FINITE ELEMENT ANALYSIS OF BLOOD FLOW AND APPLY OF PRESSURE IN THE HUMAN THUMB AND APPLICATIONS IN DISEASE INVENTION

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1 CHAPER-II FINIE ELEMEN ANALYSIS OF BLOOD FLOW AND APPLY OF PRESSURE IN HE HUMAN HUMB AND APPLICAIONS IN DISEASE INVENION his Chapter Published in International Journal of Siene and Advaned ehnology (ISSN: ) Volue 1 No (April 011) pp 67-7

2 Chapter FINIE ELEMEN ANALYSIS OF BLOOD FLOW AND APPLY OF PRESSURE IN HE HUMAN HUMB AND APPLICAIONS IN DISEASE INVENION.1. INRODUCION A bioagneti fluid is a fluid exists in a living reature and its flow is influened by the presene of agneti field. he ost harateristi bioagneti fluid is blood, whih is epitoe of universe, whih an be onsidered as a agneti fluid beause the red blood ells ontain the heoglobin oleule, a for of iron oxides, whih is present at a uniuely high onentration in the ature red blood ells. he ost abundant ells in vertebrate blood are red blood ells. Blood is irulated around the body through blood vessels by the puping ation of the heart. Blood perfors any iportant funtions within the body inluding: supply of oxygen to tissues, supply of nutrients suh as gluose, aino aids, and fatty aids, iunologial funtions, inluding irulation of white blood ells, and detetion of foreign aterial by antibodies, oagulation, whih is one part of the body's self-repair ehanis, essenger funtions, inluding the transport of horones and the signaling of tissue daage, regulation of body P H, regulation of ore body teperature, hydrauli funtions et. But supree funtion is with lungs, arterial blood arries oxygen fro inhaled air to the tissues of the body, and venous blood arries arbon dioxide, a waste produt of etabolis produed by ells, fro the tissues to the lungs to be exhaled. It is found that the erythroytes orient with their disk plane parallel to the agneti field [6] and also that the blood possesses the property of diaagneti aterial when oxygenated and paraagneti when deoxygenated [47]. hus, blood irulation plays vital role in teperature regulation and disease ontrol. he uantitative predition of the

3 relationship between heodynais and heat ass transfer is of great interest, beause it is related to huan theral ofort, drug delivery, and noninvasive easureent. Biologial tissues ontain blood and the surrounding aterials where blood is perfuse to tissues via apillary network. he energy transport in tissues inludes ondution in tissues, onvetion between blood and tissues, perfusion through iro vasular beds, and etaboli heat generation. Aong these, the heat transfer between blood and tissues ould be of the greatest iportane. he Pennes [48] bioheat euation is the ost oon ethod that is available to desribe blood perfusion in the tissue. However, this ethod annot explain the onvetion between large vessels and tissues but an only explain the unifor perfusion of blood to tissues. Researhers also intend to analyze heat transfer in living tissues by odeling the detailed ounterurrent irovasular network. Chen and Holes [10] presented a bioheat transfer odel that aounts for the therally signifiant blood vessels. hey treated the blood vessels as two groups large vessels and sall vessels. Eah vessel is treated separately in the forer group, whereas all vessels are treated as a part of a ontinuu in the latter group. he theral ontributions of the sall blood vessels were onsidered fro the euilibration of blood teperature, onvetion of the flowing blood, and the sall teperature flutuations of the nearly euilibrated blood. Weibau and Jiji [77] proposed an alternative odel that aounts for the theral effet of the diretionality of the blood vessels and the harateristi geoetry of the blood vessel arrangeent. he vasular struture in the periphery was treated individually rather than as ontinuu edia in their three layer odel. Brink and Werner [8] presented a three-diensional theral and vasular odel in whih the onvetive heat exhange between the feeder vessels and tissue was oputed by the values for the Nusselt nuber and the teperatures in and near individual vessels were

4 predited. he therally signifiant vessels were treated individually aording to their distribution harateristis in different tissue layers. Fro these odeling studies, it is evident that investigation of the theral effets of large blood vessels and sall vessels is the ost iportant aspet. However, due to the high density and oplex arrangeent of iro vessels, little inforation about vasular geoetry an be obtained and the appliation of the vasular odels are liited for sall volues of tissue. hus, it is of great iportane to develop an easy-to-use odel for desribing the blood flow in different sizes of vessels. On the other hand, a blood-perfuse biologial tissue an be desribed as a porous edia in whih the fluid phase represents the blood and the surrounding tissue is represented by the solid phase. he theory of porous edia for heat transfer in living tissues ay be the ost appropriate sine it an desribe the perfused blood with fewer assuptions as opared to other bioheat odels. Wulff [80] first dealt with the living tissue as a porous ediu and utilized the onvetive ter, inluding the Dary veloity, to replae the blood perfusion ter in the bioheat euation. Xuan and Roetzel [81] used the transport theory through porous edia to odel the tissue-blood syste. he blood and tissue were onsidered to be in a non-euilibriu state and two energy euations were used to express heat transfer in the blood phase and solid phase. he advantage of this odel is that it inludes the exat blood perfusion in tissues, blood dispersion, and effetive tissue ondutivity and is onsidered to be appropriate for odeling a blood-perfused tissue. However, the flow in large blood vessels differs fro the filtration flow through tissues and ay be onsidered separately. Mesh generation based on the realisti geoetri odel is also of signifiane in perforing theral analysis in the living tissue. Geoetrial odeling and esh generation

