The latest Family relations Between Pressure and you can PWV to possess Linear Flexible Tube Wall space

This new fresh study all display strong need for the stress, and that certainly don’t support the MK + Hughes Equations

The linear stress?strain family members for the PDMS hoses, and Eq. 4, supplies the relation within stress P and you can interior urban area A beneficial since (discover Lorsque Appendix, Notice step one getting information) P = Age ? 4 [ dilog ( An excellent + A w a great l l An effective 0 + A great w a beneficial l l ) ? dilog ( A Good 0 ) ] + Elizabeth ? 8 [ ln ( An effective + A good w a great l l A 0 + A good w a good l l ) dos ? ln ( An excellent A beneficial 0 ) dos ] , in which Age ? = Elizabeth / ( 1 ? ? 2 ) ‘s the airplane filters modulus; ? = 0.5 ‘s the Poisson’s proportion getting PDMS; A beneficial 0 = ? R 0 2 and you will An effective w an effective l l = ? ( Roentgen 0 + h 0 ) 2 ? ? Roentgen 0 dos would be the interior a portion of the artery and the part of artery wall surface, respectively, rather than tension; and dilog ‘s the dilogarithm means (24). Replacing out of Eq. 6 on Eq. 2 gives the PWV since PWV = Age ? An effective cuatro ? [ A good 0 A ( An effective ? Good 0 ) ln A A beneficial 0 ? A great 0 + A great w good l l ( An excellent + A great w a good l l ) ( An excellent ? A good 0 ) ln ( Good + An effective w a great l l A 0 + An excellent w a beneficial l l ) ] . Eqs. 6 and you may 7 is parametric equations towards family between your heart circulation wave speed PWV and you will pressure P; elimination of the brand new advanced changeable An efficiency the next scaling law between the stabilized PWV and tension P: PWV Age ? ? = grams ( P Age ? , h 0 Roentgen 0 ) , where g was a good nondimensional mode revealed when you look at the Fig. 2E. It’s clear that PWV displays a powerful significance of P. To own evaluation, the brand new MK Picture [1a] forecasts a stable PWV (independent of the tension), and it is shown during the Fig. 2E. Fig. 2F shows that, with no parameter fitting, the newest family members between PWV and you may P obtained from Eq. 8 believes well toward within the vitro tests to possess 15:step one, step 17:step one, and you will 19:step one PDMS and repaired R 0 = six.3 mm, h 0 = 0.63 mm, and you will ? = step 1,one hundred thousand kilogram/m 3 getting drinking water. The result regarding water viscosity was found when you look at the Au moment ou Appendix, Note 2 and you can Fig. S3. Similarly, Fig. 2G shows advanced arrangement which have experimental outcomes for a couple thicknesses ( h 0 = 0.63 and 0.31 mm) of tube created from 19:1 PDMS and you will fixed R 0 = 6.step 3 mm, and you can ? = step one,000 kg/yards step three , without the parameter fitted.

The newest Family members Anywhere between Blood pressure levels and you can PWV for Human Artery Walls.

The human artery walls are well characterized by the Fung hyperelastic model (21), which has the strain energy density W = C 2 e a 1 E ? ? 2 + a 2 E z z 2 ? C 2 , where E ? ? and E z z are the Green strains in the circumferential and axial directions of the artery, respectively, and a 1 , a 2 , and C are the material parameters, which are related to the elastic modulus (at zero pressure) by E 0 = C a 1 . Following the same analysis, but with the linear elastic model replaced by the Fung hyperelastic model for human arteries, yields parametric equations for the polyamory date hesap silme relation between the pulse wave velocity and pressure, similar to Eqs. 6 and 7, as (see SI Appendix, Note 1 for details) P = 1 4 C e a 2 E z z 2 ? a 1 < erfi>, PWV = C e a 2 E z z 2 a 1 A 4 ? [ 1 A 0 e a 1 ( A ? A 0 ) 2 4 A 0 2 ? 1 A 0 + A w a l l e a 1 ( A ? A 0 ) 2 4 ( A 0 + A w a l l ) 2 ] . where erfi is the imaginary error function (25). Elimination of the intermediate variable A in Eqs. 10 and 11 yields the following scaling law between the normalized pulse wave velocity PWV and blood pressure P: PWV C e a 2 E z z 2 ? = f ( P C e a 2 E z z 2 , a 1 , h 0 R 0 ) , where f is a nondimensional function, and is shown in Fig. 3A for a 1 = 0.97 (26) and h 0 / R 0 = 0.15 (19) for the human artery. Fig. 3B examines the effect of artery stretching E z z by comparing the limit E z z = 0 of Eq. 12, which takes the form PWV C ? = f ( P C , a 1 , h 0 R 0 ) , to the scaling law in Eqs. 10 and 11 for a representative a 2 = 2.69 (21) and E z z = 0.1 and 0.2. The effect of artery stretching is negligible even for 20% stretching.