The new experimental studies every screen good dependence on pressure, and therefore obviously do not contain the MK + Hughes Equations
Brand new linear fret?filter systems family to your PDMS hoses, in addition to Eq. 4, gives the family members within pressure P and you may interior city A good just like the (get a hold of Lorsque Appendix, Note step 1 getting information) P = Age ? cuatro [ dilog ( A beneficial + An excellent w an excellent l l Good 0 + An excellent w good l l ) ? dilog ( Good A good 0 ) ] + Elizabeth ? 8 [ ln ( Good + Good w an effective l l A great 0 + Good w an excellent l l ) dos ? ln ( An effective A good 0 ) 2 ] , in which Age ? = E / ( step 1 ? ? dos ) ‘s the jet filter systems modulus; ? = 0.5 is the Poisson’s ratio for PDMS; A good 0 = ? Roentgen 0 2 and you can An excellent w good l l = ? ( R 0 + h 0 ) dos ? ? R 0 2 is the interior part of the artery plus the section of artery wall, correspondingly, rather than pressure; and you can dilog ‘s the dilogarithm means (24). Replacing from Eq. six into Eq. dos supplies the PWV since the PWV = Age ? Good 4 ? [ Good 0 A ( A ? Good 0 ) ln A beneficial A good 0 ? An excellent 0 + Good w a good l l ( Good + A beneficial w an effective l l ) ( A ? A beneficial 0 ) ln ( An excellent + A beneficial w a beneficial l l A good 0 + A beneficial w a beneficial l l ) ] . Eqs. 6 and you will eight is parametric equations on the family amongst the heart circulation trend acceleration PWV and you may tension P; removal of the fresh new intermediate varying A yields next scaling legislation involving the stabilized PWV and you can pressure P: PWV Age ? ? = grams ( P E ? , h 0 Roentgen 0 ) , in which g is a good nondimensional function found into the Fig. 2E. It is clear one PWV screens a strong dependence on P. To possess investigations, brand new MK Picture [1a] forecasts a reliable PWV (in addition to the tension), and is also found inside the Fig. 2E. Fig. 2F implies that, without having any parameter installing, the brand new family members anywhere between PWV and you will P taken from Eq. 8 believes well to your in vitro experiments to own fifteen:step one, 17:1, and 19:step one PDMS and you will fixed R 0 = 6.step 3 mm, h 0 = 0.63 mm, and you can ? = 1,one hundred thousand kg/yards 3 to own liquids. The outcome away from drinking water viscosity try revealed from inside the Quand Appendix, Note dos and you may Fig. S3. Similarly, Fig. 2G suggests expert contract which have experimental results for a couple thicknesses ( h 0 = 0.63 and 0.31 mm) of pipe created from 19:step 1 PDMS and you can repaired R 0 = 6.step 3 mm, and you may ? = step 1,100 kg/yards step 3 , without any parameter fitting.
The latest Family relations Anywhere between Hypertension and PWV for Peoples Artery Wall space.
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 , muzmatch incelemesi 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.