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Rheological properties of arteries under normal and experimental hypertension conditions
151
Letters to the Editor RHEOLOGICAL
PROPERTIES
OF ARTERIES HYPERTENSION
The recent paper by Sharma and Hollis in this journal (9 293-300 1976) underlines two disagreements currently existing in the literature of the arterial wall. The first concerns the incompressibility assumption used by Sharma and Hollis in, (i) the derivation of their true stress relationship (equation (1)). and (ii) their quoted modulus-water content relationship (equation (15)). Such an assumption is based on somewhat frail experimental evidence, as has been pointed out by McCrum and Dorrington (1976) while the opposite assumption has powerful theoretical and experimental backing (McCrum and Dorrington (1976), Grut and McCrum (1974)). Should this be the case, then an increase in strain on the vessel wall such as would be induced by the condition of hypertension would introduce a corresponding volume increase resulting in the increased water concentration recorded by Sharma and Hollis. The second point concerns the mechanical state of the elastin component under the conditions experienced in the vasculature. Sharma and Hollis claim, ‘essentially a perfect elastic behaviour’ of the rabbit aortic wall up to a critical strain c,,, and attribute this largely to the elastin fibres of the composite. This is in contradiction to earlier work (Dorrington et al., 1975) suggesting a viscoelastic response for elastin under typical arterial conditions. The viscoelastic responses of elastin and other components with their associated stress induced volume changes of the arterial wall may well play a major role in its nutrition through the stress assisted diffusion mechanism proposed by Dorrington et al. (1975). Any constraints on such a mechanism, for example, as would be generated by the increased [hypertension induced] wall stiffness noted by Sharma and Hollis could have detrimental effects on the healthy functioning of the arterial wail. Biomechanics Unit, University of Surrey, Guildford, Surrey, England
AUTHOR’S
UNDER NORMAL CONDITIONS
AND
EXPERIMENTAL
REFERENCES
Dorrington. K. L., Grut. W. N. and McCrum. N. G. (1975) The mechanical state of elastin. Nature 2%. 476-478. Gruit. W. N. and McCrum. N. G. (1974) Liauid droD model of elastin. Nature 251, 165. ’ McCrum, N. G. and Dorrington, K. L. (1976) Stress induced fluid transport in the aortic wall. J. Mot. Sci.. (in press).
When I started to read the review of “Swimming 2” in J. Biomechunics 9, p. 665 I thought it was merely a fine example of scientific gobbledygook. However, a closer reading showed that you had handed the job of reviewing to a brilliant but mischievous graduate student. Please compliment him or her on a marvellous piece of parody. I particularly enjoyed “With the increased biomechanics input in the optimum track performance index parameter analysis, we stand at the threshold of major redefinitions of the maximum performance capabilities.” It was a pleasing touch to put virtually the only words that actually meant anything in the whole review (body drag) into quotes, as if contact with the real world was in some way unreal. The last paragraph was exceptionally fine, with the nonsensical sentence “Dynamics analyses help equilibrate the drag, inertia and muscle forces acting on the body segments.” (I suppose before the analyses were made there was no equilibration; poor old Newton) leading to the splendid mixed-metaphoric and bathetic last sentence. A splendid spoof-but surely a bit unfair to Clarys and Lewillie; if they really exist.
W.N. GRUT Department
of
J. D. CURREY
Biology,
University of Heslington.
York, York, YOl SDD, England
REPLY TO THE LETTER TO THE EDITOR
My colleagues, Miller and Harris are to be congratulated for having produced an attractive alternative to the MoirC fringe approach to joint analysis. Their technique is interesting and has strong advantages when making measurements during continuous movements. Although the writers claim greater measurement accuracy for their technique. it would seem that the accuracy for motions on the order of 15 degrees will be the same. Whether one uses a single target of two grids or a target of a line and a point, the photographic information provided should be of the same accuracy. The real accuracy advantage of the Moirt fringe method is revealed in the interpretation of the photographic data gathered from two closely spaced positions. For angles less than 10 degrees the uncertainty associated with the interpretation of intersections of the two nearly parallel lines leads to considerable inaccuracy. In contrast, as the angle between two positions becomes smaller, the Moiri fringes become further
apart and are thus easier to identify. The present state-ofthe-art in Moire technology will allow accurate fringe identification and measurement down to a second of an arc. Although this type of accuracy is not required for human joint motion, it should be kept in mind that it is only as the angle between positions gets small that a pole of motion becomes an instant center of rotation. Nevertheless the accuracy provided by the method of Miller and Harris should be satisfactory for clinical measurements where the measured positions are separated by more than 10 degrees. This author will look forward with interest to the further research results of Miller and Harris in this area.
Department of Mechanical University of’ Houston, Texas, U.S.A.
Engineering.
T.E. SHOUP
ERRATUM ThePublisher
wishes to apologise for the following error. In the paper by V. J. MILLER, S. R. BUSSOLARI and J. R. SHANEBROOK in J. Biomechanics 9.663-664, the caption to Fig. 1 should read: Flow pattern across a Starr-Edwards
aortic valve (Model No. 1200, size 13A). The direction of flow is from left to right.
