Nervous System with the goal of moving towards a centralized Nervous model that serves as a global controller. The primary difficulty with such a model is that most detailed Nervous models rely on differential equations that output nerve firing rates. If the frequencies of these firing rates are too high compared to the time-step used to model the equations, the solution will be unstable. Fortunately, as BioGears stability has been improved, the simulation time-step has been decreased to its current value of 0.02 s. This step size allowed us to recently implement a new chemoreceptor model that generates firing rates on a scale of 10 Hz. Future work will seek to implement a similar update to the Baroreceptor model and to create more synergy between the existing models.

Data Flow

An overview of the data flow in the BioGears Nervous system is shown in Figure 1.

Initialization and Stabilization

The BioGears initialization and stabilization is described in detail in the stabilization section of the System Methodology report. The mean arterial pressure set-point is updated after the Cardiovascular system reaches a homeostatic state.

Preprocess

Baroreceptor Feedback

The baroreceptor mechanism provides rapid negative feedback control of arterial pressure. A drop in arterial pressure is sensed by the baroreceptors and leads to an increase in heart rate, heart elastance, and vessel distensibility. These changes operate with the goal of maintaining arterial pressure at its healthy resting level. The baroreceptor mechanism may be divided into three parts: afferent, CNS, and efferent. The afferent part contains the receptors, which detect changes in the MAP. After that, the CNS portions the response into either sympathetic or parasympathetic. Lastly, the efferent part is used to provide feedback to the vasculature and organs within the Cardiovascular System [223]. The model chosen for BioGears only models the CNS and efferent portion of the baroreceptors. The fidelity of the model does require the modeling of the actual stretch receptors in the aorta or carotid arteries to provide the necessary feedback.

Chemoreceptor Feedback

The chemoreceptor mechanism provides feedback control to regulate the partial pressures of oxygen and carbon dioxide in the blood. The response is divided in to two components: peripheral and central. Peripheral chemoreceptors (which reside in the aortic arch and carotid arteries) are sensitive to deviations in both oxygen and carbon dioxide pressures. The central chemoreptors, so named because of their location in the central nervous system, respond only the carbon dioxide pressure changes. Assuming that each receptor class operates independently, the feedback from the central and peripheral chemoreceptors is summed to generate a respiratory and a cardiovascular response. The respiratory response sets the patient ventilation (which effects both the tidal volume and respiration rate) to restore blood gas levels to their set points. Likewise, a cardiovascular response is initiated by altering the patient heart rate.

Check Pain Stimulus

Pain can be initiated in BioGears via a Pain Stimulus action. The BioGears pain response takes into account both the magnitude of the pain action and the susceptibility of the virtual patient to pain (set in the Patient definition file). The result is an output corresponding to the pain Visual Analog Scale (VAS) on a 0-10 interval. The VAS score dictates the patient cardiovascular and respiratory response to the pain stimulus. Increased epinephrine production is also stimulated.

Process

Check Nervous Status

Events associated with nervous system functionality are evaluated. First, intracranial pressure is checked to determine whether or not to throw the Intracranial Hypertension or Intracranial Hypotension events. Then, the presence of fasciculation (muscle spasms) is evaluated based on the activity of the compounds Sarin and Succinylcholine. The latter drug generally produces transient fasciculation which disappear when neuromuscular block is achieved [8]. For a description of the neurological effects of Sarin, see the Nerve Agent: Sarin section in the Drugs documentation. It should be noted that fasciculation can also be caused by an ion imbalance; however, this functionality is not yet active. When completed, the criteria for this type of event will be calcium deficiency. If the patient's arterial calcium concentration falls below one milligram per deciliter, then fasciculation will be triggered [116].

SetPupilEffects

Pupil modifiers are retrieved from the Drugs System and combined with any modifiers from TBI before being applied to the eyes.

Post Process

There is no system specific functionality for the Nervous System in Post Process.

Assessments

Assessments in BioGears are data collected and packaged to resemble a report or analysis that might be ordered by a physician. No BioGears assessments are associated with the Nervous System.


Figure 1. The data flow for the Nervous System consists of Preprocess, Process and Postprocess. In Preprocess, the baroreceptor feedback is calculated. In Process, the brain metrics are checked to see if event thresholds have been reached and pupil effects are determined and applied.


Features, Capabilities, and Dependencies

Baroreceptors

The baroreceptor model implemented in BioGears is adapted from the models described by Ottesen et al [223]. The model is used to drive the current MAP towards the resting set-point of the patient. This is accomplished by calculating the sympathetic and parasympathetic response. The fraction of the baroreceptor response that corresponds to the sympathetic effects is determined from Equation 1. The parsympathetic fraction is shown in Equation 2.

\[ \eta_{s} (P_{a}) = \left[ 1+ \left( \frac{P_{a}}{P_{a,setpoint}} \right)^{ \nu} \right]^{-1} \]

Equation 1.


\[ \eta_{p} (P_{a}) = \left[ 1+ \left( \frac{P_{a}}{P_{a,setpoint}} \right)^{- \nu} \right]^{-1} \]

Equation 2.


