Heart and Circulatory Physiology

Cross-sectional area and volume compliance of porcine left coronary arteries

G. S. Kassab, S. Molloi


We have determined the cross-sectional area (CSA) compliance of the first several generations of pig coronary arteries and the volume compliance of the coronary arterial tree (vessels >0.5 mm in diameter) using a videodensitometric technique. The coronary arteries of four KCl-arrested maximally vasodilated pig hearts were perfused with iodine and 3% Cab-O-Sil. Because Cab-O-Sil occludes small arteries, the flow can be stopped and the pressure can be maintained while the trunk of the coronary artery and its subbranches are imaged using digital angiography. The coronary arteries were preconditioned several times with cyclic changes in pressure from 0 to 160 mmHg. The pressure was then varied in a triangular pattern, and the absolute CSA of each vessel and the total arterial volume were calculated using videodensitometry in conjunction with digital subtraction angiography. Our results have shown that the pressure-diameter and pressure-volume relationships are linear in the 60–140 mmHg pressure range. Furthermore, the compliance of the coronary arteries is small; i.e., the diameter of the coronary artery changes by <15% in the 80-mmHg pressure range. The compliance data couples the mechanics of the blood vessel wall to the mechanics of blood flow to yield a pressure-flow relationship for each coronary arterial segment.

  • distensibility
  • pressure-diameter relationship
  • digital subtraction angiography
  • videodensitometry

it is well established that the passive mechanical properties of blood vessel walls are important determinants of the pressure-flow (P-Q) relationship, the speed of pulse waves in vessels, the stress distribution in vessel walls, and the phenomena of mass transport through arterial walls (11). For these reasons the mechanical properties of coronary arteries have been studied extensively (2, 6, 13, 14, 16, 24, 29, 32, 36). Gregg and colleagues (16) measured (using mercury) the pressure-volume (P-V) relationship of the coronary arterial tree of dogs. Patel and Janicki (29) determined the pressure-diameter (P-D) relationship of segments of isolated left circumflex arteries of dogs. Douglas and Greenfield (6) measured the dynamic P-V relation of dog coronary arteries by obstructing the distal coronary bed with 200-μm-diameter beads. Additionally, Manor and co-workers (24) made in vivo measurements of P-V relationships of epicardial coronary arteries in dogs. The inverse of distensibility (stiffness) was determined for dog coronary arteries by Arts and colleagues (2) and Reneman and Arts (32) from wave-velocity measurements in vivo. The P-D relationship of excised coronary arteries from dogs and humans was measured by Gow and co-workers (14) and Gow and Hadfield (13), respectively; the diameters were recorded using an electrical caliper over a range of pressures. Tomoike and colleagues (36) also measured the P-D relationship of dog coronary arteries in situ (in the beating heart) using an ultrasonic dimension gauge with piezoelectric crystals. More recently, inflation and extension tests on isolated passive bovine, human, and porcine coronary arteries has been reported by Kang and co-workers (18) and Carmines and colleagues (4), respectively. Kang et al.'s study (18) revealed the general characteristics of heat-induced behavior, and Carmines et al.'s work (4) was used to formulate a two-dimensional stress-strain relationship.

Although these studies have yielded a wealth of quantitative information on the distensibility of some parts of the coronary vasculature, a systematic set of data on blood vessel elasticity in the pig heart does not exist. In this study, we present a systematic database on the compliance [the pressure-cross-sectional area (P-CSA) relationship] of the first several generations of the coronary arteries and the compliance of arterial volume (the P-V relationship).


Isolated heart preparation.

The studies were performed on four Duroc pigs weighing 19.3 ± 4.1 kg (range 15–24 kg). Surgical anesthesia was induced with ketamine (33 mg/kg im) and atropine (0.05 mg/kg im) and maintained with halothane (1–2%). Ventilation with 100% O2 was provided with a Harvard respiratory pump. Ventilator settings were adjusted during the experiments to maintain Po 2and Pco 2 within normal values. A midline sternotomy was performed and anticoagulation was induced with heparin (100 U/kg). An incision was made in the pericardium and the heart was supported in a pericardial cradle. The heart was arrested with a saturated KCl solution administered through a jugular vein. The heart was then excised with the ascending aorta clamped (to keep air bubbles out of the coronary vessels) and placed in a saline bath at room temperature. The right coronary artery (RCA) was ligated, and the left anterior descending (LAD) and left circumflex arteries were cannulated under saline to avoid air bubbles. The left coronary arteries were immediately perfused with an isoosmotic cardioplegic rinsing solution as described by Kassab and colleagues (20) to maintain a relaxed myocardium and a vasodilated vasculature. Nitroglycerin (30 μM) was added to the cardioplegic solution to dilate the large coronary arteries.

