Research Papers

A Simulation Protocol for Exercise Physiology in Fontan Patients Using a Closed Loop Lumped-Parameter Model

[+] Author and Article Information
Ethan Kung

Mechanical and Aerospace
Engineering Department,
University of California San Diego,
9500 Gilman Drive MC 0411,
La Jolla, CA 92093
e-mail: keo@ucsd.edu

Giancarlo Pennati

Laboratory of Biological Structure Mechanics,
Department of Chemistry, Materials
and Chemical Engineering “Giulio Natta”,
Politecnico di Milano,
Piazza Leonardo da Vinci, 32,
Milan 20133, Italy
e-mail: giancarlo.pennati@polimi.it

Francesco Migliavacca

Laboratory of Biological Structure Mechanics,
Department of Chemistry, Materials
and Chemical Engineering “Giulio Natta”,
Politecnico di Milano,
Piazza Leonardo da Vinci, 32,
Milan 20133, Italy
e-mail: francesco.migliavacca@polimi.it

Tain-Yen Hsia

Cardiorespiratory Unit,
Great Ormond Street Hospital for Children,
7th Floor, Nurses Home,
London WC1N 3JH, UK
e-mail: hsiat@gosh.nhs.uk

Richard Figliola

Mechanical Engineering Department,
Clemson University,
216 South Palmetto Boulevard,
Clemson, SC 29634-0921
e-mail: fgliola@clemson.edu

Alison Marsden

Mechanical and Aerospace
Engineering Department,
University of California San Diego,
9500 Gilman Drive MC 0411,
La Jolla, CA 92093
e-mail: amarsden@eng.ucsd.edu

Alessandro Giardini

Cardiorespiratory Unit,
Great Ormond Street Hospital for Children,
7th Floor, Nurses Home,
London WC1N 3JH, UK
e-mail: alessandro.giardini@gosh.nhs.uk

Manuscript received January 4, 2014; final manuscript received March 5, 2014; accepted manuscript posted March 24, 2014; published online June 5, 2014. Assoc. Editor: Tim David.

J Biomech Eng 136(8), 081007 (Jun 05, 2014) (13 pages) Paper No: BIO-14-1005; doi: 10.1115/1.4027271 History: Received January 04, 2014; Revised March 05, 2014; Accepted March 24, 2014

