BioGears Intrapericardial Pressure: World Congress of Biomechanics

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.

𝑪 =𝚫𝐕

𝚫𝐏 → 𝑷 =

𝑽

𝑪

𝑪 =𝒌𝟏

𝟏 + 𝒌𝟐𝑷𝒅𝑽𝒅𝒕

𝟑=

𝒌𝟏

𝒅𝑽𝒅𝒕

𝟑− 𝒌𝟐𝑽

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


Cardiac Output BioGears® Standard Male – Healthy


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


Blood Pressure BioGears® Standard Male – Healthy
