New artery density, typically, is not a stable for even the same people artery; the brand new density-to-distance proportion h 0 / Roentgen 0 features normally 0
New scaling rules inside the Eq. thirteen degenerates with the MK Formula [1a] throughout the restriction out-of lower hypertension, gives An excellent > A good 0 ; therefore elizabeth a-1 ( An excellent ? A 0 ) 2 / ( cuatro An excellent 0 2 ) = ? 1 and you will e a-1 ( An excellent ? An effective 0 ) 2 / [ 4 ( A good 0 + A w a beneficial l l ) dos ] = ? 1 . Eq. eleven, within restrict Age z z = 0, after that becomes PWV = C a-1 An excellent w a good l l / [ 4 ? ( A great 0 + A w an effective l l ) ] , which is just like the brand new MK Equation [1a] having a thin artery wall structure [we.elizabeth., An excellent w an excellent l l / ( Good 0 + A w a beneficial l l ) = ? dos h 0 / R 0 ] from the no blood pressure levels.
However, for similar set of hypertension, Fig
fifteen and you may a difference out of 40% (19). Fig. 3C shows the stabilized tension P / C as opposed to PWV / C / ? to own h 0 / Roentgen 0 = 0.09, 0.several, 0.fifteen, 0.18, and 0.21, comparable to ±20% and you can ±40% differences out of h 0 / Roentgen 0 = 0.15. 3C will vary by the simply ?6%. To possess a-1 = 0.97 and a frequent distribution off h 0 / Roentgen 0 to your suggest 0.15 and you will SD ?, the fresh new suggest PWV was received while the PWV C ? = f [ P C , a-1 = 0.97 , h 0 Roentgen 0 ? N ( 0.15 , ? 2 ) ] , that will be revealed from inside the Fig. 3d for some thinking off ?. The fresh bend according to research by the imply h 0 / Roentgen 0 brings an exact family relations amongst the PWV and you can blood stress.
Fig. 4 A great and you may B measures up the present model (inside Eq. 13) on the classical MK + Hughes Equations (from inside the Eqs. 1a and you loveagain indir will 1b) to own a human artery described as this new Fung hyperelastic model that have C = 39 kPa, a-1 = 0.97, and you will h 0 / R 0 = 0.15 (19, 26). The brand new arterial hardness, or the similar tangent modulus Age, was shown within the Fig. 4A instead of the latest blood pressure levels P. Regarding range of people blood pressure level (5 kPa to help you ?20 kPa), brand new arterial stiffness is used to choose the thing variables for the the brand new Hughes Formula [1b] because Age 0 = 563 kPa and you will ? = 0.121 kPa ?step 1 , and therefore yields an effective agreement between your Hughes Formula and also the establish model. 4B means that the fresh MK + Hughes Equations overestimate the new PWV by the one thing away from ?2 compared to the current model. This high discrepancy is a result of the huge change out-of distance and you will occurrence of your artery wall structure (>50%), that’s forgotten on the MK Equations (on account of expectation ii) it is taken into account in the current model.
(A) The latest arterial firmness (equivalent modulus) E versus brand new blood pressure P to possess a human artery recognized from the Fung hyperelastic design; the latest Hughes Formula is even revealed, where the parameters Elizabeth 0 and ? are determined by fitting the new arterial hardness within the list of peoples blood pressure levels (5 kPa to ?20 kPa). (B) The fresh new blood pressure P versus the fresh PWV of your person artery, provided by the current model and also by the brand new MK + Hughes Equations, in which the variables Elizabeth 0 and you will ? decided of A beneficial. (C) This new hypertension P in the place of the fresh new PWV to the people artery described as the newest Fung hyperelastic design; the brand new MK + Hughes Equations are also found, where the variables Age 0 and you can ? about Hughes Picture are determined by the suitable within the listing of person blood pressure (5 kPa to help you ?20 kPa). (D) This new artery stiffness (comparable modulus) Elizabeth in place of the latest PWV of your own human artery, provided by the present model and by brand new Hughes Equation, where details Age 0 and you can ? are determined from C.