- Email: [email protected]
Water flux through porcine aortic tissue due to a hydrostatic pressure gradient
363
Atherosclerosis, @
24 (1976)
363-367
Ellsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
WATER FLUX THROUGH PORCINE AORTIC TISSUE DUE TO A HYDROSTATIC PRESSURE GRADIENT
ROGER
G. HARRISON
*
and THOMAS A. MASSARO
Chemical Engineering Department, Madison, Wis. 53706 (U.S.A.)
The University of Wisconsin,
(Received 22nd September,
1975) (Revised, received 24th March, 1976) (Accepted 24th March, 1976)
Summary The water flux through preparations of porcine aorta has been investigated. After an initial unsteady period a stable flux of approximately 2 @/cm*-h was reached and this flux rate remained constant for several hours. Under the experimental conditions which were maintained (110 mm Hg pressure drop across a 2 mm thick section of tissue) this total flux corresponds to a hydraulic conductivity of Q 7.0 X lo-l3 cm4/dyne-sec. Since these data were obtained in tissue samples where the endothelial layer was not intact, they represent values which are in fact larger than the actual in vivo condition where the endothelial barrier would serve as an additional resistance. Thus, they demonstrate that the transmural flux of water across the aorta wall in vitro due to a pressure gradient is extremely small and, therefore, that other mass transfer mechanisms may be significant. Key
words:
Hydraulic
conductivity -Hydraulic ,.~~_~~~
permeability
-Swine
aorta - Water flux
Introduction The water transport properties of the artery wall are prominent in several widely held theories of the development of atherosclerosis. In addition to conThis research was carried out with research support from the National Heart and Lung Institute 13954) and with fellowship suport (for RGH) from the National Defense Education Act. * Present address: Dr. Roger G. Harrison, The Upjohn Company, Kalamaz~oo, Mich. 49001, U.S.A.
(HL-
364
trolling the flow of water, these properties influence the flux of lipids, proteins, ions, and other small solutes into the artery wall and thus play an extremely important role in determining the overall chemical and metabolic environment of the vessel. Yet despite this significance, relatively little is known about the transport phenomena occurring in vascular tissue. As a result a program to investigate the mass transfer characteristics of the arterial wall has been instituted. The first step has been to measure the flow of water across in vitro sections of swine aorta and from these data to estimate the hydraulic conductivity of this tissue. The swine was selected for this study because (1) it is readily available, (2) the sequelae of atherosclerosis in man and pigs are similar and (3) at normal butcher weight the swine is of comparable size to an adult male (about 200 pounds) 111. Materials and Methods Sections of the descending thoracic aorta were obtained at slaughter and placed in oxygenated Hanks’ solution within 20 min of death. While loose fat and adventitia were removed, the tissue was rinsed continually with Hanks’ solution. A 21 mm diameter disc was cut along the ventral center line and inserted into the permeability cell within 60 min of the animal’s death. The cell used was similar to standard permeability cells developed to study membrane properties. A schematic of the cell is shown in Fig. 1. The design permitted continuous oxygenation of the solution in the high pressure or upstream compartment and accommodated tissues of varying thicknesses by an easily adjustable insert. This latter modification was necessary to reduce the possibility of undue compression or deformation which could possibly affect the magnitude of the results. Inside the cell the tissue was held in place between the two compartments by
____-----1___ 1 :;;: :: .;
TO CAPILLARY TUBE
‘.
:..i ..
... %...
‘. ‘,
-8
Cl LUCITE I ARTERY WALL
'0'RING
I STANLESS STEEL RI PIOUS STAINLESS STEEL Fig. 1. Schematic
of hydraulic
SCALE e-cm-
permeability
cell.
