Saragozza 2003 A Study On Lv Regional Dyssynchrony Based On Ventricular Time Varying Elastance Computer Model

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

INTERNATIONAL CONGRESS ON COMPUTATIONAL BIOENGINEERING 24th-26th September 2003, Zaragoza, SPAIN

A STUDY ON LV REGIONAL DISSYNCHRONY BASED ON VENTRICULAR DIFFERENTIAL TIME VARYING ELASTANCE COMPUTER MODEL Maurizio Arabia M.M.A. Consulting

Francesco Maria Colacino & Domenico Lavorato University of Calabria, Mechanical Engineering Department

Fabio Piedimonte University of Rome “Tor Vergata”, D.I.S.P.

Antonino G.M. Marullo University of L’Aquila, Medicina Sperimentale Department Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Introduction • Investigation and analysis of: – Regional dissynchrony (source of contraction delay between different regions of the ventricle) – Regional reduced contractility (due to a worsening of ventricle’s elastance curves) • A computer model of the left ventricle (LV), which is divided in two regions, has been developed to allow different working conditions.

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Ventricle Model Description • LV is represented by a differential time varying elastance (DTVE) model, including internal resistance (R)

dV t  P(t )  P0   V (t ), t   R dt  V (t ), t    p V (t )   a V (t )   p V (t ) * Fiso  





a t = t3

P (mmHg)

t = t2 ; t = t4

t = t1 ; t = t5

p t6 < t < T V (cm^3) Undivided physiological LV's PV loop

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

P(t )  P0

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Mathematical Relationships dV t    V (t ), t   R dt

 V (t ), t    p V (t )   a V (t )   p V (t )* Fiso  

a  p  Emin V t   V0  

K K  Vsat  V t   V0  Vsat

2   *    V  V t     P*  a  1   *   V  V0    

t = t3

P (mmHg)

t = t2 t = t4

t = t1 t = t5

p t6 < t < T V (cm^3) Undivided physiological LV's PV loop

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Active Atrium Model Description Similar relations, but: • no internal resistance R; • lower vertex (lower P* value) for the active elastance curve; • Fiso contraction duration much shorter than LV’s and stops when ventricular contraction phase starts.

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Circulatory system model description Rvs

Lvs

Patrium

Paorta

Cvs

Pvs

Cas

Ras

Guyton and Windkessel models Pi = Patm

Pi = Patm Rvd Lv

Rvi

Valve model

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Divided Ventricle: Model Description • • • •

The divided LV has been represented by two DTVE models. Its total ventricular contractility split up. Pressure is always equal in each portion. The total volume V(t) has been divided in two portions V1(t) and V2(t) by the coefficient: pf = V1(t)/V(t)

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

mmHg

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

(V2*,P*)

(V1*,P*)

Vsat Vsat

cm^3

(V*,P*)

Vsat

Tot Portion 1

Portion 2

V(t)

pfV(t)

(1-pf)V(t)

Vsat

pfVsat

(1-pf)Vsat

V0

p f V0

(1-pf)V0

V*

p f V*

(1-pf)V*

R

R/pf

R/(1-pf)

Emin

Emin/pf

Emin/(1p f)

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Mathematical Description dV t  P(t )  P0   V (t ), t   R dt dV1 t  P(t )  P   V (t ), t   R 0

1

1

1

dt dV t  P(t )  P0   2 V2 (t ), t   R2 2 dt

 V (t ), t    p V (t )   a V (t )   p V (t )* Fiso  

 V (t ) 

 V (t )* F

1 V1 (t ), t    p1 V1 (t )   a1 V1 (t )   p1 V1 (t ) * Fiso1    2 V2 (t ), t    p 2

2

a2

V2 (t )   p 2

2

iso 2

 

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Mathematical Description  p  Emin V t   V0  

K K  Vsat  V t   V0  Vsat

pf K pf K Emin  p,1  V1 t   p f  V0   pf p f  Vsat  V1 t   p f  V0 p f  Vsat



 p,2















1 p f  K 1 p f  K Emin  V2 t   1  p f  V0   1 p f 1  p f  Vsat  V2 t   1  p f  V0 1  p f  Vsat





  







  



