Modeling the Time-Dependent Intrapericardial Pressure-Volume Relationship with Effusion Rodney Metoyer*† and Beth Smith, P.E.† *North Carolina State University †Applied Research Associates, Inc. PURPOSE METHODS RESULTS METHODS CONCLUSION The strength of ventricular contraction is related to the stretch of the ventricular wall by the Frank-Starling mechanism. Ventricular filling is driven by the myocardial transmural pressure; therefore, cardiac output is directly related to the intrapericardial pressure. The normal intrapericardial pressure approaches the pleural pressure. Pericardial effusion can increase the intrapericardial pressure, and clinically significant cardiac compression can occur if the change in fluid volume exceeds the stretch rate of the parietal pericardium. The degree to which tamponade occurs is related to the volume and the rate of the effusion. In this study, a flow-rate dependent model of the intrapericardial pressure- volume relationship was derived, and the model was analyzed by implementation in the BioGears® general purpose human physiology engine. 1. Spodick, D. (2003). “Acute Cardiac Tamponade.” N Engl J Med, 349(7), 684-690 2. Refsum, H., Junemann, M., Lipton, M. J., Skioldebrand, C., Carlsson, E., & Tyberg, J. V. (1981). “Ventricular Diastolic Pressure-Volume Relations and the Pericardium.” Circulation, 64(5), 997-1004. REFERENCES BioGears project for the U.S. Army Medical Research and Material Command (USAMRMC) Telemedicine and Advanced Technology Research Center (TATRC) FUNDING Jerry Heneghan Director of HumanSim Product Development Applied Research Associates 8537 Six Forks Road Suite 600 Raleigh, NC 27615 (919) 582-3300 [email protected] CONTACT INFORMATION Rodney Metoyer North Carolina State University 911 Oval Dr. EB3 Raleigh, NC 27695 (419) 438-5738 [email protected] Student BioGears Intrapericardial Pressure-Volume Relationship Qualitative Pressure-Volume Relationship from Reference [1] BioGears® Physiology RESULTS Model Overview BioGears® Overview Pressure-Volume Relationship from the BioGears Physiology Engine Chronic (slow) effusion Acute (rapid) effusion Model development began with the assumption that the scalar compliance of the pericardium is a function of the intrapericardial volume and of the time rate of change in volume (the rate of fluid flow into in the pericardium). From this assumption, an equation for the variable compliance was written in terms of two constant parameters. The first parameter modifies the compliance proportional to the cube of the flow rate. The second parameter modifies the compliance in proportion to the volume. = → = = + = − BioGears® Implementation Qualitative Comparison Comparison to Experimental Data from Reference [2] In the study described in Ref. [2], the intrapericardial pressure in 12 dead dogs was measured during a rapid effusion of saline. For the comparison, the model rate of effusion was assumed such that the vertical section of the pressure- volume (P-V) curve was co-located with the corresponding section of the dog P-V curve. Pericardium circuit connected to the existing cardiovascular circuit • Physiology Engine • Base physiology for model improvements and additions • Common Data Model • Defined data standards • Data validation • Automatic translations • Documentation • Assumptions, limitations, reference database • Community Support • Open source under a modified BSD license • Community interaction BioGears® Standardized Modeling • BioGears® uses the electrical circuit analogy to standardize modeling • The common fluid- dynamics analogous elements are shown in the figure to the left • Other dynamical systems can be modeled using the BioGears® structured modeling • The BioGears® cardiovascular circuit models the hemodynamics of the entire body • The compliance of the heart is modeled with variable capacitors • The pericardial effusion model was implemented by connecting a pericardium circuit to the cardiovascular circuit at the heart nodes • The heart pressure is modified by the pericardial node pressure Blood Pressure BioGears® Standard Male – Healthy BioGears® Standard Male – Slow Effusion Heart Rate BioGears® Standard Male – Healthy BioGears® Standard Male – Slow Effusion Cardiac Output BioGears® Standard Male – Healthy BioGears® Standard Male – Slow Effusion Some of the expected hemodynamic events associated with tamponading pericardial effusion include a narrowing pulse pressure and reduction in stroke volume with partial preservation of cardiac output due to an increase in heart rate. These effects are evident in the simulation results of both the rapid and slow effusions, although the effects may be more pronounced than expected in the chronic case. As expected, acute effusion rapidly results in death. Future work will include a comparison of this low fidelity model of pericardial effusion to the BioGears® implementation of a higher fidelity constitutive law model derived using the techniques of composite material analysis. Cardiac Output BioGears® Standard Male – Healthy BioGears® Standard Male – Slow Effusion Heart Rate BioGears® Standard Male – Healthy BioGears® Standard Male – Slow Effusion Blood Pressure BioGears® Standard Male – Healthy BioGears® Standard Male – Slow Effusion