Today s s Agenda. Lunch Sam Hund s Computational Presentation The Web Site Subversion Repository. Sangria Project

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1 Today s s Agenda Lunch Sam Hund s Computational Presentation The Web Site Subversion Repository

2 A Multi-Physics Approach for Predicting Platelet-Mediated Thrombosis for the Evaluation and Design of Medical Devices Samuel J. Hund James F. Antaki, PhD, CMU Biomedical Engineering June 4 th, 2010

3 Motivation

4 THROMBOSIS

5 Intricacies of Thrombosis Injured Vessel Intrinsic Activation Foreign Surface Hemolysis HMWK FV, FXI Activation vwf binding Thrombin Extrinsic Activation (TF) Coagulation Cascade fg Repair Fibrinolysis PDGF Thrombus Fluid Shear Stress ADP vwf TxA2 PAF

6 Brief Review of My Work Computational Modeling of Blood Rheological Modeling Modeling of Hemolysis Modeling of Thrombosis Computational Optimization

7 Modified Krieger Model of Blood Viscosity Modified Krieger Model η wb = η pl φ 1 φ * N ( & γ, φ ) Quemada s Model 14 Parameters 1 or 3 discontinuities 10 Parameters No discontinuities

8 1000 Viscosity (cp) * * * Aggregation * * * Viscosity Function N = N agg +N def +N N=N def +N N=N * * * * * * * Experimental Data Whole Blood Blood w/o Fg Hardened Blood w/o Fg Deformation * * * * ,000 Shear Rate (s -1 )

9 Fahraeus-Lindqvist Effect Apparent viscosity (cp) * * * o o * o * * o o o * Data from Haynes, 1960 o Model Prediction * 1.4 o Tube Radius (mm)

10 RBC Transport

1000 500 0 0.100 0.0 0.100 Radial Position (cm) 0.8 0.

11 Platelet Concentration (x 1000/μl) 1500 Hematocrit (V/V) How do we predict the RBC concentration profile? Radial Position (cm) Goldsmith and Spain, 1984 Aarts et al, 1988

12 Part 1: Transport Down a Collision Gradient Directional Transport Velocity Small Velocity Difference Large Velocity Difference Net Transport

13 Part 2: Transport Down a Resistance Gradient Directional Transport Velocity High Resistance Low Resistance Viscosity Net Transport

14 Fluid Model Du ρ Dt = p + ) [ η(γ &, Hct ( u + u T )] BLOOD

15 Steady State Prediction of RBC Concentration Hematocrit

16 Temporal Profile Development Height (microns) Time Normalized Hematocrit

17 Plasma Skimming Uniform Inlet 0.5 Profile Develops Flow Division Hematocrit Palmer

18 Platelet Transport

19 Platelet Concentration (x 1000/μl) 1500 Hematocrit (V/V) Transport of RBCs and Plts in Microchannels Radial Position (cm) Goldsmith and Spain, 1984 Aarts et al, 1988

20 Theory of RBC-enhanced Platelet Exclusion Isotropic Diffusion Directional Transport

21 Extended Convection-Diffusion iffusion Model High-Concentration Solution C1s C1m Membrane Low-Concentration Solution C2s C2m C C 1s 2s = = ψ ψ C C 1m 2m

22 Empirical Results Sorensen Enhanced Diffusivity Model Enhanced Convection- Diffusion Model

23 Height (μm) 0 sec 50 sec 100 sec 150 sec 200 sec 250 sec 300 sec [Plt]/[Plt] ave

24 Prediction of Margination in Tube Flow Platelet Concentration (1000 plt/μl) [Plt] 50,000 plt/μl 120,000 plt/μl 250,000 plt/μl 500,000 plt/μl Aarts et al ECD Radial Distance (mm)

25 Hemolysis (Cell Trauma)

26 [ [ pfhb Hb pfhb Hb ] ] = = Hemolysis Modeling Richardson s Model (from Theory) Parameter A A α β Aηγ& A' α τ 2 t t 1 β + 1 = Power-Law Model A τ η Value +/- 95%CI (6.9+/-1.2)e 1.2)e-8 (4.07+/-1.39)e 1.39)e / t Is β+1 significantly different from 1? No p-value p = 0.42 Is α significantly different from 2? No p-value p = The over-all power-law model is actually significantly better than the Richardson model (p value ), but there is no confidence in the parameter β RMS Values: Richardson Model: Power-Law Model:

27 Prediction of Hemolysis in a Blood Shearing Device Exposure Time: Index of Hemolysis (%) Shear Stress (dyn/cm 2 )

28 ADP Release from RBCs ADP (μm) Data from Alkhamis et al Best Fit Proportional Line PROPORTIONAL MODEL Slope: / μm/mg% R2: pfhb (mg%) d [ ADP] d[ pfhb] = α dt dt Hemolysis can directly lead to platelet activation through the release of ADP ADP is an often neglected factor in shear induce platelet activation.

