Download Cardiac Function Curve

Cardiac Function Curve
Clive M. Baumgarten, Ph.D.
OBJECTIVES:
1. Describe the cardiac function curve (CFC)
2. Describe he relationships between (a) length and volume and (b) tension and
pressure
3. Identify diastolic and systolic pressure-volume curves
4. Construct a pressure-volume loop and describe the determinants of stroke volume
5. Describe heterometric compensation for changes in afterload and contractility
6. Generate the CFC from changes in right atrial pressure
7. Describe the factors that modulate the CFC
I. DEFINITIONS
A. Systole: Active contraction of the heart. About 1/3 of the cardiac cycle.
B. Diastole: Relaxation and refilling of chambers.
C. Heart Rate (HR): Number of contractions per minute (beats/min).
D. Stroke Volume (SV): Amount of blood ejected during systole (ml/beat)
SV = EDV - ESV
1. End Diastolic Volume (EDV): Volume of blood in ventricle the instant
before systole begins.
2. End Systolic Volume (ESV): Volume of blood in ventricle at completion of
systole as marked by closure of the aortic and pulmonic valves.
3. Ejection Fraction = SV/EDV ≥ 0.55
E. Cardiac Output (CO) = SV X HR
SV typically is 1 ml/kg. For a 70 kg individual
70 ml/beat × 72 beats/min = 5,040 ml/min ≈ 5 liters/min
F. Cardiac Index (CI) = CO/body surface area
CI = 2.2 - 4.0 L/min/m2
II. CARDIAC FUNCTION CURVE
The cardiac function curve relates right atrial pressure (RAP or PRA), the factor
controlling blood flow into the heart, to cardiac output, the blood flow from the
heart. The basis for the curve is essentially a transformation of 1-dimensional lengthtension relationships into 3-dimensions. A change in length gives a change in
volume, and tension gives pressure.
A. 1-D to 3-D transformation: assuming heart is a thin-walled sphere.
1-Dimension 3-Dimensions
Transformation
____________________________________________________________________________
Length (L)
Volume (V)
V = 4/3πr
3
;
C = 2πr
= 4/3π(C/2π)
3
3
V∝C
____________________________________________________________________________
Tension (T)
Pressure (P)
P = 2HT/r
____________________________________________________________________________
r = radius
C = circumference
H = wall thickness
1. Geometry causes amplification of length changes: volume α (length)3
2. Law of Laplace relates tension and pressure. Remember that tension controls
sarcomere length.
P = 2HT / r
Tension and, therefore, sarcomere length is related to P, r and H
T P T r T 1/H
B. A more accurate representation of the heart is as an ellipsoid:
V = 4/3 × (Dap/2)(Dlat/2)(Dmax/2)
III. STROKE VOLUME
A. Determinants of End Diastolic Volume.
Atrial pressure is the preload on the intact heart. During diastole Patrial is initially
greater than Pvent. Blood flows into the ventricle until the pressures are equal
(ignoring the inertia of blood). The volume contained at this time is EDV; the
pressure is end diastolic pressure (EDP). The relationship between diastolic
pressure and diastolic volume is the Ventricular Diastolic Pressure Curve.
B. Determinants of End Systolic Volume.
Arterial (aortic) pressure is the afterload on the intact heart. Fiber shortening and
ejection of blood cannot occur until intraventricular pressure just exceeds aortic
pressure. For the right ventricle, pulmonary artery pressure is the afterload.
Diastolic pressure in left ventricle is greater than that in right ventricle.
C. Isovolumetric (Isometric) Systolic Pressure Curve
Relates maximum isovolumetric developed pressure to EDV. To obtain the
curve, the aorta is cross-clamped to prevent injection of blood and fiber
shortening. Upon excitation, the contraction is isovolumetric; pressure increases
from its diastolic value, set by EDV and EDP, to a maximum pressure.
Connecting the maximum isovolumetric developed pressures obtained at different
EDV gives the isovolumetric systolic P-V curve. This relationship also is known
as Starling's Law of the Heart or the Frank-Starling relationship. We usually
use the curves for the left heart, but analogous curves can be drawn for the right
heart. Therefore, scales for both right and left atrial pressure are shown.
D. Pressure-Volume Loop
A cycle of contraction, ejection, relaxation and refilling is termed a pressurevolume loop. Combining the diastolic and systolic curves, allows determination
of SV (i.e., the amount of shortening) as a function of preload (EDV), afterload
(aortic pressure), and contractility.
These curves represent changes in only one variable while the others are held
constant. Physiologically, changes in one variable often cause a change in a
second.
1. Effect of preload. Initially (A), the left atrial pressure (~5 mm Hg) sets EDV
(140 ml). Upon excitation, the heart contracts isovolumetrically until (B),
when the aortic valve opens. Ejection of blood occurs, and ventricular
volume falls (B − C). Note, ventricular pressure is not really constant
during ejection because of the compliance of the aorta and the differing
rates of blood flow into and out of the aorta with time. At (C), the aortic
valve closes (ESP, ESV), and the ventricle relaxes isovolumetrically (C to D).
Intraventricular pressure (D) is now less than atrial pressure and filling begins
(D to A). If EDV is increased (A'), SV also increases (assume constant Paortic).
2. Similarly, the effect of changes in afterload and contractility on SV can be
determined from pressure-volume loops.