2   *  V  V t    *   a  1   * P    V  V0    

 a,1

2   *  p f  V  V1 t    *    1 P   p V *  p V   1 f 0    f 

 a,2





2   *  1  p f  V  V2 t    *    1 P   1  p V *  1  p V   2 f f 0    









Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Mathematical Description dV1 t    P(t )  P0  1 V1 (t ), t   R1 dt   P(t )  P   V (t ), t   R dV2 t  0 2 2 2  dt

dV t    2 P(t )  2 P0   V (t ), t   R  dt  

R1 p f  R2 (1  p f )  2R

R R R1  ; R 2  pf 1- pf Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

How to use the model… •

The two portions’ contractility laws can work in different mode: – by setting their phase – the result is a model named “regional Dissynchrony” – by reducing the contractility of one region

1. Regional Dissynchrony is obtained by setting different timing to the ventricular contraction function Fiso of the two regions. 2. Reduced contractility is realised by introducing different values for P* (P1* and P2*) to each ventricular portion (It is possible to modify both the contractility laws or just only one of them).

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Computer Simulations • Cases a) and b) – Physiological Undivided and Divided LV validate the divided model for LV. Indeed, if its working conditions are physiologic, it behaves as an undivided physiological LV • Case c) – Regional Dissynchrony LV’s divided model with Fiso phase shift and physiological contractility • Case d) – Regional Reduced Contractility LV’s divided model without Fiso phase shift and one region reduced contractility • Case e) – Regional Dissinchrony and Reduced Contractility LV’s divided model with Fiso phase shift and one region reduced contractility Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

a) LV’s undivided physiological model HR 80 VVES 42.45 PAt-ave 8.46 VVED 114.3 PAo-ave 98.73 VAES 37.14 QA-ave 5.64 VAED 69.92 PP 0%  0 Pressure (mmHg)

Physiologic

Left Atrium Left VentricleAorta Left Ventricle Flow Rate (cm^3/s) Diastole Systole

Volumes (cm^3) Left Atrium Left Ventricle

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

b) LV’s divided physiological model The LV has been divided in two parts working in physiological conditions

The LV has been divided in equal parts working in physiological conditions Two coincident PV loops and elastance curves

ABCD - 66% Physiological Portion EFGH - 34% Physiological Portion G C

H

Volumes (cm^3) Total

Portions - 50% LV and its Portions' Volume Waveforms

F

B

D E

A

Two PV loops Volumes (cm^3) Total 66% Portion 34% Portion

LV and its Portions' Volume Waveforms

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

c) LV’s divided model with Fiso phase shift and physiological contractility – Regional Dissinchrony HR 80 VVES 56.31 PAt-ave 9.70 VVED 116.75 PAo-ave 90.79 VAES 45.78 QA-ave 4.74 VAED 75.03 PP 34%  30% C G

B F C

B F

E

ABCD - Physiologic EFGH - Pathologic D

ABCD - 66% Physiological Portion EFGH - 34% Phase Shifted Portion

H

A E

G

H

A D

PV loops

Pressure (mmHg) Left Atrium

Two PV loops. The LV has been divided in two parts

LV and its Portions' Flow Rate Waveforms (cm^3/s) 34% Path. Portion Total

Aorta Left Ventricle

Left Ventricle Flow Rate (cm^3/s) Systole Diastole

66% Phys. Portion LV and its Portions' Volume Waveforms (cm^3) 66% Phys. Portion Total

Volumes (cm^3) Left Ventricle Left Atrium 34% Path. Portion

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

d) LV’s divided model without Fiso phase shift and one region reduced contractility – Regional Reduced Contractility

C

D

G

H

HR 80 VVES 75.19 PAt-ave 9.65 VVED 138.58 PAo-ave 91.09 VAES 47.61 QA-ave 4.97 VAED 75 0 34%  PP * * 480 P 2 150 P1 B

F

A

E

ABCD - 66% Physiological Portion EFG - 34% Portion with Reduced Contractility C

G F B

ABCD - Physiologic EFGH - Pathologic

PV loops

E

Pressure (mmHg)

D

A

Two PV loops. The LV has been divided in two parts Left Atrium

Aorta Left Ventricle

Left Ventricle Flow Rate (cm^3/s) Systole Diastole

Volumes (cm^3) Left Ventricle

Left Atrium

Volumes (cm^3) 34% Path. Portion 66% Phys. Portion

Total

LV and its Portions' Volume Waveforms

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

e) LV’s divided model with Fiso phase shift and one region reduced contractility – Regional Dissynchrony and Reduced Contractility HR 80 VVES PAt-ave 17.76 VVED PAo-ave 90.43 VAES QA-ave 4.52 VAED PP P*1 C