Background: Reduced exercise capacity is nearly universal among Fontan patients, though its etiology is not yet fully understood. While previous computational studies have attempted to model Fontan exercise, they did not fully account for global physiologic mechanisms nor directly compare results against clinical and physiologic data. Methods: In this study, we developed a protocol to simulate Fontan lower-body exercise using a closed-loop lumped-parameter model describing the entire circulation. We analyzed clinical exercise data from a cohort of Fontan patients, incorporated previous clinical findings from literature, quantified a comprehensive list of physiological changes during exercise, translated them into a computational model of the Fontan circulation, and designed a general protocol to model Fontan exercise behavior. Using inputs of patient weight, height, and if available, patient-specific reference heart rate (HR) and oxygen consumption, this protocol enables the derivation of a full set of parameters necessary to model a typical Fontan patient of a given body-size over a range of physiologic exercise levels. Results: In light of previous literature data and clinical knowledge, the model successfully produced realistic trends in physiological parameters with exercise level. Applying this method retrospectively to a set of clinical Fontan exercise data, direct comparison between simulation results and clinical data demonstrated that the model successfully reproduced the average exercise response of a cohort of typical Fontan patients. Conclusion: This work is intended to offer a foundation for future advances in modeling Fontan exercise, highlight the needs in clinical data collection, and provide clinicians with quantitative reference exercise physiologies for Fontan patients.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Marino, B., 2002, “Outcomes after the Fontan Procedure,” Curr. Opin. Pediatr., 14(5), pp. 620–626. [CrossRef]
Gewillig, M. H., Lundström, U. R., Bull, C., Wyse, R. K., and Deanfield, J. E., 1990, “Exercise Responses in Patients With Congenital Heart Disease After Fontan Repair: Patterns and Determinants of Performance,” J. Am. Coll. Cardiol., 15(6), pp. 1424–1432. [CrossRef]
Durongpisitkul, K., Driscoll, D. J., Mahoney, D. W., Wollan, P. C., Mottram, C. D., Puga, F. J., and Danielson, G. K., 1997, “Cardiorespiratory Response to Exercise After Modified Fontan Operation: Determinants of Performance,” J. Am. Coll. Cardiol., 29(4), pp. 785–790. [CrossRef]
Yang, W., Vignon-Clementel, I. E., Troianowski, G., Reddy, V. M., Feinstein, J. A., and Marsden, A. L., 2011, “Hepatic Blood Flow Distribution and Performance in Conventional and Novel Y-Graft Fontan Geometries: A Case Series Computational Fluid Dynamics Study,” J. Thorac. Cardiovasc. Surg., 143, pp. 1086–1097. [CrossRef]
Whitehead, K. K., Pekkan, K., Kitajima, H. D., Paridon, S. M., Yoganathan, A. P., and Fogel, M. A., 2007, “Nonlinear Power Loss During Exercise in Single-Ventricle Patients After the Fontan: Insights From Computational Fluid Dynamics,” Circulation, 116(11 Suppl), pp. I165–I171. [CrossRef]
Justino, H., Benson, L., and Freedom, R., 2001, “Development of Unilateral Pulmonary Arteriovenous Malformations Due to Unequal Distribution of Hepatic Venous Flow,” Circulation, 103(8), pp. E39–E40. [CrossRef]
Srivastava, D., Preminger, T., Lock, J. E., Mandell, V., Keane, J. F., Mayer, J. E., Kozakewich, H., and Spevak, P. J., 1995, “Hepatic Venous Blood and the Development of Pulmonary Arteriovenous Malformations in Congenital Heart Disease,” Circulation, 92(5), pp. 1217–1222. [CrossRef]
