A Computational model for Sympathetically Mediated ...

A Computational model for Sympathetically Mediated Stress Estimation Midhun P Unni*, Srinivasan Jayaraman, Balamuralidhar P

TCS Innovations lab , Bangalore, India ABSTRACT AND INTRODUCTION Abstract—Detecting sympathetic activity can be thought of as a first step towards stress estimation, as stress sympathetically mediates blood pressure (BP) and heart rate. Clinical observations also suggest a relationship between myocardial infarction and increased sympathetic activity in mornings. In this study, we built a computational model combining modules of BP regulation, sympathetic activation and fluid structure interactions of the arterial dynamics to generate synthetic PPG data. This PPG data was then used to train a neural network to build an inference engine which was used to estimate the parameter ‘𝑭𝑺𝑵’ of the model. The inference engine was then tested on the real PPG data that was collected during morning and evening. We observed a higher 𝑭𝑺𝑵 value in the morning compared to evening. This result is in accordance with the experimental observation that sympathetic activity is higher in the mornings thus validating the model. Introduction: A “ stressor” activates the physiologic response which is mediated through sympatho-medullary axis. This in turn regulates the blood pressure by influencing heart rate and vasoconstriction [1,2]. Current stress estimation methodologies which make use of the PPG or ECG (Electrocardiogram) signals do not account for renin angiotensin system, vasoconstriction and sympathetic nervous system “explicitly” [3]. This study takes these factors into consideration by building a modified computational model of [2]. The model is tested for the clinical observation of heightened sympathetic activity in the mornings [4]. Stressor

ARTERIAL SYSTEM MODEL 𝜕𝐴 𝜕 𝐴𝑈 + 𝜕𝑡 𝜕𝑥 𝜕𝑈 𝜕𝑈 +𝑈 𝜕𝑡 𝜕𝑥

=0

(7)

1 𝜕𝑃 𝜌 𝜕𝑥

+

=

𝑓 𝜌𝐴

(8)

Where 𝑃=

𝛽 𝑃𝑒𝑥𝑡 + 𝐴0

𝛽 𝑥 =

𝛤 𝑥 =

4 3

𝐴−

𝜕𝐴 𝐴0 + 𝛤 𝜕𝑡

𝜋𝐸ℎ

(9) (10)

𝛾

(11)

2 𝜋𝐴0

The 𝑃𝑒𝑥𝑡 = 0 𝑎𝑠 𝑛𝑜 𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑖𝑠 𝑎𝑝𝑝𝑙𝑖𝑒𝑑, Where 𝐴∈ℜ

𝜕𝐴 0 𝜕𝑥

=

𝑈 ∈ ℜ 𝑈(0) =

𝜕𝐴 𝐿 0, =0 𝜕𝑥 𝜕𝑈 𝐿 𝑈(𝑡), = 𝜕𝑥

(12) 0

(13)

Building the inference engine: Sampling of simulation parameters from a uniform distribution in the physiological range 20 real and imaginary frequency components were used for training a neural network Model

Features

Learn the mapping

Figure. 3 Diagram showing the information flow in the algorithm

Model testing: PPG data was collected for 5 mins from 13 subjects at morning (Before 11 AM) and evening (After 3PM) and parameter 𝐹𝑆𝑁 was estimated using the above described inference engine.

RESULTS AND DISCUSSION

Neural control

BP Control

Sympathetically mediated effects

HPA

Figure 1: The stress is known to act in two different ways resulting in sympathetically mediated activities [1]. This increase in sympathetically mediated activities control the BP regulation mechanism [1].

METHODS Computational model: Modified model of Beard et al(2013)[1] Sympathetic control of the BP regulation model (ODEs) Partial differential equations governing the arterial dynamics Arterial dynamics

BP regulation model involving 𝐅𝐒𝐍

Synthetic PPG signal

Building the inference engine Figure 2. A system of ODEs governing the blood pressure regulation and two PDEs governing the arterial dynamics is used to model the signal. The Modelled signal and input parameter FSN is used to build an inference engine and the inference engine is used to estimate FSN from the measured signal. STRESS GOVERNING DYNAMICS: dϵ τs dt ds = dt

= ε−ε a 1−s −

fBR t = f0 s(t) dϕSN dt

(1) δϵ bs δϵ +δ0

δϵ δϵ +δ0

= (SI + fSN ) 1 − ϕSN − fBR ϕSN

SI + fSN ≝ FSN Thus dϕSN dt

= FSN 1 − ϕSN − fBR ϕSN

(2) (3) (4) (5) (6)

Figure. 4 Mean and standard deviation of estimated 𝐹𝑆𝑁 for mornings and evenings.

The results showed that the estimated 𝐹𝑆𝑁 is significantly higher (p