Finite Element Modeling of Vasoreactivity Using COMSOL Multiphysics Software

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1 Finite Element Modeling of Vasoreactivity Using COMSOL Multiphysics Software Jaimit Parikh, Adam Kapela and Nikolaos Tsoukias 9 th October 2014

or many layers of SMCs Role of Microcirculation: Regulate blood flow Tissue

2 INTRODUCTION Microvascularture: Blood vessels < 150 µm Longitudinally arranged single layer of ECs surrounded by perpendicular arrangement of one or many layers of SMCs Role of Microcirculation: Regulate blood flow Tissue perfusion Regulates blood pressure and responses to inflammation Microcirculation EC SMC 2

SIGNIFICANCE High blood pressure: 1 in 3 adults in US.

all models of hypertension and altered arteriolar tone can

3 SIGNIFICANCE High blood pressure: 1 in 3 adults in US. [1] Almost 3 of 4 patients that experience their first heart attack or stroke are hypertensive. [1] Peripheral vascular resistance is increased in virtually all models of hypertension and altered arteriolar tone can affect renal function and the ability of the kidneys to regulate blood pressure. [2] [3] 3

4 GOAL Complex mechanisms at the molecular, cellular levels participate in the regulation of vascular resistance and hence the vessel tone. Develop theoretical models to better understand mechanisms modulating 2+ and V m dynamics that regulate vascular resistance, blood flow and pressure in health and in hypertension In particular: Quantification and role localized 2+ signals via TRPV4 channels and localized NO signaling in vessel tone modulation rdiac Output Blood Pressure SMC Membrane Voltage Total Peripheral Resistance Diameters of Small Arteries Constriction/Re laxation of SMC s SMC Cytosolic 2+ 4

5 STEP 1: Ion Channels METHODS Fitting of current-voltage data for the individual channel provides a mathematical description for each channel K ir2.1 I G Kir V = Kir,max G = V m Kir ( V E ) Kir,max m V V 1 + e = G E K υ Kir Kir,h ( + [K ] ) o K n Kir 5

Model: 11 ODEs 26 ODEs solved solved using using Gear s Gear s backward backward

6 STEP 2:Single Cell Models METHODS Incorporates major channels, pumps and accounts for balance of 2+, Na +, K +, Cl -, and IP 3 Endothelial Smooth Muscle Cell Cell Model: Model: 11 ODEs 26 ODEs solved solved using using Gear s Gear s backward backward differentiation differentiation formula method formula for method stiff systems for stiff systems 6

EC MODEL SET OF ODEs METHODS dvm 1 = ( I Cm d I i = d I S1 IP = d I S 2 = SOC, 3R CICR I 2I NCX P NSC, SERCA, S1 Ileak, S1 I IP3R SERCA, S 2 ICICR Ileak, S 2 SERCA, S1 2 F vols1 I SERCA, S 2 2 F vols

7 EC MODEL SET OF ODEs METHODS dvm 1 = ( I Cm d I i = d I S1 IP = d I S 2 = SOC, 3R CICR I 2I NCX P NSC, SERCA, S1 Ileak, S1 I IP3R SERCA, S 2 ICICR Ileak, S 2 SERCA, S1 2 F vols1 I SERCA, S 2 2 F vols 2 leak, S1 leak, S 2 db = kbon i dna I SOC Na + 3I i NCX NSC, Na + 3I = F voli dk I SK i IK Kir NSC K 2I = F voli dcl I i NaKCl _ Cl VRAC CC = 1 F voli dip 3 = Q IP GIP3 kdip3 3 dq dp GIP3 ( BT B ) kboff B, NaK 0. 5 IP3 O, CC ( t) PO, CC, SS PO, CC Q = GIP3, SS = τ SOC Q GIP3 τ NSC CC VRAC I, NaK 0. 5 ( t) CC NaKCl _ Cl I K IK SK NaK ir NCX + 2 F vol NaKCl _ Cl I PMCA ) 11 Nonlinear ODE ~ 60 Model parameters Values acquired from RMA-EC, other EC, other cell types 7 GSAW:SCHOLARLY FORUM

8 MICROPROPJECTIONS Traditional transmission electron photomicrograph ( 15,000) of the arterial wall [5] Schematic of channels and cellular components localized in the microprojections 2. Hbα 1. enos TRPV4 8

STEP 3: FINITE ELEMENT EC-SMC MODEL METHODS Q NO = Q NO,max 4.2 i 4.2 i + K NO m, 4.

