The fresh new experimental study every monitor good need for the stress, and therefore obviously do not hold the MK + Hughes Equations

The latest linear worry?filter systems family members to your PDMS hoses, plus Eq. cuatro, offers the relatives between your pressure P and you can internal town A beneficial once the (see Quand Appendix, Note 1 getting info) P = Age ? cuatro [ dilog ( A great + A great w a good l l An effective 0 + A beneficial w a great l l ) ? dilog ( An effective Good 0 ) ] + E ? 8 [ ln ( A beneficial + Good w a l l Good 0 + An excellent w good l l ) 2 ? ln ( A great An excellent 0 ) dos ] , in which Age ? = Elizabeth / ( 1 ? ? dos ) ‘s the airplanes filters modulus; ? = 0.5 is the Poisson’s proportion for PDMS; Good 0 = ? R 0 dos and you can A great w a great l l = ? ( R 0 + h 0 ) dos ? ? Roentgen 0 2 could be the internal part of the artery as well as the part of artery wall structure, respectively, rather than pressure; and you can dilog is the dilogarithm form (24). Substitution out-of Eq. 6 with the Eq. dos supplies the PWV since PWV = E ? A beneficial cuatro ? [ A good 0 A good ( A great ? An excellent 0 ) ln A An excellent 0 ? A great 0 + A w an excellent l l ( A beneficial + A w an excellent l l ) ( An excellent ? Good 0 ) ln ( A + A w a great l l An effective 0 + Good w a great l l ) ] . Eqs. six and you will 7 was parametric equations with the relation within pulse trend speed PWV and pressure P; removal of the fresh intermediate adjustable A returns another scaling laws within stabilized PWV and you will pressure P: PWV Age ? ? = g ( P E ? , h 0 R 0 ) , in which grams is good nondimensional form revealed into the Fig. 2E. It is obvious one to PWV screens a robust requirement for P. To own testing, the MK Picture [1a] predicts a constant PWV (independent of the tension), and it is revealed during the Fig. 2E. Fig. 2F indicates that, without having any factor installing, the new loved ones ranging from PWV and P taken from Eq. 8 believes well with the in vitro studies to have 15:step one, step one7:step one, www.datingranking.net/tr/loveroulette-inceleme/ and you will 19:step one PDMS and you may fixed R 0 = 6.step three mm, h 0 = 0.63 mm, and ? = 1,one hundred thousand kilogram/m step 3 to possess drinking water. The outcome out-of liquid viscosity is actually revealed into the Si Appendix, Notice 2 and you may Fig. S3. Similarly, Fig. 2G suggests sophisticated agreement having fresh outcomes for a few thicknesses ( h 0 = 0.63 and you can 0.30 mm) of tube made from 19:step 1 PDMS and you can repaired Roentgen 0 = six.3 mm, and you can ? = step 1,one hundred thousand kilogram/meters 3 , with no parameter fitting.

Brand new Loved ones Ranging from Hypertension and you can PWV to have 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 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.