Medical & Biological Engineering & Computing

Patient-specific finite element modeling of the Cardiokinetix Parachute® device: Effects on left ventricular wall stress and function.

Medical & Biological Engineering & Computing

Online Resources 3

LikChuan Lee1,2,4, PhD, Liang Ge, PhD1,2,4, Zhihong Zhang, MS4, Matthew Pease5, Serjan D. Nikolic5, PhD, Rakesh Mishra, MD3,4, Mark B. Ratcliffe, MD1,2,4 and Julius M. Guccione, PhD1,2,4

From the Departments of Surgery1, Bioengineering2, and Medicine3, and from the University of California, San Francisco, California and the Veterans Affairs Medical Center, San Francisco, California4 and Cardiokinetix, Inc., Menlo Park, California5

Corresponding Author: Mark B. Ratcliffe, MD, Division of Surgical Services (112), San Francisco Veterans Affairs Medical Center, 4150 Clement Street, San Francisco, California 94121. Telephone: (415) 221-4810. FAX: (415) 750-2181. E-mail:

Sensitivity of Results to a Change in Parameters

To assess the effects associated with a variation of the modeling input parameters, we performed a sensitivity analysis by perturbing the parameters individually in each of the 3 models described in the main text, namely, the PRE-OP, VIRTUAL-Parachute and POST-OP models. The effects on myofiber stress due to each individual perturbation are described in detail below.

A)CHANGE IN MYOFIBER ORIENTATION

In the original model, the myofiber orientation has a +60º/-60º configuration (i.e. a linear transmural variation from +60º at the endocardium to -60º at the epicardium). To assess the effects on myofiber stress associated with a change in myofiber orientation, we re-ran our simulations for the 3 cases withboth +35º/-35º and +85º/-85º myofiber orientation configurations (Fig. A1).The greatest percentage change in myofiber stress due to a change in myofiber orientation was -9.6%, andwas found in the upper chamber of the VIRTUAL-Parachute case with a +85º/-85º myofiber orientation (Table A1).

Figure A1: Myofiber orientation in the LV. Blue, red and green denote the +85º/-85º, +60º/-60º and +35º/-35º myyofiber orientation configurations, respectively.

Case / Lower ED Stress / Upper ED Stress / Total ED Stress / Lower ES Stress / Upper ES Stress / Total ES Stress
PRE-OP (+35º/-35º ) / 11 ± 7.8
(-5.2) / 5.9 ± 4.9
(-0.68) / 8.2 ± 7.0
(-2.5) / 61.5 ± 42.3
(-7.76) / 29.2 ± 20.4
(-7.63) / 44.7 ± 36.9
(-5.36)
VIRTUAL PARACHUTE (+35º/-35º ) / 4.6 ± 3.8
(1.8) / 6.0 ± 5.0
(3.7) / 5.2 ± 4.4
(2.6) / 59.7 ± 40.2
(-7.0) / 31.0 ± 22.4
(-3.1) / 43.7 ± 34.9
(-5.4)
POST-OP (+35º/-35º ) / 2.5 ± 2.8
(-0.8) / 4.4 ± 4.5
(4.0) / 3.5 ± 3.8
(2.5) / 63.3 ± 43.5
(-7.0) / 31.6 ± 24.1
(-3.3) / 45.6 ± 37.9
(-5.4)
PRE-OP (+85º/-85º ) / 11.6 ± 8.4
(0.3) / 5.5 ± 4.3
(-6.7) / 8.2 ± 7.3
(-2.0) / 69.3 ± 53.2
(4.0) / 30.6 ± 25.7
(-3.2) / 48.0 ± 45.4
(1.6)
VIRTUAL PARACHUTE (+85º/-85º ) / 4.2 ± 3.8
(-6.3) / 5.2 ± 4.3
(-9.6) / 4.7 ± 3.9
(-7.8) / 66.2 ± 50.2
(3.2) / 31.1 ± 25.9
(-2.8) / 46.7 ± 42.8
(1.2)
POST-OP (+85º/-85º ) / 2.3 ± 2.7
(-7.3) / 3.9 ± 3.5
(-9.2) / 3.1 ± 3.0
(-8.3) / 69.7 ± 54.2
(3.0) / 31.6 ± 27.1
(-2.0) / 48.5 ± 46.0
(1.2)

