Abstract
This examination of brachial artery (BA) differential characteristic impedance, ΔZ c, illustrates that changes in Z c can occur from changes in either BA wall stiffness (Young’s modulus, E) and/or its diameter, D. Furthermore, we assessed how changes in both E and D combine in either an isolated, synergistic, or antagonistic manner to yield the net change in BA Z c. The basis of this analysis is a partial differential equation which approximates ΔZ c as a total differential. The effects on BA ΔZ c of acetylcholine, atenolol, fenoldapine, nitroglycerin, hydrochlorothiazide and other medications are examined using data from previously published studies. Clinical situations which alter BA Z c, such as congestive heart failure, hypertension, and hyperemia, are also analyzed. Results illustrate the usefulness of the present approach in differentiating how medications, hyperemia, and pathological conditions affect BA ΔZ c by causing independent changes to E and/or D.
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Appendix: Derivation of the Approximate Total Differential for Characteristic Impedance
Appendix: Derivation of the Approximate Total Differential for Characteristic Impedance
The definition of characteristic impedance, based upon pulse wave velocity, from Eq. 4 is:
Substituting diameter (D), for area (A), where \( A = \pi D^{2} /4 \) yields:
Substituting the Moens–Korteweg equation (8), for pulse wave velocity, V pw:
Squaring both sides of (30) yields:
Using implicit differentiation:
The total differential is then approximated as:
Where:
and
Note that the following terms are also used:
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Atlas, G., Li, J.KJ. Brachial Artery Differential Characteristic Impedance: Contributions from Changes in Young’s Modulus and Diameter. Cardiovasc Eng 9, 11–17 (2009). https://doi.org/10.1007/s10558-009-9071-6
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DOI: https://doi.org/10.1007/s10558-009-9071-6