3. SV depends on:
•
•
Preload (EDV or PRA)
↑ preload → ↑ SV
and ↓ preload → ↓ SV
Afterload (Paortic)
↑ afterload → ↓ SV
and ↓ afterload → ↑ SV
$ Contractility
↑ contractility → ↑ SV and ↓ contractility → ↓ SV
E. Heterometric (Frank-Starling) Compensation
Pressure-volume loops and venous return combine to compensate for changes in
SV and help maintain CO. Compensation implies a return of SV towards
"normal" in response to a change in EDV, afterload or contractility.
The basis for compensation is a shift of blood volume (BV) between arterial and
venous circulation. Compensation operates over several beats and is incomplete.
(Because compensation is incomplete, physiologically HR is reflexively adjusted
to maintain CO and blood pressure.)
IV. CARDIAC FUNCTION CURVE
The cardiac function curve describes relationship between a right heart (input)
parameter (RAP) and a left heart (output) parameter (CO). To isolate effects of
RAP on CO, contractility, total peripheral resistance, and HR are held constant.
In contrast, afterload (aortic pressure) is allowed to vary as a function of flow (CO).
A. Linkage of right and left heart parameters follows from the series organization of
the system. Flow from the right ventricle (QR) is a function of RAP described by a
pressure-volume loop for the right heart. In turn, LAP is a function of QR. Finally,
LAP is a determinant of QL, i.e., CO.
B. To obtain the CFC, right atrium is attached to an infinite reservoir. The reservoir
height controls RAP. RAP is set to different values, and CO is determined at
each. At a constant HR, CO is a proportional to SV. Each pressure-volume loop
(see diagram) corresponds to a different RAP. Note, because TPR is held
constant, increased SV causes increased aortic pressure: Flow = ΔP/TPR .
Typical Values of P-V Loops (from previous Figure) for Constructing CFC Graph:
P-V Loops
RAP
EDV
ESV
SV
__________________________________________________________________
I
II
III
IV
0
4
7
10
140
240
335
510
60
100
160
335
80
140
175
175
__________________________________________________________________
Steepest part of cardiac function
curve is between RAP = 0 and 4
mm Hg; at RAP ≥7 mm Hg, the
CO reaches a plateau.
C. CO when RAP < 0. When RAP < 0, one might expect no flow into right atrium
and, consequently, a CO of 0. But, transmural pressure (PTrans = PIn - Pout) must
be considered. For practical purposes, the heart sits in the intrapleural space,
which has a negative pressure (about −4 mm Hg);. Note, pressures are measured
relative to atmospheric pressure (0 mm Hg). Thus, if RAP = −1, then PIn = −1
and PTrans = (−1) − (−4) = +3. Thus, heart will expand and fill with blood.
D. Plateau of Cardiac Function Curve. Several factors tend to limit CO as RAP
increases.
1. Increasing afterload − Increased afterload offsets increased preload (See
table above; compare EDV and SV at RAP of 7 and 10 mm Hg.)
•
As SV increases at a constant TPR, aortic pressure (afterload) increases.
FLOW = ΔP/TPR
The increase in afterload tends to limit SV.
•
The force-velocity relationship indicates that at high EDV, ejection of
blood is faster than at low EDV. With faster ejection of blood, Paortic
increases.
2. Pericardium − The pericardium is inelastic and limits EDV.
IV. MODULATION OF CARDIAC FUNCTION CURVE
A. Contractility:
$ ↑ contractility (positive inotropic intervention) → ↑ SV and ↑ CO.
$ ↓ contractility (negative inotropic intervention) → ↓ SV and ↓ CO.
B. Total peripheral resistance:
$ TPR → ↑ Paortic → ↓ SV and ↓ CO
$ TPR → ↓ Paortic → ↑ SV and ↑ CO
C. HR:
At a constant SV, an increase in HR
must increase CO. At HR > 100 bpm,
diastole is too brief for complete
filling, and EDV is reduced. HR × SV
peaks at ~125 bpm under the
conditions used to obtain the cardiac
function curve. Increases in contractility and vascular compensation can
give increases in CO up to HR of ~175
bpm in a healthy and fit patient.
D. Atrial contraction. During tachycardia, atrial contraction ("atrial kick")
makes an important contribution to
ventricular filling (up to 20%). At the
resting HR, however, atrial contraction
has only a minor effect on EDV (5%).
E. The time for diastolic filling of ventricle is inversely proportional to HR. At HR
≤100 bpm, filling is complete. At HR > 100 bpm, filling is incomplete, and if
TPR and contractility are constant, CO falls at HR > 125 bpm.
F. Effect of Heart Rate on Cardiac Output and Stroke Volume
1. Curve 1 makes the unphysiologic assumption that SV is independent of HR,
and therefore, CO is directly proportional to HR.
2. Curve 2 considers only the effect of ventricular filling time on SV and CO.
At HR > 125/min, CO falls.
3. Curve 3 considers the intact system and includes physiologic responses
normally seen at elevated HR (increased contractility and decreased TPR).
V. REFERENCES
A. Koeppen, B.M. and Stanton, B.A. Berne & Levy Physiology, 6th Ed., 2008. pp
325-328, 376-380.
B. Costanzo, L.S. Physiology, 3rd Ed., Saunders, 2006. Chapter 4, pp. 141-146.
3-cardiac function curve-2009.doc 8/28/2008