Letters to the Editor RHEOLOGICAL
PROPERTIES
OF ARTERIES HYPERTENSION
The recent paper by Sharma and Hollis in this journal (9 293-300 1976) underlines two disagreements currently existing in the literature of the arterial wall. The first concerns the incompressibility assumption used by Sharma and Hollis in, (i) the derivation of their true stress relationship (equation (1)). and (ii) their quoted modulus-water content relationship (equation (15)). Such an assumption is based on somewhat frail experimental evidence, as has been pointed out by McCrum and Dorrington (1976) while the opposite assumption has powerful theoretical and experimental backing (McCrum and Dorrington (1976), Grut and McCrum (1974)). Should this be the case, then an increase in strain on the vessel wall such as would be induced by the condition of hypertension would introduce a corresponding volume increase resulting in the increased water concentration recorded by Sharma and Hollis. The second point concerns the mechanical state of the elastin component under the conditions experienced in the vasculature. Sharma and Hollis claim, ‘essentially a perfect elastic behaviour’ of the rabbit aortic wall up to a critical strain c,,, and attribute this largely to the elastin fibres of the composite. This is in contradiction to earlier work (Dorrington et al., 1975) suggesting a viscoelastic response for elastin under typical arterial conditions. The viscoelastic responses of elastin and other components with their associated stress induced volume changes of the arterial wall may well play a major role in its nutrition through the stress assisted diffusion mechanism proposed by Dorrington et al. (1975). Any constraints on such a mechanism, for example, as would be generated by the increased [hypertension induced] wall stiffness noted by Sharma and Hollis could have detrimental effects on the healthy functioning of the arterial wail. Biomechanics Unit, University of Surrey, Guildford, Surrey, England
AUTHOR’S
UNDER NORMAL CONDITIONS
AND
EXPERIMENTAL
REFERENCES
Dorrington. K. L., Grut. W. N. and McCrum. N. G. (1975) The mechanical state of elastin. Nature 2%. 476-478. Gruit. W. N. and McCrum. N. G. (1974) Liauid droD model of elastin. Nature 251, 165. ’ McCrum, N. G. and Dorrington, K. L. (1976) Stress induced fluid transport in the aortic wall. J. Mot. Sci.. (in press).
When I started to read the review of “Swimming 2” in J. Biomechunics 9, p. 665 I thought it was merely a fine example of scientific gobbledygook. However, a closer reading showed that you had handed the job of reviewing to a brilliant but mischievous graduate student. Please compliment him or her on a marvellous piece of parody. I particularly enjoyed “With the increased biomechanics input in the optimum track performance index parameter analysis, we stand at the threshold of major redefinitions of the maximum performance capabilities.” It was a pleasing touch to put virtually the only words that actually meant anything in the whole review (body drag) into quotes, as if contact with the real world was in some way unreal. The last paragraph was exceptionally fine, with the nonsensical sentence “Dynamics analyses help equilibrate the drag, inertia and muscle forces acting on the body segments.” (I suppose before the analyses were made there was no equilibration; poor old Newton) leading to the splendid mixed-metaphoric and bathetic last sentence. A splendid spoof-but surely a bit unfair to Clarys and Lewillie; if they really exist.
W.N. GRUT Department
of
J. D. CURREY
Biology,
University of Heslington.
York, York, YOl SDD, England
REPLY TO THE LETTER TO THE EDITOR
My colleagues, Miller and Harris are to be congratulated for having produced an attractive alternative to the MoirC fringe approach to joint analysis. Their technique is interesting and has strong advantages when making measurements during continuous movements. Although the writers claim greater measurement accuracy for their technique. it would seem that the accuracy for motions on the order of 15 degrees will be the same. Whether one uses a single target of two grids or a target of a line and a point, the photographic information provided should be of the same accuracy. The real accuracy advantage of the Moirt fringe method is revealed in the interpretation of the photographic data gathered from two closely spaced positions. For angles less than 10 degrees the uncertainty associated with the interpretation of intersections of the two nearly parallel lines leads to considerable inaccuracy. In contrast, as the angle between two positions becomes smaller, the Moiri fringes become further
apart and are thus easier to identify. The present state-ofthe-art in Moire technology will allow accurate fringe identification and measurement down to a second of an arc. Although this type of accuracy is not required for human joint motion, it should be kept in mind that it is only as the angle between positions gets small that a pole of motion becomes an instant center of rotation. Nevertheless the accuracy provided by the method of Miller and Harris should be satisfactory for clinical measurements where the measured positions are separated by more than 10 degrees. This author will look forward with interest to the further research results of Miller and Harris in this area.
Department of Mechanical University of’ Houston, Texas, U.S.A.
Engineering.
T.E. SHOUP
ERRATUM ThePublisher
wishes to apologise for the following error. In the paper by V. J. MILLER, S. R. BUSSOLARI and J. R. SHANEBROOK in J. Biomechanics 9.663-664, the caption to Fig. 1 should read: Flow pattern across a Starr-Edwards
aortic valve (Model No. 1200, size 13A). The direction of flow is from left to right.