Determination of the P-CSA relationship.

The method of quantitative coronary angiography was used to determine the elasticity of the coronary arteries (vessels >0.5 mm in diameter) in the isolated heart preparation. The left coronary arteries were perfused with iodinated contrast material (Omnipaque; Nycomed Amersham; Princeton, NJ) and 3% Cab-O-Sil (Eastman Kodak), which is a colloidal silica that forms agglomerated particles with effective diameters that exceed those of small arteries (20). Hence the flow of iodine is zero during mechanical testing such that the imposed pressure is uniform throughout the coronary arteries that were imaged using digital subtraction angiography. The postmortem imaging experiments were completed within 1–2 h of euthanasia.

The arterial CSA change, as a function of pressure, was recorded for various vessel sizes. The coronary arteries were preconditioned with five cyclic changes in pressure from 0 to 160 mmHg, a procedure that improves the reproducibility of the stress-strain curves of the arteries (10). The pressure was varied in a triangular pattern with a slope of ∼1 mmHg/s. Coronary arteriograms were acquired at 1 frame every 5 s during the loading and unloading processes. The imposed pressure and X-ray tube voltage were continuously recorded (Biopac Systems; Santa Barbara, CA). This information was used to determine the arterial pressure during each image acquisition. For calibration purposes, a cylindrical vessel phantom that consisted of plastic tubing with different inside diameters (ranging from 0.95 to 4.75 mm) filled with contrast material was imaged over the heart region. The integrated gray levels in the vessel profiles were related to the known CSA values of the vessel phantoms. This information was used to directly convert the integrated gray levels to CSA values for the coronary angiograms. Once the CSA was measured, the effective diameter (D) could be easily computed (D = 4CSA½/π) for various pressures assuming that the coronary arteries were cylindrical.

Image acquisition and processing.

All images were acquired using a conventional X-ray tube (Dynamax 79-45/120; Machlett Laboratories; Stamford, CT), a constant potential X-ray generator (Optimus M200; Philips Medical Systems; Shelton, CT), a 23/15-cm cesium-iodine image intensifier, a focused grid (8:1 grid ratio, 36 lines/cm), and a charge-coupled device camera (Multicam MC-1134GN; Texas Instruments; Dallas, TX). Light intensity for the camera was controlled by an adjustable aperture. The video signal was linearly digitized to 640 × 480 × 8-bit precision using a Matrox Pulsar frame grabber (Matrox Electronics Systems; Dorval, Quebec, Canada) and a Pentium III computer.

The images were acquired using the 15-cm image-intensifier mode and the large (1.2 mm nominal) focal spot. Corrections were made for the spatially varying scatter and veiling glare. A convolution-filtering technique was employed to estimate scatter-glare distribution in images to avoid the need to sample the scatter-glare intensity for each experiment (8). This technique utilizes exposure parameters and the detected intensity distribution to estimate scatter-glare intensity by prediction of the total thickness at every pixel in the image. The thickness information is used to estimate scatter glare on a pixel-by-pixel basis.

Determination of the P-V relationship.

The determination of coronary arterial volume using digital angiography was recently reported (39). In brief, temporal subtraction images were formed after the images were corrected for scatter and veiling glare (8). A region of interest (ROI) that approximately outlined the visible epicardial arteries was manually drawn. A narrow background shell was drawn just outside the arterial ROI. The background ROI was used to correct for the iodine signal in the myocardium. The integrated videodensitometric signal was converted to iodine mass by using the system iodine-calibration curve. The calculated iodine mass was converted to volume by using the known iodine concentration of the contrast material.

Data analysis.