Table A1: Effects on myofiber stress due to a change in myofiber orientation from +60º/-60º to +35º/-35º and +85º/-85º. Stress is given in kPa and the value inside each parenthesis ( ) indicates the percentage change of the above averaged stress value when compared to the corresponding original cases described in the main text. Shaded box indicates the greatest percentage change of the stress value. Refer to the main text for a description of the PRE-OP, VIRTUAL-Parachute and POST-OP cases. ED = end diastole; ES = end systole.

B)CHANGE IN INFARCT ANISOTROPY

In the original model, the infarct has the same degree of anisotropy as the remote region,where it is approximately 3 times stiffer in the myofiber direction than in directions transverse to it. To assess the effects due to a change in infarct anisotropy, we re-ran our simulations for the 3 caseswith anisotropic infarct and compared the result with those from the original models with an anisotropic infarct. The infarct was modeled as anisotropic material byadjusting the passive material parameters so that (previous values were, and). Thegreatest percentage change in myofiber stressdue to a change in infarct anisotropy was -16.8%, and was found in the lower chamber of the PRE-OP case (Table B1).

Case / Lower ED Stress / Upper ED Stress / Total ED Stress / Lower ES Stress / Upper ES Stress / Total ES Stress
PRE-OP
(ISOTROPIC INFARCT) / 9.7 ± 6.3
(-16.8) / 5.5 ± 4.2
(-5.5) / 7.3 ± 5.7
(-12.5) / 59.4 ± 38.5
(-10.9) / 30.2 ± 21
(-4.4) / 43.3 ± 33.9
(-8.3)
VIRTUAL PARACHUTE
(ISOTROPIC INFARCT) / 4 ± 3.5
(-10.5) / 5.5 ± 4.4
(-5.4) / 4.7 ± 3.9
(-7.1) / 57.5 ± 36.9
(-10.4) / 30.8 ± 21.5
(-3.8) / 42.6 ± 32.5
(-7.7)
POST-OP
(ISOTROPIC INFARCT) / 2.2 ± 2.4
(-11.3) / 4 ± 3.5
(-5.6) / 3.2 ± 3.1
(-6.8) / 60.1 ± 39.9
(-11.3) / 31.5 ± 23.1
(-2.2) / 44.1 ± 34.9
(-8.1)

Table B1: Effects on myofiber stress when the infarct is isotropic. Refer to Table A1 for a description and the unit of the tabulated values.ED = end diastole; ES = end systole.

C)CHANGE IN THE EXTENT OF INFARCT DYSFUNCTION

In the original model, the infarct was assumed to be akinetic (i.e., the infarct contains myocytes so that its wall thickness remained constant during systole). To assess the effects on myofiber stress due to a change in the extent of infarct dysfunction, we re-ran our simulations for the 3 caseswith a dyskinetic infarct (i.e., the infarct does not contain any myocytes and does not generate any active contractive forces). To model the dyskinetic infarct, we set the active material parameter reflecting the tissue contractility to zero. The greatest percentage change in myofiber stress due to a change in the extent of infarct dysfunction was 13.7%, andwas foundin the lower chamber at ES in the POST-OP case (Table C1). Also, ED stress was unchanged in the Table because the passive material parameters were not altered.