Where ν is a parameter that represents the response slope of the baroreceptors, pa is the current MAP, and pa,setpoint is the MAP set-point. An example of the sympathetic and parasympathetic responses as a function of MAP are shown in Figure 1. These were calculated with an assumed MAP set-point of 87 mmHg.

Figure 2. The sympathetic and parasympatheric response fractions are displayed as a function of mean arterial pressure (MAP). Both fractional forms show asymptotic behavior as divergence from the MAP set-point occurs. The response fractions are additive, always summing to a value of 1.0. At homeostasis (MAP equal to the set-point), the fractions are both equal to 0.5.


As described in the cardiovascular methodology report, the BioGears cardiovascular system is initialized according to patient definitions and the stabilized to a homeostatic state. The set-point is the resultant mean arterial pressure following the engine stabilization period. The set-point is adjusted dynamically with certain actions and insults, as shown in Equation 3.

\[ P^{n+1}_{a,setpoint} = P^{n}_{a,setpoint} + \Delta P_{a,drugs} + \Delta P_{a,exercise} \]

Equation 3.


Where Δpa,drugs and Δpa,exercise are changes in MAP due to drugs and exercise, respectively.

The sympathetic and parasympathetic fractional responses are used to determine the response of the following cardiovascular parameters:

  • heart rate
  • heart elastance
  • systemic vascular resistance
  • systemic vascular compliance

This is accomplished by tracking the time-dependent values of each parameter relative to their value at the MAP set-point. The time-dependent behavior of these parameters is presented via a set of ordinary differential equations, as shown in Equations 4-7.

\[ \frac{dx_{HR}}{dt} = \left(- \frac{1}{ \tau_{HR}} \right) \left( -x_{HR} + \alpha_{HR} \eta_{s}(P_{a}) + \beta_{HR} \eta_{p}(P_{a}) + \gamma_{HR} \right) \]

Equation 4.


\[ \frac{dx_{E}}{dt} = \left(- \frac{1}{ \tau_{E}} \right) \left( -x_{E} + \alpha_{E} \eta_{s}(P_{a}) + \gamma_{E} \right) \]

Equation 5.


\[ \frac{dx_{R}}{dt} = \left(- \frac{1}{ \tau_{R}} \right) \left( -x_{R} + \alpha_{R} \eta_{s}(P_{a}) + \gamma_{R} \right) \]

Equation 6.


\[ \frac{dx_{C}}{dt} = \left(- \frac{1}{ \tau_{C}} \right) \left( -x_{C} + \alpha_{C} \eta_{p}(P_{a}) + \gamma_{C} \right) \]

Equation 7.


Where xHR, xE, xR and xC are the relative values of heart rate, heart elastance, vascular resistance and vascular compliance, respectively. τHR, τE, τR and τC are the time constants for heart rate, heart elastance, vascular resistance and vascular compliance, respectively. The remaining α, β and γ parameters are a set of tuning variables used to achieve the correct responses in the Cardiovascular System during arterial pressure shifts. Note that the heart rate feedback is a function of both the sympathetic response and parasympathetic response, whereas the elastance feedback and vascular tone feedback depend on the sympathetic or parasympathetic responses individually. Figure 3 shows the normalized response curves.

Figure 3. The plot array demonstrates the normalized organ responses to sympathetic or parasympathetic activity, plotted against the normalized mean arterial pressure.

Chemoreceptors

The chemoreceptors are cells that are sensitive to changes in blood gas concentration. Peripheral chemosensitive cells–located in the aortic arch–detect fluctuations in both arterial carbon dioxide and oxygen partial pressures. The central chemoreceptors, which reside in the central nervous system (CNS), respond to changes in cerebral blood pH caused by irregular carbon dioxide levels. It is assumed in this model that carbon dioxide transport across the blood-brain barrier and equilibration therein are rapid processes; that is, it assumed that the central chemoreceptor response is proportional to deviations in arterial carbon dioxide. As sympathetic activators, the chemoreceptors also increase the heart rate and contractility.

Respiratory Control

Control of respiration is based on the model developed by Albanese, Magosso, and Ursino in [ursino2001acute], [magosso2001mathematical], and [ursino2002theoretical]. It is assumed that the central and peripheral feedback define deviations from baseline patient ventilation (set in BioGears during system stabilization) and that their contributions are independent (and thus additive).

\[\dot{V_{target}} = \dot{V_{base}} + \delta\dot{V_{c}} + \delta\dot{V_{p}} \]

Equation 8.


Clearly, the blood gas levels are normal, central (

{Vc}) and peripheral ({Vp}) changes in ventilation are 0, and target ventilation ( {Vtarget}) equals patient baseline ventilation ({Vbase}).