Blood vessels were grouped in size ranges corresponding to the largest three orders, and respective P-CSA values were determined. Kassab and colleagues (20) have previously shown that the diameter ranges of 0.5–1.0, 1.01–2.0, and 2.01–3.5 mm correspond to orders 9, 10, and 11, respectively. The P-D relationships were computed from the P-CSA values for the cylindrical arterial vessels. The P-D relationships in the 60- to 140-mmHg pressure range were then curve-fitted using linear regression, and the respective compliances were determined. The elastic deformation can be described by the equation D= αP + β, where D is the diameter at a given intravascular pressure (P) and α and β are constants. For the ease of comparing the compliance (α) of different-sized vessels, we computed the distensibility of each vessel segment by normalizing the compliance with respect to the diameter at the in vivo pressure (taken as 100 mmHg). Student's t-test and ANOVA were used to detect differences in compliance among the various sized vessels within a heart and among different hearts.


A typical postmortem coronary angiogram that was used to measure the CSA and volume of the different branches of the coronary arterial tree is shown in Fig. 1. The CSA and volume were determined from images corresponding to different pressures. The P-CSA relationship for an epicardial artery is shown in Fig. 2; the hysteresis loop can be seen during the loading and unloading ramps of pressure. The loading P-CSA relationship for the first several generations of left coronary arteries is shown in Fig. 3. The P-D relationship was computed from these data assuming that the coronary arteries had a circular cross section (as described inmethods). Our results show that the P-Drelationship is linear in the 60- to 140-mmHg pressure range. The means ± SD of α and β were computed using a linear least-squares fit in the 60- to 140-mmHg pressure range; these are summarized in Table 1 for the three largest orders. It is apparent that the compliance of the coronary arteries is small; i.e., the diameter of the coronary artery changes by <15% (5.4, 9.6, and 13% for orders 11, 10, and9, respectively) in the 80-mmHg pressure range.

Fig. 1.

X-ray image of the left coronary arterial tree.

Fig. 2.

Relationship between pressure (P) and cross-sectional area (CSA) for an epicardial artery. Least-square curves are of third-order polynomials (CSA = 1.0e −6P3 − 4.2e −4P2 + 4.3e −2P + 2.7;R 2 = 0.991 for loading, and CSA = 2.1e −6P3 − 5.3e −4P2 + 5.7e −2P + 2.7;R 2 = 0.987 for unloading).

Fig. 3.

Relationship between pressure and CSA for the first several generations of left coronary arteries. All curves correspond to a loading pressure ramp.

View this table:
Table 1.

Data for diameter compliance of the first several generations of the coronary arteries

The P-V relationship is also found to be linear in the same pressure range. The mean ± SD of the volume compliance of the four hearts was found to be (1.1 ± 0.45) × 10−3 ml/mmHg (R 2 = 0.965–0.999). The corresponding volume distensibility was found to be (1.1 ± 0.36) × 10−3 mmHg−1 (R 2 = 0.972–0.999). Figure 4 shows an example of the hysteresis loop of the P-V relationship for the main branches of the LAD arterial tree (vessels >0.5 mm in diameter). Figure 5 shows the loading P-V relationships of the four animals. The volume was normalized with respect to the volume at 100 mmHg.

Fig. 4.

Relationship between pressure (P) and volume (V) for the main branches (vessels >0.5 mm in diameter) of the left coronary artery. Least-square curves are of third-order polynomials (V = 1.1e −7P3 − 6.0e −5P2 + 7.9e −3P + 0.76; R 2= 0.998 for loading, and V = 2.1e −7P3 − 8.0e −5P2 + 1.0e −2P + 0.77;R 2 = 0.999 for unloading).

Fig. 5.

Relationship between arterial volume (V) [normalized with respect to volume at 100 mmHg (V100)] and pressure (P) for the four pigs. All curves correspond to a loading pressure ramp. Least-square curves are of third-order polynomials (V/V100 = 9.56e −8P3 − 4.09e −5P2 + 6.58e −3P + 0.660;R 2 = 0.984) volume at 100 mmHg pressure.