To incorporate exact geometries of microdomain structures like micorprojections and implement spatial localization of cellular components

] i [K + ] i [ 2+ ] i 3R RyR SERCA leak _ V _ m _ K V K leak PMCA + + + CSQN Na ER + K + Cl - IP NCX 3R SERCA CM IP 3 [Cl - ] i [Na + ] i

9 STEP 3: FINITE ELEMENT EC-SMC MODEL METHODS Q NO = Q NO,max 4.2 i 4.2 i + K NO m, 4.2 [ enos] [ enos] avg Allow to examine spatiotemporal changes in 2+ and V m dynamics. To incorporate exact geometries of microdomain structures like micorprojections and implement spatial localization of cellular components SMC EC NE NSC VOCC SOC Cl R G PLC DAG + NCX NaKCl BK NaKα1 2+ 3Na + _ 3Na + Na + -K + -2Cl - 2K + PIP2 IP 3 CSQN CM SR [Cl IP - ] i [Na + ] i [K + ] i [ 2+ ] i 3R RyR SERCA leak _ V _ m _ K V K leak PMCA CSQN Na ER + K + Cl - IP NCX 3R SERCA CM IP 3 [Cl - ] i [Na + ] i [K + ] i [ 2+ ] i _ G PLC A ev m K IR SK NSC SOC VRAC CC NaK PMCA COMSOL Multiphysics Membrane Currents implemented as boundary 1 n. N S = conditions I S, K z F Electro-diffusion for ionic transport Diffusion for second messenger S K 12

10 TRPV4 SPARKLET ACTIVITY Time =100 =200 =4000 ms ms 2+ (mm) SMC RESULTS µμ peak 2+ concentrations locally Activation of IK channels 6 µm away from TRPV4 channel 0.2µm EC 3 µm IK EC 50 EC RELAXATION OF VESSEL TONE

11 RESULTS NO DIFFUSION DURING SMC STIMULATION SMC SMC EC RBCs NO (nm) NNNN SSSSSS (nm) enos U L L L Hbα - - U L [2x10-4 fmole] GSAW:SCHOLARLY FORUM 11 EC enos Hbα

SUMMARY The developed models serves as a tool for assisting investigations on the regulation of vascular tone in health and disease, and development of rationale therapeutic strategies for disease

Activation of single TRPV4 channel can result in few mm peak 2+ concentrations locally which may result in 8-10 mv hyperpolarization of SMC and vessel relaxation.

12 SUMMARY The developed models serves as a tool for assisting investigations on the regulation of vascular tone in health and disease, and development of rationale therapeutic strategies for disease like hypertension. Allows quantification and better understanding of 2+ dynamics regulation. Activation of single TRPV4 channel can result in few mm peak 2+ concentrations locally which may result in 8-10 mv hyperpolarization of SMC and vessel relaxation. Localization of enos in the vicinity of MP may result in NO mediated feedback during SMC stimulation (i.e. PE, NE) Modulation of NO biovailability by Hbα is enhanced by the colocalization in the MP RBC perfusion will decrease the ability of Hbα to modulate NO levels and μm levels of EC Hbα are required for a significant modulation of SMC NO availability 1. TRPV4 12

13 REFRENCES 1. AS, Lloyd-Jones DM et al Heart disease and stroke statistics update: a report from the American Heart Association. Circulation 125: e2-e220, Tsoukias NM. et al. A theoretical model of nitric oxide transport in arterioles: frequency- vs.amplitude-dependent control of cgmp formation. Am J Physiol Heart Circ Physiol 286: H1043 H1056, Tran CH. et al. Endothelial 2+ wavelets and the induction of myoendothelial feedback. Am J Physiol Cell Physiol 302: C ,

14 ACKNOWLEDGEMENTS Florida International University Biomedical Engineering Department American Heart Association National Institutes of Health COMSOL CONFERENCE Samantha Dages Angelica Arias Jennifer Ardila

15 THANK YOU 15

Nature Neuroscience: doi: /nn Supplementary Figure 1

Nature Neuroscience: doi: /nn Supplementary Figure 1 Supplementary Figure 1 Relative expression of K IR2.1 transcript to enos was reduced 29-fold in capillaries from knockout animals. Relative expression of K IR2.1 transcript to enos was reduced 29-fold