Shachar, G. B., Fuhrman, B. P., Wang, Y., Lucas, R. V., and Lock, J. E., 1982, “Rest and Exercise Hemodynamics After the Fontan Procedure,” Circulation, 65(6), pp. 1043–1048. [CrossRef]
Goldstein, B. H., Connor, C. E., Gooding, L., and Rocchini, A. P., 2010, “Relation of Systemic Venous Return, Pulmonary Vascular Resistance, and Diastolic Dysfunction to Exercise Capacity in Patients With Single Ventricle Receiving Fontan Palliation,” Am. J. Cardiol., 105(8), pp. 1169–1175. [CrossRef]
Migliavacca, F., Balossino, R., Pennati, G., Dubini, G., Hsia, T. Y., De Leval, M. R., and Bove, E. L., 2006, “Multiscale Modelling in Biofluidynamics: Application to Reconstructive Paediatric Cardiac Surgery,” J. Biomech., 39(6), pp. 1010–1020. [CrossRef]
Taylor, C. A., Draney, M. T., Ku, J. P., Parker, D., Steele, B. N., Wang, K., and Zarins, C. K., 1999, “Predictive Medicine: Computational Techniques in Therapeutic Decision-Making,” Comput. Aided Surg., 4(5), pp. 231–247. [CrossRef]
Degroff, C. G., 2008, “Modeling the Fontan Circulation: Where We Are and Where We Need to Go,” Pediatr. Cardiol., 29(1), pp. 3–12. [CrossRef]
Marsden, A. L., Vignon-Clementel, I. E., Chan, F. P., Feinstein, J. A., and Taylor, C. A., 2007, “Effects of Exercise and Respiration on Hemodynamic Efficiency in Cfd Simulations of the Total Cavopulmonary Connection,” Ann. Biomed. Eng., 35(2), pp. 250–263. [CrossRef]
Baretta, A., Corsini, C., Marsden, A. L., Vignon-Clementel, I. E., Hsia, T. Y., Dubini, G., Migliavacca, F., and Pennati, G., 2012, “Respiratory Effects on Hemodynamics in Patient-Specific CFD Models of the Fontan Circulation Under Exercise Conditions,” Eur. J. Mech. B, 35, pp. 61–69 [CrossRef].
Snyder, M. F., and Rideout, V. C., 1969, “Computer Simulation Studies of the Venous Circulation,” IEEE Trans. Biomed Eng., 16(4), pp. 325–334. [CrossRef]
Kung, E., Baretta, A., Baker, C., Arbia, G., Biglino, G., Corsini, C., Schievano, S., Vignon-Clementel, I. E., Dubini, G., and Pennati, G., 2012, “Predictive Modeling of the Virtual Hemi-Fontan Operation for Second Stage Single Ventricle Palliation: Two Patient-Specific Cases,” J. Biomech., 46, pp. 423–429. [CrossRef]
Migliavacca, F., Pennati, G., Dubini, G., Fumero, R., Pietrabissa, R., Urcelay, G., Bove, E., Hsia, T., and De Leval, M., 2001, “Modeling of the Norwood Circulation: Effects of Shunt Size, Vascular Resistances, and Heart Rate,” Am. J. Physiol. Heart Circ. Physiol., 280(5), pp. H2076–H2086. Available at: http://ajpheart.physiology.org/content/280/5/H2076
Corsini, C., Baker, C., Kung, E., Schievano, S., Arbia, G., Baretta, A., Biglino, G., Migliavacca, F., Dubini, G., and Pennati, G., 2013, “An Integrated Approach to Patient-Specific Predictive Modeling for Single Ventricle Heart Palliation,” Comput. Methods Biomech. Biomed. Eng, (in press). [CrossRef]
Giardini, A., Balducci, A., Specchia, S., Gargiulo, G., Bonvicini, M., and Picchio, F., 2008, “Effect of Sildenafil on Haemodynamic Response to Exercise and Exercise Capacity in Fontan Patients,” Eur. Heart J., 29(13), pp. 1681–1687. [CrossRef]
Gabrielsen, A., Videbaek, R., Schou, M., Damgaard, M., Kastrup, J., and Norsk, P., 2002, “Non-Invasive Measurement of Cardiac Output in Heart Failure Patients Using a New Foreign Gas Rebreathing Technique,” Clin. Sci., 102(2), pp. 247–252. [CrossRef]
Sheth, S. S., Maxey, D. M., Drain, A. E., and Feinstein, J. A., 2012, “Validation of the Innocor Device for Noninvasive Measurement of Oxygen Consumption in Children and Adults,” Pediatr. Cardiol., 34, pp. 847–852. [CrossRef]