In the present study, the CSA and volume of the coronary arteries were determined using videodensitometric techniques. Using digital subtraction coronary arteriography, Molloi and colleagues (25-27) previously investigated new X-ray imaging techniques for quantification of coronary arterial CSA and volume. Videodensitometry techniques are based on the theoretical relationship between the thickness of contrast material present in the path of an incident X-ray beam and the detected intensity. The integrated gray levels along a scan line perpendicular to a vessel in a logarithmically transformed image yield a measurement of the CSA of the vessel if the nonlinear degradation factors (such as X-ray scatter, veiling glare, and beam hardening) are negligible or corrected (23, 25,26). The advantage of these techniques is that it is possible to quantitate absolute CSA without any assumption regarding the cross-sectional geometry. Moreover, the integrated gray levels in a vessel segment can result in a measurement of the lumen volume. These methods were used in the present study to quantitate the P-CSA relationship of the large left coronary arteries and the P-V relationship of the coronary arterial tree proximal to vessels of 0.5 mm in diameter.

Mechanical properties of blood vessels.

It is well known that blood vessels exhibit viscoelastic properties (10) such as creep (time-dependent increase in length while force is constant), relaxation (time-dependent decrease in force while length is constant), and hysteresis (differences in the loading and unloading curves). In the present study, we focused on the initial elastic response of the coronary vessels, which can be expressed in terms of compliance, distensibility, stiffness, or elastic modulus. Compliance is defined as the change in luminal dimension (diameter, CSA, or volume) divided by the corresponding change in pressure; stiffness is the reciprocal of compliance, and distensibility is a normalized compliance. Compliance can be measured under static or dynamic loading; the latter is referred to as the dynamic compliance or capacitance. In the present study, the loading history was relatively slow (i.e., slope of the ramp was ∼1 mm/s). Hence the reported measurements correspond to those of a static compliance.

Variation of distensibility with vessel diameter.

It can be shown that the distensibility [(ΔD/D 0)/ΔP] of a vessel is proportional to the diameter-wall thickness ratio (D/h) of the vessel and inversely proportional to the Young's modulus (E) of the vessel wall material (38); i.e., (ΔD/D 0)/ΔP = (D/2h)(1/E), where D0 is the diameter at 0 pressure. Our data show a statistically significant decrease in distensibility as vessel diameter increases (P = 0.001). This may be either due to a change in the diameter-to-wall thickness ratio or a change in Young's modulus due to changes in the proportion of various microstructural components (e.g., elastin, collagen, smooth muscle cells, ground substance, etc.). The variation in distensibility with diameter of coronary arteries is similar to that of pulmonary veins in cats (37).

Application of P-D relationship: determination of P-Q relationship of coronary circulation.

The question of mechanical properties can be formulated in many different ways. The P-D relationship has been extremely popular among cardiovascular physiologists because it plays an important role in the P-Q relationship of blood flow through an organ. Indeed, it can be shown that the compliance of the vasculature is an important determinant of the nonlinearity of the P-Q relationship (9). Kassab (19) has recently shown that a linear P-D relationship and a small compliance lead to a second-order P-Q relationship in a vessel segment. The second-order relationship is a modification of Poiseuille's law, which takes into account the distensibility of the blood vessel under the conditions of Newtonian steady-state laminar flow. Distensibility data in the literature suggest that the smaller coronary arteries and arterioles also obey a linear P-D relationship in the physiological pressure range with relatively small compliance (see review in Ref.5). Hence the second-order P-Q relationship may hold in the various segments of the coronary arterial tree. It should be noted, however, that in addition to compliance, the curvature of the P-Q relationship depends on a number of other factors such as the geometry and branching pattern of the vascular network, vessel-myocardium interaction, vascular tone, and blood rheology. It is interesting to note that in a diastolic vasodilated coronary vasculature the P-Q relationship reveals a second-order relationship (17).

Nonlinearity of the P-D relationship.

Our results show that the P-D relationship is nonlinear over the full range of pressure (0–160 mmHg). The P-Drelationship will be linear ifD(2hE)−1 remains constant as the pressure varies. In general, with increasing pressure, Dincreases and h decreases, whereas E increases (12, 30). The P-D relationship will remain linear only if the changes in D and hE are proportional. In the present study, we found that this occurs over the 60- to 140-mmHg pressure range. The linearity between pressure and diameter for the coronary arteries has been reported by other investigators in a similar pressure range (13, 14, 29,36).

Comparison with other works.

In Table 2, the diameter-distensibility data determined in this study are compared with those from the literature. Our results are in agreement with the in vivo and in vitro data from dogs (14, 29, 36). There are differences, however, between the elasticity of human coronary arteries and those of dogs and pigs (13). These differences are likely due to postmortem changes, because the human coronary arteries were stored overnight before being measured.