365
a circular porous stainless steel plate on the low pressue or downstream side. Both the upstream and downstream compartments were charged with Hanks’ solution which was buffered with 0.01 M Tris carbonate. After loading was completed and all air bubbles removed, the upstream compartment was connected to an oxygen supply regulated to 110 mm Hg pressure. The flux of water moving through the tissue under these conditions was measured by observing the motion of the meniscus in a calibrated capillary tube connected to the downstream chamber. The entire cell (including the capillary tube) was maintained in a 37” C water bath for the entire experiment. Light-microscopic observations of the intimal surface stained with silver nitrate indicate that the endothelial layer does not survive the mounting and incubation in the permeability cell. Results
The results from four permeability experiments different animals are shown in Fig. 2. After a period stable flux of approximately 2 /.#zrn*--h was reached several hours.
using tissue from four of decreasing total flux a and remained steady for
Discussion The total flux shown on the ordinate in Fig. 2 is a combination of several complex factors. In addition to the water flowing through the tissue due to the pressure gradient, i.e. hydraulic permeability, other mechanisms, such as flow due to viscous creep and water uptake or desorption by the cells of the tissue all enter into the total flux measurement. Additionally, in order for the hydraulic permeability to apply to the artery wall in its in vivo cylindrical geometry, a correction must be made for the direct effect on the hydraulic permeability of compression of the artery wall in the present experimental arrangement. Several experiments have been performed to evaluate the magnitude and
TIME
AFTER AP APPLIED. HR
Fig. 2. Four measurements of hydraulic permeability under identical conditions. with Hanks’ solution buffered with 0.01 M Tris carbonate without glucose.
Permeability
cell charged
366 importance of these various mechanisms [2] . Although determination of an exact value for each of these phenomena is very difficult and there is some variability in the data, the steady state flux due to hydraulic permeability alone was calculated to be less than or equal to 1.8 E.tl/cm’-h after all the above corrections are accounted for. The hydraulic conductivity (flux X thickness + pressure drop) corresponding to this flux is 7.0 X lo-l3 cm4/dyne-set assuming typical values of 2 mm for tissue thickness and 110 mm Hg for pressure drop. Colton et al. 133 using a similar permeability cell have found flux values across the pig aorta which are consistent with the present results although the time course of their experiment shows the total flux and the flux due to hydraulic permeability to be rising with time after an initial period and no steady state flux such as shown in Fig. 2. Yamartino et al. [4] found that for rabbit aorta the values for the hydraulic permeability obtained depend on the geometry of the experimental system. For a cell with planar geometry as in the present work, the permeability is approximately 1.5 pi/cm*-h at ‘a pressure drop of 100 mm Hg. However, for tissue in a cylindrical geometry the measured permeability rises to about 15 /A/cm*-h at this same pressure drop. They also reported the hydraulic conductivity to be 2.2 X lo-l3 cm4/dyne-set for the cylindrical geometry. Thus, a reasonable agreement is obtained between the flat tissue section used in the present study and a cylindrical geometry which more closely approximates the in situ condition. Wilens and McCluskey [5,6] reported fluxes of 15.6 and 12.2 /A/cm*-h at a pressure drop of 120 mm Hg for the human common iliac and external iliac arteries respectively in cylindrical geometry. They indicated that the flow across the human aorta was much smaller, but no numerical values were given. It is impossible to compute the hydraulic conductivity from their results since no tissue thicknesses were given, Jaeger [7] and Boughner and Roach [8] also measured fluid flow through the vascular wall in cylindrical geometry, but it is impossible to convert their reported perfusion values to flux data. Therefore, their results cannot be qualitatively compared to the present work. Since the tissue preparations used in the present study differ from the in vivo conditions in that the endothelial barrier is not intact during the permeability experiments, the total flux measurements obtained represent the absohte maximum that can be considered for the in vivo situation. In all probability, if it were technically possible to maintain the integrity of the endothelial layer during the mounting