Heart rate control and variability

Transcription

1 Heart rate control and variability Na (Lina) Li (CDS13 ) SEAS Harvard University 20

2 The persistent mystery Young, fit, healthy more extreme Resting Heart Rate (bpm) Time (seconds) Noise?

3 Young, fit, healthy more extreme Heart Rate High mean, low variability Low mean, high variability Time (seconds) Workload data (Watts) One subject Three experiments +150w +100w

4 Doyle s Physiology Lab

5 Thanks to Theory/tools Jerry Cruz Simon Chien Somayeh Sojoudi Ben Recht John Doyle Equipment Philips Science Trans Med & PNAS & Anonymous reviewers Medical Marie Csete MD PhD David Stone MD Dan Bahmiller MD SCAI and ICCAI Subjects Caltech Faculty & Students Funding NIH Army Pfizer Braun family AFOSR/NSF

6 Heart Rate High mean, low variability Low mean, high variability Time (seconds)

7 Many diseases associated w/decrease V Poon et al, Decrease of cardiac chaos in congestive heart failure, Nature, Carney et al, Depression, heart rate variability, and acute myocardial infarction, Circulation, Malpas et al, Heart-rate variability and cardiac autonomic function in diabetes, Diabetes, Pontet et al, Heart rate variability as early marker of multiple organ dysfunction syndrome in septic patients, Journal of critical care, Tateishi et al, Depressed heart rate variability is associated with high IL-6 blood level and decline in the blood pressure in septic patients, Shock, Roche et al, Depressed heart rate variability is associated with high IL-6 blood level and decline in the blood pressure in septic patients, Circulation, Kleiger et al, Decreased heart rate variability and its association with increased mortality after acute myocardial infarction, Am Journal of Cardiology, Liao et al, Age, race, and sex differences in autonomic cardiac function measured by spectral analysis of heart rate variability, Am Journal of Cardiology, 1995.

8 1 fractals? chaos?

9 1 1 fractals? chaos? System Constraints and Tradeoff? Seeking mechanistic explanations

10 controls heart rate ventilation vasodilation coagulation inflammation digestion storage Homeostasis errors O2 BP ph Glucose Energy store Blood volume energy trauma external disturbances infection

11 controls heart rate ventilation Homeostasis errors O2 BP energy Minimal mechanistic model and experiment external disturbances

12 System Identification Model First Principle Model Physiology + Optimal Control Output Black-box fitting Input Optimal Control Output Input

13 Two experiments w Data: Watts W time(sec) Input= background+perturbation 0

14 Two experiments with same subject #1 data (bpm) Watts? High avg low var Low avg high var time(sec) Data: Watts and

15 Two experiments with same subject #1 data (bpm) Watts? High avg low var Low avg high var time(sec) Data: Watts and

16 static nonlinear(piecewise linear) fit data (bpm) H = aw + b For each workout, i=1,2,3 i i

17 dynamic nonlinear (piecewise linear) fit data (bpm) Two different 1 st order linear fit(s) ht = ht+ 1 ht () = aht + bwt + c ( ) ( ) ( ) ( )

18 Nonlinearity data Explain differences between these fits??? Both static (steady state) and dynamic

19 High frequency data Explain differences between the fits and the data dynamic NL (piecewise linear) fit Lower mean, higher variability (RSA)

20 Static model: vs W Slope Slope Workload w The simplest case of changing V, mean and variability

21 Standard picture slope decreases as watts increase watts

22 slope still decreases as watts increase watts

23 Nonlinearity in the data = h( w) Workload W

24 Why? = h( w) Proximal cause: Autonomic nervous system balance Between sympathetic and para-sympathetic Workload W Deeper why: evolution and physiology Accident or necessity?

25 controls heart rate ventilation Homeostasis errors O2 BP energy Minimal mechanistic model external disturbances

26 Physiological model = h( w) Workload w Physiology model Mean Arterial Blood Pressure P as ΔO 2 Oxygen drop across muscle ( BP, O ) = F( w, H ) 2

27 The simplified physiological model: CBF H Lung H P as ( BP, O ) = F( w, H ) 2 w Muscle O 2

28 Intuition = h( w) Workload w P as ΔO 2

29 = h( w) Workload w P as ΔO 2 H low w high Ideally P as low O 2 low Oxygen drop across muscle

30 Why? Necessary? = h( w) Workload w Actual P as ΔO 2

31 Why? Intuition = h( w) Workload W P as ΔO 2 At low watts and, BP not an issue, so only metabolism matters.

32 Why? = h( w) Workload W At high watts and, high BP is an issue, P as 200 At low watts and, BP not an issue, so only metabolism matters ΔO 2