G B

A H

D

34%  480 P*2

113.17 170.87 90.71 103.32 30% 150

ABCD - Physiologic EFGH - Pathologic

C B

F

F

E

E

PV loops

A

Two PV loops. The LV has been divided in two parts

Pressure (mmHg) Left Atrium

ABC - 66% Physiological Portion EF - 34% Portion with Phase Shifting and Reduced Contractility

LV and its Portions' Flow Rate Waveforms (cm^3/s) Total

Left Ventricle Aorta

Left Ventricle Flow Rate (cm^3/s) Diastole Systole

34% Path. Portion

66% Phys. Portion

LV and its Portions' Volume Waveforms (cm^3) Total 34% Path. Portion 66% Phys. Portion

Volumes (cm^3) Left Ventricle Left Atrium

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte Cases a) & b) Pressure (mmHg) Pressure (mmHg) Case c) Left Atrium Left VentricleAorta

Left Atrium

Left Ventricle Flow Rate (cm^3/s) Systole Diastole

Left Ventricle Flow Rate (cm^3/s) Diastole Systole

Volumes (cm^3)

Volumes (cm^3) Left Atrium Left Ventricle

Case d) Left Atrium

Aorta Left Ventricle

Left Ventricle Flow Rate (cm^3/s) Systole Diastole

Volumes (cm^3) Left Ventricle

Left Ventricle Left Atrium

Case e)

Pressure (mmHg)

Left Atrium

Aorta Left Ventricle

Pressure (mmHg)

Left Atrium

Left Ventricle Aorta

Left Ventricle Flow Rate (cm^3/s) Diastole Systole

Volumes (cm^3) Left Ventricle Left Atrium

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Cases a) & b) HR 80 VVES 42.45 PAt-ave 8.46 VVED 114.3 PAo-ave 98.73 VAES 37.14 QA-ave 5.64 VAED 69.92 PP 0%  0

Case c)

HR 80 VVES 56.31 PAt-ave 9.70 VVED 116.75 PAo-ave 90.79 VAES 45.78 QA-ave 4.74 VAED 75.03 PP 34%  30%

C G

B F

ABCD - Physiologic EFGH - Pathologic

Physiologic

D

Case d)

C

G

HR 80 VVES 75.19 PAt-ave 9.65 VVED 138.58 PAo-ave 91.09 VAES 47.61 QA-ave 4.97 VAED 75 0 34%  PP * 480 P 2 150 P*1 B

D

H

A

F

H

Case e)

C

ABCD - Physiologic EFGH - Pathologic

A E

PV loops80 HR PAt-ave 17.76 PAo-ave 90.43 QA-ave 4.52 PP P*1

VVES 113.17 VVED 170.87 VAES 90.71 VAED 103.32 34%  30% * 150 480 P 2

G

ABCD - Physiologic EFGH - Pathologic

B

E D

PV loops

A H

F

E

PV loops

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

80 VVES 42.45 PAt-ave 8.46 VVED 114.3 PAo-ave 98.73 VAES 37.14 QA-ave 5.64 VAED 69.92 PP 0%  0

Cases a) & b) HR

Case c) ABCD - 66% Physiological Portion EFGH - 34% Phase Shifted Portion

B F C E

Physiologic

G

H

A D

Two PV loops. The LV has been divided in two parts

Case d)

ABC - 66% Physiological Portion EF - 34% Portion with Phase Shifting and Reduced Contractility

ABCD - 66% Physiological Portion EFG - 34% Portion with Reduced Contractility C

Case e)

C

G

B

F

F B

E E

D

A

A

Two PV loops. The LV has been divided in two parts

Two PV loops. The LV has been divided in two parts

Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.

26.09.2003

M. Arabia; F. M. Colacino; D. Lavorato; A. G. M. Marullo; F. Piedimonte

Conclusions

• Computer test showed the strong influence of the pathologies on the LV performance. – From external point of view the Starling flowrate-preloadafterload relation worsened and, as a consequence, flowrate decreased and preload and pulmonary venous pressure increased; moreover, pressure and flow waveforms morphology worsened. – From internal point of view mean ventricular volume and wall stress increased, mechanical efficiency decreased, and pressure volume loop worsened. • This study can be used as a tool for the evaluation of the follow-up of a ventricle affected by LV regional dissinchrony after pacing. • New ways for regional dissynchrony diagnosis. ECG does not reveal its presence. If we would have an estimation of the main parameters to be used in our model, we could depict the LV’s performance of a patient. Univ. of Calabria, Mechanical Eng Dept; MMA Consulting; Univ. of L’Aquila, Medicina Sperimentale Dept; Univ. of Rome “Tor Vergata”, D.I.S.P.