and incubation and fluid mixing involved in the permeability cell measurements, the measured total flux would be considerably less than the very small values shown in Fig. 2. Thus, the hydraulic permeability contribution to mass flux across the arterial wall may be much smaller than previously estimated and other mass transfer processes may be relatively more important. The present data can be used to provide additional insight into some of these other transport processes. For example, an estimate of lipoprotein concentration polarization at the aorta surface can be made following the analysis developed by Keller [9] . Using the upper limit for hydraulic conductivity found in this study, assuming a diffusion layer thickness of 0.05 cm and a lipoprotein
361
diffusion coefficient of 2.3 X lo-’ cm-‘/set, the concentration of low density lipoprotein at the wall of the thoracic pig aorta for normal blood pressures can be estimated to be only 10% greater than the concentration in the bulk stream [2]. This small concentration polarization is much less than that found in in vitro studies [lo] . In conclusion, the results of this study indicate that the transmural flux of water across the artery wall is very small. These results, which are consistent with other work, provide a quantitative basis on which to study other mass transfer phenomena in the vascular wall. References 1 Ratcliffe, H.L. and Luginbtihl. H.. The domestic pig -A model for experimental atherosclerosis, Atherosclerosis, 13 (19’71) 133-136. 2 Harrison, R.G.. Water Flow across the Isolated Artery Wall (Ph.D. Thesis), Madison, Wisconsin, The University of Wisconsin, 1976. 3 Colton. C.K., Smith, K.A.. Bratzler. R.L. and Lees, R.S., Transport properties of aortic tissue. Paper presented to the 65th Annual Meeting of the American Institute of Chemical Engineers. New York City, Nov. 29. 1972. 4 Yamartino, E.. Bratzler. R.. Colton. C. and Smith, K., Hydraulic permeability of arterial tissue, Circulation, 49 and 50 (Suppl. III) (1974) 273. 5 Wilens, S.L. and McCluskey, R.T.. The permeability of excised arteries and other tissues to serum lipid, Circ. Res.. 2 (1954) 175-182. 6 Wilens, S.L. and McCluskey. R.T.. The comparative filtration properties of excised arteries and veins, Amer. J. Med. Sci., 224 (1952) 540-547. 7 Jaeger, M., The flow through the artery wall. In: E.O. Attinger (ed.), Pulsatile Blood Flow, McGrawHill. New York, N.Y., 1964. pp. 307322. 8 Boughner, D.R. and Roach, M.R., Effect of low frequency vibration on the arterial wall, Circ. Res., 29 (1971) 136-144. 9 Keller, K.H., Maa transport in biological systems. In: L. Stark and G. Agarwal (Eds.), Biomaterials, Plenum Press, New York, N.Y.. 1969. pp. 103-118. 10 Colton, C.K., Friedman, S., Wilson, D.A. and Leeds, R.S.. Ultrafiltration of lipoproteins through a synthetic membrane, J. Clin. Invest., 61 (1972) 2472-2481.
Atherosclerosis, @
24 (1976)
363-367
Ellsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
WATER FLUX THROUGH PORCINE AORTIC TISSUE DUE TO A HYDROSTATIC PRESSURE GRADIENT
ROGER
G. HARRISON
*
and THOMAS A. MASSARO
Chemical Engineering Department, Madison, Wis. 53706 (U.S.A.)
The University of Wisconsin,
(Received 22nd September,
1975) (Revised, received 24th March, 1976) (Accepted 24th March, 1976)
Summary The water flux through preparations of porcine aorta has been investigated. After an initial unsteady period a stable flux of approximately 2 @/cm*-h was reached and this flux rate remained constant for several hours. Under the experimental conditions which were maintained (110 mm Hg pressure drop across a 2 mm thick section of tissue) this total flux corresponds to a hydraulic conductivity of Q 7.0 X lo-l3 cm4/dyne-sec. Since these data were obtained in tissue samples where the endothelial layer was not intact, they represent values which are in fact larger than the actual in vivo condition where the endothelial barrier would serve as an additional resistance. Thus, they demonstrate that the transmural flux of water across the aorta wall in vitro due to a pressure gradient is extremely small and, therefore, that other mass transfer mechanisms may be significant. Key
words:
Hydraulic
conductivity -Hydraulic ,.~~_~~~
permeability
-Swine
aorta - Water flux
Introduction The water transport properties of the artery wall are prominent in several widely held theories of the development of atherosclerosis. In addition to conThis research was carried out with research support from the National Heart and Lung Institute 13954) and with fellowship suport (for RGH) from the National Defense Education Act. * Present address: Dr. Roger G. Harrison, The Upjohn Company, Kalamaz~oo, Mich. 49001, U.S.A.
