lumped-parameter modeling of the cardiovascular system

IntroductionLumped-parameter modeling

ResultsConclusions

Lumped-parameter modeling of thecardiovascular system

Stefania Scarsoglio1

Andrea Guala2 Carlo Camporeale2 Luca Ridolfi2

1DIMEAS, Politecnico di Torino, Italy2DIATI, Politecnico di Torino, Italy

San Giovanni Battista Hospital18 February 2015, Torino

S. Scarsoglio Lumped-parameter modeling of atrial fibrillation


ResultsConclusions

Present work

Motivation and Goal

Understand and quantify, through a stochastic modeling approach,the impact of paroxysmal AF on the cardiovascular system ofa healthy young adult (structural remodeling effects neglected);

AF can be analyzed without other pathologies ⇒ highlight sin-gle cause-effect relations, trying to address the cardiovascularfeedbacks which are currently poorly understood;The main cardiac parameters can all be obtained at the same time(clinical studies usually focus only on a few of them at a time) ⇒overall good agreement with the current clinical measures;Accurate statistical analysis of the cardiovascular dynamics, whichis not easily accomplished by in vivo measurements.



ResultsConclusions

Present work

Motivation and Goal

Understand and quantify, through a stochastic modeling approach,the impact of paroxysmal AF on the cardiovascular system ofa healthy young adult (structural remodeling effects neglected);AF can be analyzed without other pathologies ⇒ highlight sin-gle cause-effect relations, trying to address the cardiovascularfeedbacks which are currently poorly understood;

The main cardiac parameters can all be obtained at the same time(clinical studies usually focus only on a few of them at a time) ⇒overall good agreement with the current clinical measures;Accurate statistical analysis of the cardiovascular dynamics, whichis not easily accomplished by in vivo measurements.



ResultsConclusions

Present work

Motivation and Goal

Understand and quantify, through a stochastic modeling approach,the impact of paroxysmal AF on the cardiovascular system ofa healthy young adult (structural remodeling effects neglected);AF can be analyzed without other pathologies ⇒ highlight sin-gle cause-effect relations, trying to address the cardiovascularfeedbacks which are currently poorly understood;The main cardiac parameters can all be obtained at the same time(clinical studies usually focus only on a few of them at a time) ⇒overall good agreement with the current clinical measures;

Accurate statistical analysis of the cardiovascular dynamics, whichis not easily accomplished by in vivo measurements.



ResultsConclusions

Present work

Motivation and Goal

Understand and quantify, through a stochastic modeling approach,the impact of paroxysmal AF on the cardiovascular system ofa healthy young adult (structural remodeling effects neglected);AF can be analyzed without other pathologies ⇒ highlight sin-gle cause-effect relations, trying to address the cardiovascularfeedbacks which are currently poorly understood;The main cardiac parameters can all be obtained at the same time(clinical studies usually focus only on a few of them at a time) ⇒overall good agreement with the current clinical measures;Accurate statistical analysis of the cardiovascular dynamics, whichis not easily accomplished by in vivo measurements.



ResultsConclusions

Mathematical frameworkCardiac cycle simulation

Cardiovascular scheme

P: pressure

V: volume

Q: flow rate

C: compliance

E: elastance

L: inductance

R: resistanceSystemic Circuit

P_svn

V_ra

V_rv

P_ra V_laP_la

P_lv V_lv

Q_aoQ_po

Q_miQ_ti

Systemic

Aortic

Sinus

P_sas

Systemic

Artery

P_rv

Q_svn

Systemic

Arteriole

Systemic

Capillary

Pulmonary Circuit

Systemic

Vein

P_pas

Q_pas

P_pat

Q_pat

P_pvn

Pulmonary

Arterial Sinus

Pulmonary

Artery

Pulmonary

Arteriole

Pulmonary

Capillary

Pulmonary

Vein

Q_pvn

C_pas

R_pas L_pas

C_pat

R_pat L_pat R_par R_pcp R_pvn

C_pvn

E_laE_ra

C_sas R_sas

L_sas

Q_sas P_sat

C_sat

L_sat

R_sat

Q_satR_sarR_scp

C_svn

R_svn

CQ_ti CQ_mi

E_lv

CQ_ao

E_rv

CQ_po

Right Heart Left Heart



ResultsConclusions


Reconstructed physiologic and fibrillated beating

Normal Sinus Rhythm (NSR)RR extracted from a correlated pink Gaussian distribution;Time varying (right and left) atrial elastance;