5 based on edial iages. (C or MR iages) are widely used in biofluid ehanis and bioehanis analysis [9, 8]. he onventional steps to onstrut a oputational odel are iage proessing, geoetrial odeling, and esh generation. Although the different tehniues in edial iaging and oputational siulation need to be integrated, this tehniue to be integrated, this tehniue provides a rapid and valid ethod to odel the thero fluid and ehanis probles in living tissues. In this work it is aied to explain the finite eleent odel to analyze the blood flow and heat transport in the huan thub. he huan thub has diret link with brain, pituitary gland, pineal gland, ental nerves, head nerves, nek et. In partiular point of the thub pressure will be apply partiular part only stiulate and ativate. he finite eleent odels to analyze the blood perfusion and heat transport in the huan thub were developed based on the transport theory in porous edia with applying of pressure. Beause blood perfused biologial tissue an be desribed as a porous edia in whih the fluid phase represents the blood and surrounding tissue is prepared by the solid phase. he blood pressure and veloity at partiular tie were first oputed and orresponding values for the thub were subseuently transferred to the finite eleent odel as the boundary onditions. he purpose of this study is to odel blood-tissue heat transfer aording to the different harateristis of blood flow in large vessels and tissues. he systeati blood irulation in the upper lib has been odeled based on the onediensional flow in an elasti tube, and the finite eleent (FE) odel based on the heat transport in the huan thub. Further, the realisti geoetri odel for the huan thub was onstruted on the base of MR iage data. After oputing the apillary pressure and blood veloity in the tissue, the teperatures of the large vessels and the thub tissue were oputed siultaneously by nuerially solving the energy euation in the porous edia. he realisti geoetri odel for the thub was onstruted.

6 .. MAHEMAICAL FORMULAION FOR BLOOD FLOW DYNAMICS he blood flow in vessels has been odeled to be a one diensional flow in an elasti tube, and governing euations, inluding ontinuity and oentu, are expressed as B 0 t y (..1) B p vr t y B y B (..) Where y is the distane fro the heart, t is the tie, B is the ross- setional area of the blood vessel, is the blood flow rate, P is the Pressure, ρ is the blood density, v is the kineati visosity, δ is the boundary layer thikness, and r is the radius of the blood vessel. he pressure- area relationship for the arteries and veins is as follows: 4 Eh A 0 P( x, t) P0 1 3 r0 A (..3) p p 0 k p 1 A A 0 3 (..4) Where E is young s odulus, h is the wall thikness of the blood vessel, and k p is the oeffiient that is proportional to the bending stiffness of the tube wall..3. DARCY MODEL AND ENERGY EQUAION FOR BIOLOGICAL ISSUES

7 he Dary odel is onsidered to be the earliest flow transport odel in porous edia and is expressed as v K P (.3.1) Where K is the pereability of the tissues, μ is the visosity and v is the Dary veloity. Based on the assuption that there is loal theral euilibriu between solid tissues and blood flow, the energy euation is expressed as f s f s f p f p s p k k v t (.3.) Where t b 1 (.3.3) t b k k k 1 (.3.4) t b 1 (.3.5) Are the overall heat apaity per unit volue, overall theral ondutivity and overall heat prodution per unit volue of the tissue, respetively and φ is the porosity of the tissue. Considering the ontinuity euation and oentu euation, the diensionless pressure in porous edia is expressed as 0 y P x P (.3.6) he diensionless veloity is expressed as

8 x P Da u Re (.3.7) y P Da v Re (.3.8) Where Da is the Dary nuber and is expressed as D K Da (.3.9) he diensionless energy euation is as follows Pe y x Pe y v x u t 1 1 (.3.10) Where Pe,, and * are expressed as follows; D U Pe (.3.11) b ) ( ) ( (.3.1) a k D ) ( (.3.13) Euation (.3.10) an be suitably applied for heat transport in both large vessels and tissues. When it is applied to the heat transport in large vessels, both ε and φ attain a value of 1. Euation (.3.6)-(.3.8) and (.3.10) have been disretized using the finite eleent ethod (FEM), and the finite eleent euation has been developed using the Galerkin weighted residual ethod. First the onjugate gradient (CG) ethod was eployed to solve the euation (.3.6). he value of the pressure in the large vessel was obtained fro the blood