(HL-
364
trolling the flow of water, these properties influence the flux of lipids, proteins, ions, and other small solutes into the artery wall and thus play an extremely important role in determining the overall chemical and metabolic environment of the vessel. Yet despite this significance, relatively little is known about the transport phenomena occurring in vascular tissue. As a result a program to investigate the mass transfer characteristics of the arterial wall has been instituted. The first step has been to measure the flow of water across in vitro sections of swine aorta and from these data to estimate the hydraulic conductivity of this tissue. The swine was selected for this study because (1) it is readily available, (2) the sequelae of atherosclerosis in man and pigs are similar and (3) at normal butcher weight the swine is of comparable size to an adult male (about 200 pounds) 111. Materials and Methods Sections of the descending thoracic aorta were obtained at slaughter and placed in oxygenated Hanks’ solution within 20 min of death. While loose fat and adventitia were removed, the tissue was rinsed continually with Hanks’ solution. A 21 mm diameter disc was cut along the ventral center line and inserted into the permeability cell within 60 min of the animal’s death. The cell used was similar to standard permeability cells developed to study membrane properties. A schematic of the cell is shown in Fig. 1. The design permitted continuous oxygenation of the solution in the high pressure or upstream compartment and accommodated tissues of varying thicknesses by an easily adjustable insert. This latter modification was necessary to reduce the possibility of undue compression or deformation which could possibly affect the magnitude of the results. Inside the cell the tissue was held in place between the two compartments by
____-----1___ 1 :;;: :: .;
TO CAPILLARY TUBE
‘.
:..i ..
... %...
‘. ‘,
-8
Cl LUCITE I ARTERY WALL
'0'RING
I STANLESS STEEL RI PIOUS STAINLESS STEEL Fig. 1. Schematic
of hydraulic
SCALE e-cm-
permeability
cell.
365
a circular porous stainless steel plate on the low pressue or downstream side. Both the upstream and downstream compartments were charged with Hanks’ solution which was buffered with 0.01 M Tris carbonate. After loading was completed and all air bubbles removed, the upstream compartment was connected to an oxygen supply regulated to 110 mm Hg pressure. The flux of water moving through the tissue under these conditions was measured by observing the motion of the meniscus in a calibrated capillary tube connected to the downstream chamber. The entire cell (including the capillary tube) was maintained in a 37” C water bath for the entire experiment. Light-microscopic observations of the intimal surface stained with silver nitrate indicate that the endothelial layer does not survive the mounting and incubation in the permeability cell. Results
The results from four permeability experiments different animals are shown in Fig. 2. After a period stable flux of approximately 2 /.#zrn*--h was reached several hours.
using tissue from four of decreasing total flux a and remained steady for
Discussion The total flux shown on the ordinate in Fig. 2 is a combination of several complex factors. In addition to the water flowing through the tissue due to the pressure gradient, i.e. hydraulic permeability, other mechanisms, such as flow due to viscous creep and water uptake or desorption by the cells of the tissue all enter into the total flux measurement. Additionally, in order for the hydraulic permeability to apply to the artery wall in its in vivo cylindrical geometry, a correction must be made for the direct effect on the hydraulic permeability of compression of the artery wall in the present experimental arrangement. Several experiments have been performed to evaluate the magnitude and
TIME
AFTER AP APPLIED. HR
Fig. 2. Four measurements of hydraulic permeability under identical conditions. with Hanks’ solution buffered with 0.01 M Tris carbonate without glucose.