West, G. B., and Brown, J. H., 2005, “The Origin of Allometric Scaling Laws in Biology From Genomes to Ecosystems: Towards a Quantitative Unifying Theory of Biological Structure and Organization,” J. Exp. Biol., 208(Pt 9), pp. 1575–1592. [CrossRef]
Dewey, F. E., Rosenthal, D., Murphy, D. J., Froelicher, V. F., and Ashley, E. A., 2008, “Does Size Matter? Clinical Applications of Scaling Cardiac Size and Function for Body Size,” Circulation, 117(17), pp. 2279–2287. [CrossRef]
Gewillig, M., Brown, S. C., Eyskens, B., Heying, R., Ganame, J., Budts, W., La Gerche, A., and Gorenflo, M., 2010, “The Fontan Circulation: Who Controls Cardiac Output?,” Interact. Cardiovasc. Thorac. Surg., 10(3), pp. 428–433. [CrossRef]
Stickland, M. K., Welsh, R. C., Petersen, S. R., Tyberg, J. V., Anderson, W. D., Jones, R. L., Taylor, D. A., Bouffard, M., and Haykowsky, M. J., 2006, “Does Fitness Level Modulate the Cardiovascular Hemodynamic Response to Exercise?,” J. Appl. Physiol., 100(6), pp. 1895–1901. [CrossRef]
Cui, W., Roberson, D., Chen, Z., Madronero, L., and Cuneo, B., 2008, “Systolic and Diastolic Time Intervals Measured from Doppler Tissue Imaging: Normal Values and Z-Score Tables, and Effects of Age, Heart Rate, and Body Surface Area,” J. Am. Soc. Echocardiogr., 21(4), pp. 361–370. [CrossRef]
Gemignani, V., Bianchini, E., Faita, F., Giannoni, M., Pasanisi, E., Picano, E., and Bombardini, T., 2008, “Assessment of Cardiologic Systole and Diastole Duration in Exercise Stress Tests With a Transcutaneous Accelerometer Sensor,” Comput. Cardiol., 35, pp. 153–156. [CrossRef]
Mitchell, J. H., 1963, “Mechanisms of Adaptation of the Left Ventricle to Muscular Exercise,” Pediatrics, 32(4), pp. 660–670. Available at: http://pediatrics.aappublications.org/content/32/4/660.short
Alpert, B. S., Benson, L., and Olley, P. M., 1981, “Peak Left Ventricular Pressure/Volume (Emax) During Exercise in Control Subjects and Children With Left-Sided Cardiac Disease,” Cathet. Cardiovasc. Diagn., 7(2), pp. 145–153. [CrossRef]
Bombardini, T., Nevola, E., Giorgetti, A., Landi, P., Picano, E., and Neglia, D., 2008, “Prognostic Value of Left-Ventricular and Peripheral Vascular Performance in Patients With Dilated Cardiomyopathy,” J. Nucl. Cardiol., 15(3), pp. 353–362. [CrossRef]
Dexter, L., Whittenberger, J. L., Haynes, F. W., Goodale, W. T., Gorlin, R., and Sawyer, C. G., 1951, “Effect of Exercise on Circulatory Dynamics of Normal Individuals,” J. Appl. Physiol., 3(8), pp. 439–453. Available at: http://journals.lww.com/ajpmr/Citation/1952/12000/Effect_of_Exercise_on_Circulatory_Dynamics_of.7.aspx
Kasalický, J., Hurych, J., Widimský, J., Dejdar, R., Metys, R., and Stanĕk, V., 1968, “Left Heart Haemodynamics at Rest and During Exercise in Patients With Mitral Stenosis,” Br. Heart J., 30(2), pp. 188–195. [CrossRef]
Yu, P. N., Murphy, G. W., Schreiner, Jr, B. F., and James, D. H., 1967, “Distensibility Characteristics of the Human Pulmonary Vascular Bed: Study of the Pressure-Volume Response to Exercise in Patients With and Without Heart Disease,” Circulation, 35(4), pp. 710–723. [CrossRef]
Ekelund, L. G., and Holmgren, A., 1964, “Circulatory and Respiratory Adaptation, During Long‐Term, Non‐Steady State Exercise, in the Sitting Position,” Acta Physiol. Scand., 62(3), pp. 240–255. [CrossRef]
Holmgren, A., Jonsson, B., and Sjöstrand, T., 1960, “Circulatory Data in Normal Subjects at Rest and During Exercise in Recumbent Position, With Special Reference to the Stroke Volume at Different Work Intensities,” Acta Physiol. Scand., 49(4), pp. 343–363. [CrossRef]
