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Cold Therapeutic Treatment: Analysis of Thermal Conduction on Structurally Damaged Tissue

This study aims to determine the optimal conditions for cold therapy in treating bruises and damaged tissues by analyzing the thermal conduction of structurally damaged tissue. The effectiveness of cold therapy at different temperatures and treatment durations is evaluated. The results suggest that icing the bruise at a higher temperature for a longer time is more effective.

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Cold Therapeutic Treatment: Analysis of Thermal Conduction on Structurally Damaged Tissue

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  1. Cold Therapeutic Treatment- Analysis of Thermal Conduction on Structurally Damaged Tissue - ABEN 453 - Group IX Sherry Lai Jeff S. Lee Bill Pottle Nicole Schlesinger

  2. Introduction to Cold Therapy • Bruises, or damaged tissues, are caused by an excessive external force. As a result, blood leakage into the interstitial layer occurs. • P.R.I.C.E. Injury Therapy • Ice packs are used to reduce swelling and inflammation.

  3. A Cause of Bruises

  4. Figure 2 (Geometric Mesh)

  5. Problem Objectives • Determine optimal conditions for cold therapy • Effectiveness number (tissue depth at 34°C/tissue depth at 5°C) • Dependent on: • Temperature of cold pack • Duration of treatment

  6. Cross Section of Tissue at 600 sec

  7. Assumptions • No Heat Generation in Damaged Tissue (Bruised Fat and Bruised Muscle) • Heat Generation + Bioheat Term (Skin and Muscle) • Weighted Properties in Bruised Tissue Layer ( = mass %) Cpa(tissue) =  Cp(blood) + (1- ) Cp(tissue) a(tissue) =  (blood) + (1- ) (tissue) a(tissue) =  (blood) + (1- ) (tissue) • Vm as a function of T • 36°C < T  Vm is a linear function of T • 36°C > T > 34  Vm approaches minimum value • T < 34  Vm is at a minimum value (0.02 m3/m3 sec)

  8. Linearization of Bioheat Source Term Q

  9. The Governing Equations Continuity Equation (ux/x) + (uy /y) + (uz/z) = 0 Energy Equation T/t =  (2T/x2 + 2T/ y2 + 2T/ z2) + Q/cp Bioheat Equation T/t =  (2T/x2+ 2T/y2 + 2T/z2) +Q/cp + Vmcp b(T-Ta)/cp   Heat SourceBioheat Term

  10. Geometry Initial and Boundary Conditions • Initial Conditions: • T(x,y,z,0) = 37ºC

  11. Material Properties:

  12. Results • Original Mesh (4,805 nodes) vs. Fine Mesh (15,376 nodes) • Less than 1% difference in temperature at t = 10 min • Effectivenss of cold therapy for Ticepack= 0, 1, 2, 3, 4°C and t = 5, 10, 15, 20 min • Effectiveness = (Depth at 34°C) (Depth at 5ºC)

  13. Effectiveness Vs. Time and Temperature

  14. Conclusion • In general, it is better to ice the bruise at a higher temperature for a longer time. • In practice, several things limit the time of icing. • Vasodilation occurs after 20 minutes of cold • Ice melting • Warmer temperatures are not effective for cooling

  15. Problems • AVOID SUBROUTINES AND CTC AT ALL COST! • SUBROUTINE USRSRC (NELT,NE,NG,SORCE,VARI,DVARI,NDFCD,LDOFU,SHP, • 1 DSDX,XYZL,PROP,TIME,NPTS,ndp,MNDP,IERR,IOPT) • C • C USER DEFINED SOURCE FOR ENERGY OR SPECIES EQUATIONS • C • C NELT = GLOBAL ELEMENT NUMBER • C NE = LOCAL ELEMENT NUMBER • C NG = GROUP NUMBER • C SORCE = HEAT OR SPECIES SOURCE (RETURNED VALUES) • C VARI = ARRAY OF SOLUTION VARIBLES AT INTEGRATION POINTS • C DVARI = GRADIENTS OF SOLUTION VARIABLES AT INTEGRATION POINTS • C LDOFU = pointer array for accessing vari and dvari information • C XYZL = X,Y,Z COORDINATES • C SHP = ELEMENT SHAPE FUNCTIONS • C DSDX = SHAPE FUNCTION DERIVATIVES IN THE X,Y,Z DIRECTION • C PROP = USER DEFINED PARAMETERS • C MNDP = FIRST DIMENSION OF SHAPE FUNCTION MATRICES • C TIME = TIME • C NPTS = NUMBER OF POINTS • C IOPT = 0 ENERGY EQUATION • C IOPT = N TRANSPORT EQUATION FOR SPECIES N (0<N<16) • C • #include "IMPLCT.COM" • #include "PARUSR.COM" • DIMENSION SORCE(NPTS) • DIMENSION SHP(NPTS,MNDP),DSDX(NPTS,NDFCD,MNDP),XYZL(NPTS,NDFCD) • DIMENSION PROP(*),VARI(NPTS,*),DVARI(NPTS,NDFCD,*),LDOFU(*) • ZRO = 0.D0 • C Begin Code defined by group 9 :Bruises • DO 100 I = 1,NPTS • IF (VARI(I,KDT)<34) THEN • SORCE(I)=53086-(1399*VARI(I,KDT)) • ELSE • IF ((VARI(I,KDT)>34) * (VARI(I,KDT)<36.4)) THEN • SORCE(I)=3497*VARI(I,KDT)*VARI(I,KDT)-38282*VARI(I,KDT)+3370000 • ELSE • IF (VARI(I,KDT)>36.4) THEN • SORCE(I)=11194*VARI(I,KDT)*VARI(I,KDT)-411225*VARI(I,KDT)-107402 • ENDIF • ENDIF • ENDIF • IF (IOPT.EQ.0) THEN • CALL ERMSGS (7001, 0, 3, • 1 0,0,0,0,0,ZRO,ZRO,ZRO,' ',' ',' ') • ELSE • CALL ERMSGS (7002, 0, 3, • 1 IOPT,0,0,0,0,ZRO,ZRO,ZRO,' ',' ',' ') • ENDIF • 100 CONTINUE • RETURN • END

  16. Solutions and Future Recommendations • A 2D model simulation • More accurate material properties • Mass Transfer • Size of bruise changes as a function of time

  17. Acknowledgments • Jifeng “Mr. FIDAP” Zhang • Professor Datta

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