Permeability
cell charged
366 importance of these various mechanisms [2] . Although determination of an exact value for each of these phenomena is very difficult and there is some variability in the data, the steady state flux due to hydraulic permeability alone was calculated to be less than or equal to 1.8 E.tl/cm’-h after all the above corrections are accounted for. The hydraulic conductivity (flux X thickness + pressure drop) corresponding to this flux is 7.0 X lo-l3 cm4/dyne-set assuming typical values of 2 mm for tissue thickness and 110 mm Hg for pressure drop. Colton et al. 133 using a similar permeability cell have found flux values across the pig aorta which are consistent with the present results although the time course of their experiment shows the total flux and the flux due to hydraulic permeability to be rising with time after an initial period and no steady state flux such as shown in Fig. 2. Yamartino et al. [4] found that for rabbit aorta the values for the hydraulic permeability obtained depend on the geometry of the experimental system. For a cell with planar geometry as in the present work, the permeability is approximately 1.5 pi/cm*-h at ‘a pressure drop of 100 mm Hg. However, for tissue in a cylindrical geometry the measured permeability rises to about 15 /A/cm*-h at this same pressure drop. They also reported the hydraulic conductivity to be 2.2 X lo-l3 cm4/dyne-set for the cylindrical geometry. Thus, a reasonable agreement is obtained between the flat tissue section used in the present study and a cylindrical geometry which more closely approximates the in situ condition. Wilens and McCluskey [5,6] reported fluxes of 15.6 and 12.2 /A/cm*-h at a pressure drop of 120 mm Hg for the human common iliac and external iliac arteries respectively in cylindrical geometry. They indicated that the flow across the human aorta was much smaller, but no numerical values were given. It is impossible to compute the hydraulic conductivity from their results since no tissue thicknesses were given, Jaeger [7] and Boughner and Roach [8] also measured fluid flow through the vascular wall in cylindrical geometry, but it is impossible to convert their reported perfusion values to flux data. Therefore, their results cannot be qualitatively compared to the present work. Since the tissue preparations used in the present study differ from the in vivo conditions in that the endothelial barrier is not intact during the permeability experiments, the total flux measurements obtained represent the absohte maximum that can be considered for the in vivo situation. In all probability, if it were technically possible to maintain the integrity of the endothelial layer during the mounting and incubation and fluid mixing involved in the permeability cell measurements, the measured total flux would be considerably less than the very small values shown in Fig. 2. Thus, the hydraulic permeability contribution to mass flux across the arterial wall may be much smaller than previously estimated and other mass transfer processes may be relatively more important. The present data can be used to provide additional insight into some of these other transport processes. For example, an estimate of lipoprotein concentration polarization at the aorta surface can be made following the analysis developed by Keller [9] . Using the upper limit for hydraulic conductivity found in this study, assuming a diffusion layer thickness of 0.05 cm and a lipoprotein
361
diffusion coefficient of 2.3 X lo-’ cm-‘/set, the concentration of low density lipoprotein at the wall of the thoracic pig aorta for normal blood pressures can be estimated to be only 10% greater than the concentration in the bulk stream [2]. This small concentration polarization is much less than that found in in vitro studies [lo] . In conclusion, the results of this study indicate that the transmural flux of water across the artery wall is very small. These results, which are consistent with other work, provide a quantitative basis on which to study other mass transfer phenomena in the vascular wall. References 1 Ratcliffe, H.L. and Luginbtihl. H.. The domestic pig -A model for experimental atherosclerosis, Atherosclerosis, 13 (19’71) 133-136. 2 Harrison, R.G.. Water Flow across the Isolated Artery Wall (Ph.D. Thesis), Madison, Wisconsin, The University of Wisconsin, 1976. 3 Colton. C.K., Smith, K.A.. Bratzler. R.L. and Lees, R.S., Transport properties of aortic tissue. Paper presented to the 65th Annual Meeting of the American Institute of Chemical Engineers. New York City, Nov. 29. 1972. 4 Yamartino, E.. Bratzler. R.. Colton. C. and Smith, K., Hydraulic permeability of arterial tissue, Circulation, 49 and 50 (Suppl. III) (1974) 273. 5 Wilens, S.L. and McCluskey, R.T.. The permeability of excised arteries and other tissues to serum lipid, Circ. Res.. 2 (1954) 175-182. 6 Wilens, S.L. and McCluskey. R.T.. The comparative filtration properties of excised arteries and veins, Amer. J. Med. Sci., 224 (1952) 540-547. 7 Jaeger, M., The flow through the artery wall. In: E.O. Attinger (ed.), Pulsatile Blood Flow, McGrawHill. New York, N.Y., 1964. pp. 307322. 8 Boughner, D.R. and Roach, M.R., Effect of low frequency vibration on the arterial wall, Circ. Res., 29 (1971) 136-144. 9 Keller, K.H., Maa transport in biological systems. In: L. Stark and G. Agarwal (Eds.), Biomaterials, Plenum Press, New York, N.Y.. 1969. pp. 103-118. 10 Colton, C.K., Friedman, S., Wilson, D.A. and Leeds, R.S.. Ultrafiltration of lipoproteins through a synthetic membrane, J. Clin. Invest., 61 (1972) 2472-2481.