Luepker, R. V., Holmberg, S., and Varnauskas, E., 1971, “Left Atrial Pressure During Exercise in Hemodynamic Normals,” Am. Heart J., 81(4), pp. 494–497. [CrossRef]
Slonim, N. B., Ravin, A., Balchum, O. J., and Dressler, S. H., 1954, “The Effect of Mild Exercise in the Supine Position on the Pulmonary Arterial Pressure of Five Normal Human Subjects,” J. Clin. Invest., 33(7), pp. 1022–1030. [CrossRef]
Barratt-Boyes, B. G., and Wood, E. H., 1957, “Hemodynamic Response of Healthy Subjects to Exercise in the Supine Position While Breathing Oxygen,” J. Appl. Physiol., 11(1), pp. 129–135. Available at: http://jap.physiology.org/content/11/1/129.short
Sancetta, S. M., and Rakita, L., 1957, “Response of Pulmonary Artery Pressure and Total Pulmonary Resistance of Untrained, Convalescent Man to Prolonged Mild Steady State Exercise,” J. Clin. Invest., 36(7), pp. 1138–1149. [CrossRef]
Widimsky, J., Berglund, E., and Malmberg, R., 1963, “Effect of Repeated Exercise on the Lesser Circulation,” J. Appl. Physiol., 18(5), pp. 983–986. Available at: http://jap.physiology.org/content/18/5/983.short
Wallace, A. G., Mitchell, J. H., Skinner, N. S., and Sarnoff, S. J., 1963, “Hemodynamic Variables Affecting the Relation Between Mean Left Atrial and Left Ventricular End-Diastolic Pressures,” Circ. Res., 13, pp. 261–270. [CrossRef]
Manohar, M., 1993, “Pulmonary Artery Wedge Pressure Increases With High-Intensity Exercise in Horses,” Am. J. Vet. Res., 54(1), pp. 142–146. Available at: http://www.ncbi.nlm.nih.gov/pubmed/8427458
Cheng, C. P., Igarashi, Y., and Little, W. C., 1992, “Mechanism of Augmented Rate of Left Ventricular Filling During Exercise,” Circ. Res., 70(1), pp. 9–19. [CrossRef]
Nevsky, G., Jacobs, J. E., Lim, R. P., Donnino, R., Babb, J. S., and Srichai, M. B., 2011, “Sex-Specific Normalized Reference Values of Heart and Great Vessel Dimensions in Cardiac CT Angiography,” AJR Am. J. Roentgenol., 196(4), pp. 788–794. [CrossRef]
Carroll, J. D., Hess, O. M., Hirzel, H. O., and Krayenbuehl, H. P., 1983, “Dynamics of Left Ventricular Filling at Rest and During Exercise,” Circulation, 68(1), pp. 59–67. [CrossRef]
Grimby, G., Goldman, M., and Mead, J., 1976, “Respiratory Muscle Action Inferred from Rib Cage and Abdominal Vp Partitioning,” J. Appl. Physiol., 41(5), pp. 739–751. Available at: http://www.jappl.org/content/41/5/739.short
Armstrong, R. B., Delp, M. D., Goljan, E. F., and Laughlin, M. H., 1987, “Distribution of Blood Flow in Muscles of Miniature Swine During Exercise,” J. Appl. Physiol., 62(3), pp. 1285–1298. Avaiable at: http://www.jappl.org/content/62/3/1285.short
Pennati, G., and Fumero, R., 2000, “Scaling Approach to Study the Changes Through the Gestation of Human Fetal Cardiac and Circulatory Behaviors,” Ann. Biomed. Eng., 28, pp. 442–452. [CrossRef]
Clausen, J. P., Klausen, K., Rasmussen, B., and Trap-Jensen, J., 1973, “Central and Peripheral Circulatory Changes After Training of the Arms or Legs,” Am. J. Physiol., 225(3), pp. 675–682. Available at: http://ajplegacy.physiology.org/content/225/3/675.extract
Hjortdal, V. E., Emmertsen, K., Stenbøg, E., Fründ, T., Schmidt, M. R., Kromann, O., Sørensen, K., and Pedersen, E. M., 2003, “Effects of Exercise and Respiration on Blood Flow in Total Cavopulmonary Connection: A Real-Time Magnetic Resonance Flow Study,” Circulation, 108(10), pp. 1227–1231. [CrossRef]