View this table:
Table 2.

Comparison of diameter distensibility data

Our data on the volume compliance are also in reasonable agreement with previous studies. Salisbury and colleagues (34) found that coronary arterial blood volume was a linear function of coronary arterial pressure between 30 and 125 mmHg. Morgenstern and co-workers (28) also found that total blood volume varies linearly with intravascular pressure in the 70- to 170-mmHg pressure range. The first estimate of arterial volume compliance in the passive arrested heart was provided by Gregg and colleagues (16). They obtained a static compliance value of ∼1 × 10−3ml/mmHg at a mean pressure of 80 mmHg. Subsequently, Patel and Janicki (29), using a similar method, obtained a value of 0.5 × 10−3 ml/mmHg. These data are in agreement with the value of (1.1 ± 0.45) × 10−3 ml/mmHg in the pressure range of 60–140 mmHg that was found in the present study.

Critique of methods.

Because edema may have an important effect on the distensibility of the coronary vessels, we attempted to prevent it in our isolated heart preparation. To avoid edema, we restricted the highest perfusion pressure to 160 mmHg. Furthermore, the cardioplegic solution used to perfuse the heart contained 6% dextran to ensure proper colloidal osmotic pressure. Finally, the hearts were weighed immediately after removal from the animal and at the conclusion of the distensibility experiments. We did not find a statistically significant change in heart weight. Hence it can be concluded that there was no significant edema in our isolated heart preparations.

An additional concern with a nonbeating isolated heart preparation is the accumulation of iodine in the tissue during the experiment. Because iodine is not washed out, it accumulates in the tissue of the passive arrested heart. Dimensional measurements (particularly volume) may be sensitive to this accumulation; therefore we were very careful about the choice of the ROI for volume measurements, and we excluded smaller vessels where iodine accumulation makes the vessel edge less distinguishable. We estimated the amount of diffused iodine and found it to be ∼1% during the time of measurements.

Finally, the compliance data in the present study correspond to those of dilated myocardium and vessels. Because the compliance of the myocardium and the smooth muscle tone of the blood vessels varies throughout the cardiac cycle and depends on the state of the heart, it is important to determine the compliance in a well-defined and reproducible state. The effects of myocardial contraction and smooth muscle tone can then be studied in relation to the relaxed myocardium in the vasodilated state. Myocardial contraction will increase the compliance of the vessels whereas the tone of vascular smooth muscle will decrease it.

Future investigations.

The mechanical properties of blood vessels are derived from collagen and elastin fibers, smooth muscle cells, and ground substances. There are numerous references in the literature to blood vessels and corresponding material components (see review in Ref. 11). The mechanical properties of blood vessels depend not only on the intrinsic properties of the blood vessel wall but also on the properties of neighboring tissue. The intramural coronary blood vessels are embedded in the myocardium where the interactions of blood pressure, vessel elasticity, smooth muscle tone, and tissue stress lead to complex time-dependent interactions between blood flow and muscle contraction. The transient muscle-vessel interaction is an important determinant of blood flow because the period of the cardiac cycle is considerably smaller than the time constant of coronary blood flow (35). The dynamics of the muscle-vessel interaction have been a subject of great interest to coronary physiologists. The systolic extravascular resistance model (15, 33), waterfall model (7, 31), nonlinear intramyocardial pump model (1, 3), and variable elastance model (21,22) have all been proposed to explain interactions between contraction and coronary blood flow. Hence a study of vessel compliance must take into account the vessel-myocardium interaction. The vessel-myocardium interaction is small for the large epicardial vessels (orders 10 and 11) and becomes more significant for the smaller intramural vessels (orders <10). Therefore the interaction of muscle contraction and intramural blood vessel elasticity during the cardiac cycle remains to be studied.


The authors thank Dr. John Breault and Ayesha Mian for excellent technical assistance.


  • This research was supported in part by National Heart, Lung, and Blood Institute Grant 5-R29-HL-55554 (to G. S. Kassab) and by an Established Investigation Award from the American Heart Association (to S. Molloi).

  • Address for reprint requests and other correspondence: G. S. Kassab, Dept. of Bioengineering, Univ. of California, 9500 Gilman Dr., La Jolla, CA 92093-0412 (E-mail:kassab{at}bioeng.ucsd.edu).

  • The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


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