Atrial Fibrillation (AF)RR extracted from an exponentially modified Gaussian distribution;Constant (right and left) atrial elastance ⇒ No atrial kick;

0 0.6 1.2 1.80

2

4

6

8

RR[s]

p(R

R)

NSR

AF

0 1000 2000 30000

0.5

1

1.5

2

RR

[s]

t [s]

AFNSR



ResultsConclusions


Real RR series (MIT Database)

0 0.5 1 1.5 20

1

2

3

4

5

6

RR

p(R

R)

NSR 16773NSR 18177AF 71AF 202

(a)

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

τ [min]

R

NSR 16773NSR 18177AF 71AF 202

(b)

µ [s] σ [s] cv Sex AgeNSR 16773 1.03 0.13 0.12 M 26NSR 18177 0.78 0.08 0.10 F 26

AF 71 0.76 0.15 0.19 / /AF 202 0.65 0.17 0.27 / /



ResultsConclusions

Hemodynamic parametersSystemic arterial pressureLeft heartReal series analysis

Left ventricle

40 80 1200

40

80

120

Vlv

[ml]

Plv

[mm

Hg]

40 80 1200

40

80

120

Vlv

[ml]

Plv

[mm

Hg]

0 5.000

4

8

Cardiac Cycles

CO

[l/m

in]

0 5.00020

40

60

EF

[%]

Cardiac Cycles

NSR AFCO [l/min] 4.80 4.38

SV [ml] 63.84 47.21EF [%] 53.27 37.12SW [J] 0.87 0.57



ResultsConclusions


Arterial pressure: time series and statistics

589 590 591 592 59340

60

80

100

120

t[s]

Psa

s [mm

Hg]

(a)

40 60 80 100 1200

0.15

0.3

Psas

p(P

sas)

NSR systAF systNSR diasAF dias

(b)

Psas [mmHg] Mean Systolic Diastolic PulsatileNSR 99.52 116.22 83.24 32.99AF 89.12 103.66 77.24 26.42

Scarsoglio, Guala, Camporeale, Ridolfi, Med. Biol. Eng. Comput., 2014.



ResultsConclusions


Atrial pressure and volume

589 590 591 592 593

8

10

12

t[s]

Pla

[mm

Hg]

(a)

atrial kickrapidgrow

plateau

589 590 591 592 593

40

60

80

t[s]

Vla

[ml]

(b) plateau

rapid growatrial kick

Vla [ml] Mean End-Systolic End-DiastolicNSR 56.53 64.41 55.37AF 65.95 71.41 68.84



ResultsConclusions


Mitral and aortic flow rates

589 590 591 592 593

0

500

1000

t[s]

Qm

i [ml/s

]

(a) atrialkick

589 590 591 592 593

0

500

1000

1500

t[s]

Qao

[ml/s

]

47% reduction(b)

NSR AFMitral RF [%] 13.59 9.94Aortic RF [%] 7.62 10.91

Different backflow valve openings during AF: Mi ↓, Ao ↑;Peak E wave velocity does not correlate with RF.