33 CBF P as P as 200 Cerebral Blood Flow CBF ΔO 2 Oxygen drop across muscle

34 CBF Mean Arterial Pressure P as P as Cerebral Blood Flow CBF

35 CBF 200 P as Cerebral Perfusion Pressure P as Ideal (mm Hg) Cerebral Blood Flow (CBF) (ml/100g/min)

36 CBF 200 P as Pressure Normal Autoregulation Flow

37 200 P as Actuator saturation Normal Autoreg CBF

38 = h( w) Safer Workload w P as ΔO 2 Oxygen drop across muscle

39 = h( w) Safer Workload W P as ΔO 2 Safer Safer worse ΔO 2 metabolic cost

40 Control H V V E F = ( P P )/ R = cp ap ap ap [ O ] = a ap vp p V = cp vp vp vp Blood flow 200 = h( w) 150 R A [ O ] + R s = Q = F = c H P r V 2 v s0 vs = cp V = cp vs vs vs as as as W H F = ( P P )/ R as vs s F( O ) = ρw + M 2 0 BP, O2 = F w, ( ) ( ) static optimization problem min hw ( ) Q = F = c H P l vp O = [ O ] [ O ] 2 2 a 2 v {( ( ) 2 ( ) 2 ( ) 2 p BP + q O2 + r ) = h( w) BP, O2 = F w, ( ) ( )} Watts

41 200 = h( w) At low watts and, high BP is not an issue, so only metabolism matters BP min hw ( ) p,r: very small O2t Watts { 2 2 ( p(bp) 2 + q ( O2) + r ( ) )}

42 Architecture Low watts and fragile Low W& robust Ideally efficient wasteful

43 Not sustainable 200 High BP > matters, as does > = h( w) 200 BP min hw ( ) p,r: very small O2t Watts { 2 2 ( p(bp) 2 + q ( O2) + r ( ) )}

44 So penalizing BP and more here = h( w) min hw ( ) 200 BP { ( pˆ( BP) + q ( O2) + rˆ( ) )} pˆ > p rˆ> r Watts min hw ( ) { 2 2 ( p(bp) 2 + q ( O2) + r ( ) )} p,r: very small O2t

45 Laws & Architecture fragile Low W& Good architectures allow for effective tradeoffs robust Ideally efficient High W& wasteful

46 This idea can be used directly with a dynamic model data (bpm) = h( w) Workload W

47 Organized complexity, circa 1972 Plumbing and chemistry Guyton

48 This idea can be used directly with a dynamic model Thousands of States??? CBF 11 States 9 States H Lung P as 5 States H 4 States Muscle O 2 2 States w

49 Dynamic optimal control min hw ( ) { ( p( BP) + q( O2t ) + rˆ ( ) )} p > 0 rˆ > r q P P q O O q H H dt ( ) 2 ( ) 2 ( ) 2 2 * 2 * 2 * min P as as + o H H= u() 2 min { 2 2 ( ( 2) + ( ) )} hw ( ) q O r

50 P as (mmhg) [O 2 ] T (ml O 2 / 1 L blood) model Penalize BP and more 0 Workload (watts) data Time (seconds) q P P q O O q H H dt ( ) 2 ( ) 2 ( ) 2 2 * 2 * 2 * min P as as + o H H= u() 2

51 So far fragile Low W& Good architectures allow for effective tradeoffs robust Ideally efficient High W& wasteful

52 P as (mmhg) [O 2 ] T (ml O 2 / 1 L blood) model Explain differences between models & data? Workload (watts) data Time (seconds)

53 controls heart rate ventilation vasodilation coagulation inflammation digestion storage Homeostasis errors O2 BP ph Glucose Energy store Blood volume energy trauma external disturbances infection

54 controls heart rate ventilation vasodilation coagulation inflammation digestion storage Homeostasis errors O2 BP ph Glucose Energy store Blood volume energy trauma external disturbances infection breath heart beat sensor internal noise

55 controls heart rate ventilation Homeostasis errors O2 BP breath internal noise

56 60 raw data breath velocity at mouth Respiratory Sinus Arrhythmia (RSA)

57 Second order piecewise linear dynamic model fitting Heart Rate Data 50 w Fit@ 0 W Ventilation flow rate 50 W Ventilation flow rate 0 W Time (seconds)

58 controls heart rate ventilation Homeostasis errors BP Need mechanical coupling Speculation breath internal noise

59 CBF 200 P as Cerebral Perfusion Pressure P as Normal Autoregulation 50 Max dilation Cerebral Blood Flow (CBF)

60 Universals + low variability outputs + large disturbances high variability controls Independent of variability measure Universal in biology and technology Most important nonlinearity is actuator saturation

61 high variability Health low variability Controls CBF output CBF medium pump H Lung H SaO 2 high P as medium Muscle O 2 low Disturbance: w w

62 1 st order linear model dynamic linear (global) fit data dynamic NL (local linear) fit ( ) ( 1 ) () ( ) ( ) ht = ht+ ht = aht + bwt + c

63 1 st order linear model Best fit, but misleading? data dynamic NL (local linear) fit ( ) ( 1 ) () ( ) ( ) ht = ht+ ht = aht + bwt + c

64 Model Watts VO 2 (L/min) V E VCO (L/min) -VO 2 2 (L/min)

65 First principles aerobic model (L/min) 2 0 VO V E (L/min) Time (minutes)

66 VCO VO nd order nonlinear fit aerobic model Aerobic models can be way off at high watts Can still fit with simple black box models, but Need nonlinear dynamics Mechanistic models? (Redox ) Need anaerobic mechanisms Control of arterial ph is critical (and hard to model)

67 Summary data (bpm) Watts 100 CBF V E H Lung H CBF SaO 2 0 R s Muscle P as W O 2 fragile Low W& + robust efficient High W& wasteful

68 Summary data (bpm) Watts 100 CBF V E H Lung H CBF SaO 2 0 R s Muscle P as W O 2 fragile Low W& + robust efficient High W& wasteful