9 flow odel and was assigned as the boundary ondition of euation (.3.6). Seond the blood flow veloities in the tissues ware oputed. he slip ondution was eployed at the large vessel wall. Finally, the teperatures in large vessels and tissues were oputed siultaneously. A onstant blood teperature ondition is assigned to an inlet of a large artery in the finger. he heat transfer at the skin surfae is due to heat onvetion, radiation, and evaporation. hus, the boundary ondition at the surfae an be expressed as n r Bi r hrad s r E sk (.3.14) he flowhart of the oputational ethod is shown in the following Fig:.1. Blood Pressure Pressure Distribution of blood in tissues FE Model eperatures Cirulation in large vessels Model Veloity Veloities of blood in tissues and tissues Fig:.1: he flow hart of the oputational ethod

10 .4. GEOMERICAL MODELING FOR HE BLOOD VESSELS AND HUMAN HUMB Sine we use a one diensional flow odel to desribe the blood flow in arteries and veins the data of the ross-setional area and the length of the blood vessel are reuired and are defined on the basis of the statistial data [59]. he arterial blood flows into the arteries fro the base and it flows out fro the veins. he nuber of vessels in thub tip is large, and it is diffiult to desribe the blood flow through eah vessel. herefore, the thub tip part is desribed as a porous edia with higher porosity. he finite eleent eshes were thus developed aording to this odel. Fig.. shows the proess for onstruting the finite eleent odel fro MR iages. he MR iages of the vertial setion of the huan thub and the blood vessels were first taken. Subseuently, several iage proessing operators were applied in turns to redue the noise present in the original iage and substrate the iage data fro the bakground. he iage proessing inludes soothing, enhaning ontrast, and aritheti subtrating. A proessed iage was thus obtained and a text file with inforation on the brightness of eah pixel in the iage was reated. he text file of the iage inforation was then inputted and the oordinate of eah pixel for the thub was identified and the original finite eleent odel was onstruted. In order to generate a finite eleent odel for thero fluid oputation, the surfae of the original odel reuires soothing. he soothing approah is to fit disrete surfae areas by linear interpolation and generate eshes over these areas. After surfae soothing, the esh sizes were regulated suh that the eshes around the boundary part were saller and those in the inner part were oarse.

11 Iage Proessing Original esh Generation fro the pixel data Surfae soothing and esh regulating Identifying blood and other aterials in the eshes Coputational finite eleent odel Fig... he proess to onstrut finite eleent odel fro MR iages..5. RESULS he thero physial properties have been listed in able.1, whih are referred to the referenes [6, 60]. It is onsidered that the porosity of the tissue does not norally exeed

12 0.6 [44]. Based on the data in [60] we defined the porosity in the bone, tendon, skin, and fingertip as 0, 0.1, 0., and 0.3, respetively. Due to the large density of the vessels in the thub tip, the porosity was assigned a larger value. issue pereability was defined as [44]. It an be observed that the pressure differene is greater in the artery, whereas there is only a slight differene in the vein. hese data were assigned to the nodes that represent the artery and vein in the finite eleent odel and the pressure was set suh that it varied along the blood flow diretion but did not hange in the diretion noral to the flow diretion. he oputed inflow veloities in the finger artery and vein are 19 /s and 3.5 /s, respetively, and the Reynolds nuber in the oputation is 50 when the arterial veloity is the referene veloity. Sine the oputed veloity along the flow diretion slightly hanges in the large vessels, it is assigned to the blood nodes with unifor values. able. 1. hero Physial properties and porosities of soe organs

13 Bone endon Skin hub tip Blood 3 kg/ C J / KgK W / K eta W / DISCUSSION Iportant harateristi of this study is that the iage-based odeling ethod was eployed to onstrut the finite eleent odel. he realisti geoetry of the thub an be onstruted fro edial iages and this odel an be applied in analyzing other heat transfer probles in other living tissues. Further, the oputational tie an be signifiantly shortened as opared to that using through two diensional odel [60] to express the blood

14 flow in living tissues. he liitation of this ethod is that it reuires the onversion of the one-diensional blood veloity into the two-diensional inforation in the finite eleent odel..7. CONCLUSION With this the uantitative predition of blood flow rate, pressure variation and theral generation are great iportane for diagnosing daage or disorder or illness of above said partiular part.

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