Scarsoglio, Camporeale, Guala, Ridolfi, in preparation, 2015.S. Scarsoglio Lumped-parameter modeling of atrial fibrillation


ResultsConclusions


Oxygen Consumption

0.6

0.8

1

1.2

1.4

x 104

2200

2400

2600

2800

3000

3200

60

70

80

90

100

110

120

70

72

74

76

78RPP [mmHg/min]

PVA/min[J/min]

TTI/min[mmHgs/min]

LVE[%]

Bigger expense for the oxygen consumption (RPP, TTI/min, PVA/min)and decreased left ventricular efficiency (LVE) during AF;The major effects of AF are due to HR acceleration, being rhythmchanges less impacting.

Scarsoglio, Med. Eng. & Phys., under review 2015.



ResultsConclusions

Conclusions

Discussion and Conclusive Remarks

Analysis of the role of acute AF on the whole cardiovascularsystem through a stochastic modeling:

Anatomical remodeling due to long-term effects and short-term reg-ulation effects of the baroreceptor mechanism are absent;

Isolate single cause-effect relations, a thing which is not possi-ble in real medical monitoring;Present results should be interpreted as pure consequences ofAF alone and not induced by other pathologies;Accurate statistical description of the cardiovascular dynamics,a task which is rarely accomplished by in vivo measurements;New information on hemodynamic parameters (e.g., flow rates,right ventricle dynamics), difficult to measure and almost nevertreated in literature.



ResultsConclusions

Conclusions




Isolate single cause-effect relations, a thing which is not possi-ble in real medical monitoring;

Present results should be interpreted as pure consequences ofAF alone and not induced by other pathologies;Accurate statistical description of the cardiovascular dynamics,a task which is rarely accomplished by in vivo measurements;New information on hemodynamic parameters (e.g., flow rates,right ventricle dynamics), difficult to measure and almost nevertreated in literature.



ResultsConclusions

Conclusions




Isolate single cause-effect relations, a thing which is not possi-ble in real medical monitoring;Present results should be interpreted as pure consequences ofAF alone and not induced by other pathologies;

Accurate statistical description of the cardiovascular dynamics,a task which is rarely accomplished by in vivo measurements;New information on hemodynamic parameters (e.g., flow rates,right ventricle dynamics), difficult to measure and almost nevertreated in literature.



ResultsConclusions

Conclusions




Isolate single cause-effect relations, a thing which is not possi-ble in real medical monitoring;Present results should be interpreted as pure consequences ofAF alone and not induced by other pathologies;Accurate statistical description of the cardiovascular dynamics,a task which is rarely accomplished by in vivo measurements;

New information on hemodynamic parameters (e.g., flow rates,right ventricle dynamics), difficult to measure and almost nevertreated in literature.



ResultsConclusions

Conclusions




Isolate single cause-effect relations, a thing which is not possi-ble in real medical monitoring;Present results should be interpreted as pure consequences ofAF alone and not induced by other pathologies;Accurate statistical description of the cardiovascular dynamics,a task which is rarely accomplished by in vivo measurements;New information on hemodynamic parameters (e.g., flow rates,right ventricle dynamics), difficult to measure and almost nevertreated in literature.



ResultsConclusions

Conclusions

Perspectives and future work

Future work can be addressed to study:Response to AF together with altered physical conditions (e.g.,during exertion, left atrial appendage clamping, etc);

Combined presence of other cardiovascular pathologies (e.g.,mitral insufficiency, hypertension, etc);Inclusion of the baroregulation mechanisms.



ResultsConclusions

Conclusions


Future work can be addressed to study:Response to AF together with altered physical conditions (e.g.,during exertion, left atrial appendage clamping, etc);Combined presence of other cardiovascular pathologies (e.g.,mitral insufficiency, hypertension, etc);

Inclusion of the baroregulation mechanisms.



ResultsConclusions

Conclusions


Future work can be addressed to study:Response to AF together with altered physical conditions (e.g.,during exertion, left atrial appendage clamping, etc);Combined presence of other cardiovascular pathologies (e.g.,mitral insufficiency, hypertension, etc);Inclusion of the baroregulation mechanisms.


lumped-parameter modeling of the cardiovascular system

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