Case / Lower ED Stress / Upper ED Stress / Total ED Stress / Lower ES Stress / Upper ES Stress / Total ES Stress
FE PRE-OP
(DYSKINETIC INFARCT) / 11.6 ± 8.2
(0) / 5.9 ± 4.5
(0) / 8.4 ± 7.1
(0) / 75 ± 59.5
(12.6) / 34.1 ± 27.5
(8.05) / 52.3 ± 49.5
(10.8)
FE VIRTUAL PARACHUTE
(DYSKINETIC INFARCT) / 4.5 ± 3.8
(0) / 5.8 ± 4.7
(0) / 5.1 ± 4.1
(0) / 71.4 ± 55.2
(11.2) / 34.1 ± 26.4
(6.6) / 50.6 ± 46
(9.62)
FE POST-OP
(DYSKINETIC INFARCT) / 2.5 ± 3.0
(0) / 4.3 ± 3.9
(0) / 3.4 ± 3.4
(0) / 77 ± 62.5
(13.7) / 34.7 ± 29.0
(7.6) / 53.6 ± 52.1
(11.8)

Table C1: Effects on myofiber stress due to a change in the extent of infarct dysfunction. Refer to Table A1 for a description and the unit of the tabulated values.ED = end diastole; ES = end systole.

D)CHANGE IN BORDERZONE WIDTH

Figure D1: Prescription of different borderzone width in the LV. Left, center and right show the LV with borderzone with of 2cm, 3cm and 4cm, respectively.

In the original model, the infarct borderzone was assumed to have a width of3cm. To assess the effects on myofiber stress due to a change in the borderzone width, we re-ran our simulations for the 2 cases with a borderzone width of 2cm and 4cm (Fig. D1), and compared the result with those from the original models with a borderzone width of 3cm. The greatest percentage change in myofiber stress due to a change in the borderzone widthwas 1.3%, andwas foundin the upper chamber at ES in the PRE-OP case (Table D1). Also, ED stress was unchanged in the Table because the passive material parameters were not altered.

Case / Lower ED Stress / Upper ED Stress / Total ED Stress / Lower ES Stress / Upper ES Stress / Total ES Stress
PRE-OP
(BZ 2cm) / 11.6 ± 8.2
(0) / 5.9 ± 4.5
(0) / 8.4 ± 7.1
(0) / 66.2 ± 48.3
(-0.7) / 31.2 ± 23.8
(-1.3) / 46.8 ± 41.1
(-0.8)
VIRTUAL PARACHUTE (BZ 2cm) / 4.5 ± 3.8
(0) / 5.8 ± 4.7
(0) / 5.1 ± 4.1
(0) / 63.7 ± 45.4
(-0.8) / 31.7 ± 23.5
(-1.0) / 45.8 ± 38.7
(-0.8)
POST-OP
(BZ 2cm) / 2.5 ± 3.0
(0) / 4.3 ± 3.9
(0) / 3.4 ± 3.4
(0) / 67.1 ± 48.9
(-0.9) / 32.1 ± 25.0
(-0.3) / 47.5 ± 41.8
(-0.9)
PRE-OP
(BZ 4cm) / 11.6 ± 8.2
(0) / 5.9 ± 4.5
(0) / 8.4 ± 7.1
(0) / 67.1 ± 48.8
(0.8) / 31.8 ± 23.9
(0.6) / 47.5 ± 41.4
(0.6)
VIRTUAL PARACHUTE (BZ 4cm) / 4.5 ± 3.8
(0) / 5.8 ± 4.7
(0) / 5.1 ± 4.1
(0) / 64.5 ± 45.9
(0.5) / 32.2 ± 23.7
(0.6) / 46.4 ± 39.0
(0.4)
POST-OP
(BZ 4cm) / 2.5 ± 3.0
(0) / 4.3 ± 3.9
(0) / 3.4 ± 3.4
(0) / 68.2 ± 49.5
(0.7) / 32.6 ± 25.3
(1.2) / 48.3 ± 42.3
(0.8)

Table D1: Effects on myofiber stress due to a change in the borderzone (BZ) width. Refer to Table A1 for a description and the unit of the tabulated values.ED = end diastole; ES = end systole.