Marsden, A. L., Reddy, V. M., Shadden, S. C., Chan, F. P., Taylor, C. A., and Feinstein, J. A., 2010, “A New Multiparameter Approach to Computational Simulation for Fontan Assessment and Redesign,” Congenit Heart Dis., 5(2), pp. 104–117. [CrossRef]
Koeken, Y., Arts, T., and Delhaas, T., 2012, “Simulation of the Fontan Circulation During Rest and Exercise,” Annual International Conference of the IEEE Engineering in Medicine and Biology Society, San Diego, CA, Aug. 28–Sept. 1, 2012, pp. 6673–6676.
Sundareswaran, K. S., Pekkan, K., Dasi, L. P., Whitehead, K., Sharma, S., Kanter, K. R., Fogel, M. A., and Yoganathan, A. P., 2008, “The Total Cavopulmonary Connection Resistance: A Significant Impact on Single Ventricle Hemodynamics at Rest and Exercise,” Am. J. Physiol. Heart Circ. Physiol., 295(6), pp. H2427–H2435. [CrossRef]
Folkow, B., Gaskell, P., and Waaler, B. A., 1970, “Blood Flow through Limb Muscles During Heavy Rhythmic Exercise,” Acta Physiol. Scand., 80(1), pp. 61–72. [CrossRef]
Suga, H., Sagawa, K., and Shoukas, A. A., 1973, “Load Independence of the Instantaneous Pressure-Volume Ratio of the Canine Left Ventricle and Effects of Epinephrine and Heart Rate on the Ratio,” Circulation Research, 32(3), pp. 314–322. [CrossRef]
Senzaki, H., Chen, C., and Kass, D., 1996, “Single-Beat Estimation of End-Systolic Pressure-Volume Relation in Humans: A New Method with the Potential for Noninvasive Application,” Circulation, 94(10), pp. 2497–2506. [CrossRef]
Segers, P., Stergiopulos, N., Westerhof, N., Wouters, P., Kolh, P., and Verdonck, P., 2003, “Systemic and Pulmonary Hemodynamics Assessed With a Lumped-Parameter Heart-Arterial Interaction Model,” J. Eng. Math., 47, pp. 185–199. [CrossRef]
Avanzolini, G., Barbini, P., Cappello, A., and Cevese, A., 1985, “Time-Varying Mechanical Properties of the Left Ventricle-A Computer Simulation,” Biomed. Eng. IEEE Trans., 10, pp. 756–763. [CrossRef]
Lau, V.-K., and Sagawa, K., 1979, “Model Analysis of the Contribution of Atrial Contraction to Ventricular Filling,” Ann. Biomed. Eng., 7(2), pp. 167–201. [CrossRef]
Peskin, C. S., 1982, “The Fluid Dynamics of Heart Valves: Experimental, Theoretical, and Computational Methods,” Ann. Rev. Fluid Mech., 14(1), pp. 235–259. [CrossRef]


Grahic Jump Location
Fig. 1

Closed-loop lumped-parameter network of the Fontan circulation. Rsubscript, Lsubscript, and Psubscript are labels for resistor components, inductor components, and nodal pressures, respectively.

Grahic Jump Location
Fig. 2

Exercise clinical data from nine Fontan patients. Plots show correlations of (a) normalized HR, and (b) normalized TVR, to exercise level expressed in MET.

Grahic Jump Location
Fig. 3

Flow diagram for computing resistance values in the LPN. Highlighted items represent lists of resistance values used to construct the final list of resistance values in the LPN for a simulation.

Grahic Jump Location
Fig. 4

Simulation results of two example patients at various exercise levels

Grahic Jump Location
Fig. 5

Model validation of (a) CO and (b) O2 extraction against clinical data. Points connected by lines are results of the same patient at different exercise levels.

Grahic Jump Location
Fig. 6

(a) Atrial activation function and (b) intrathoracic pressure waveform. Note that values of APith and Pithoffset are typically negative during natural, nonmechanically ventilated breathing.

Grahic Jump Location
Fig. 7

Comparison of (a) CO and (b) O2 extraction between simulation and Appendix B equation estimation for the two example patients at six MET levels




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In