29 Hemolysis in a Nozzle

30 Early Predictions

31 New Predictors

33 Device Design

34 Cannula Simulation Asysimmetric, Laminar Flow Newtonian Flow Flow Rate: Q = 6 lpm

35 Platelet Activation in Various 375% increase Cannula Tips 40% increase 215% increase Blunt Tip QVC Blunt Tip

36 Flow Deviation Angle φ Comparative Index 14,

37 Stagnation Area skip

40 HemoGlide Bearing Strut Optimization Degrees of Freedom Moving Bezier Point Fixed Bezier Point Maximum Thickness Distance to Max Thickness Chord Length 40

41 Preliminary Results 41

42 Mathematical Model of (Platelet-Mediated) Thrombosis

43 The Role of Platelets TXB2 RP PPACK k pa Thrombin (Thr) Thombin- Antithrombin (TAT) Flow and Passive Transport TXA2 ADP AP + Heparin (Hep) Archodonic Acid Prothrombin (PT) Anitthrombin III (ATIII) Plt Deposition 43

44 Platelets Active: [AP] Resting: [RP] Agonists ADP [ADP] TxA2: [TxA2] Thrombin: [Thr] Coagulation Cascade Prothrombin: [PT] Antithrombin III [AT3] Sorensen Model of Platelet Deposition C t i u t v + u u S = F v + u C i ( k ) i Ci = Si 44

45 Reaction Rate Models PLATELET ACTIVATION GRANULE RELEASE Archodonic Acid SURFACE MEDIATED REACTION k pa S k [RP] ap = ADP Sadp = λ adp k pa[rp] TxA2 TxB2 S tx pa = λ [ AP] k [ TxA2] tx tx PT Thr TAT 45 ATIII S thr = ( k [ AP] + k [ RP] )[ PT ] Γ[ AT3][ Thr] at rt

46 Binary Activation Model TxA2 Ω = k pa w ADP ADP Thr [ ADP] [ ADP]* k pa + w TxA2 0 = Ω S Internal Signaling [ TxA2] [ TxA2]* Ω < 1 Ω 1 ap = + w Thr k pa Activation Rate [ Thr] [ Thr]* [RP]

47 Deposition Kinetics Κ r-as Transport Κ rs Κ aa k pa Κ aa 47 Platelet Deposition to Surface Platelet Deposition onto Active platelets

48 Weakness of Existing Model 1. Activation Kinetics 2. No Shear Dependent Activation 3. Active Cellular Transport 4. Valid for Collagen Only 5. Lacks Coagulation Cascade 6. Lacks Protein Deposition 7. Limited Anticoagulation/Plt 8. Effect of Growing Thrombus on Flow 48

49 Advanced Activation Kinetics

50 Internal Signaling Moer et al., New Perspectives on Drugs, 2004

51 Synergistic Activation of Platelets Platelets are activated by lower levels of agonist when in combination Example: Take: [Thr] and Current Model: Ω =.75, hence k pa = 0 Experimental Data Shows Activation (Ware( et al.)

52 Initial Model of Plt Activation 1 A 1 * A1 A 2 1 A * 2 TxA2 ADP Thr Internal Signaling Internal Signaling + Activation Activation Rate A 3 1 A * 3

53 Expanded Model of Plt Activation A 1 A 2 A 3 P1(s) P2(s) P3(s) 1 A * 1 1 A * 2 1 A * 3 + Activation Signal

54 Synergy Model of Plt Activation S 31 A 1 A 2 A 3 P1(s) P2(s) P3(s) S 1 S 21 S 2 S 3 W 1 W 2 W 3 1 S * 1 1 S * 2 1 S * 3 + Activation Signal

55 Synergy Model of Plt Activation A 1 A 2 A 3 * ~ 1 A 1 ~ 1 * A 2 * ~ 1 A 3 + A * i = A *0 exp i j= 1, i Activation Signal N β j j A j

56 Synergistic Activation Aggregation Rate Experiment Model Results Ω d[ AP] = k pa[ RP] dt 0 Ω < 1 k pa = Ω Ω 1 Ω = α * j j= 1.. N = o α j ω j exp i j i= 1.. N ciα i Model was fit to data for ADP, Thrombin, and Epinephrine. Data from Ware et al., J. Clin. Invest, 1987

57 Aggregometry Experiments Gives ATP release and % aggregation as a function of time Optical Morphological changes versus time???

58 Shear Induced Blood Trauma

59 Classic Shear Activation Model Shear Serotonin Released (Dense Granules) PSF Platelets Activated = τ t = 1000 Safe Zone Exposure Data: Hellums et al PSF: Boreda et al Jesty et al. 2003

60 D( PAF) S k = pa Dt τ = Damage Function = 0 PAF PAF * N T + PAF PAF * PAF PAF S * ( ) τ, t, x, PAF,[ RP] < 1 1 v

61 Validation Case Experiments The FDA/Marina s s Nozzles Coupling of Stress and Agonists Linkam Cell Stress alone (must define activation) Stress + Agonist Contracting Micro-channels channels

62 Surface Reactivity

63 Deposition Kinetics

64 Unknowns: Experiments Maximum surface coverage Rate of Resting and Active Platelet Deposition onto the Surface Rate of Active Platelets onto Other Platelets θ,, the instantaneous effect or rate at which a material by itself activates platelets Mass transfer rate

65 Deposition Kinetics

66 Experiments Flow Between Parallel Plates (k aa, k as, k rs ) (required) Direct measurement of platelets/area Possibly platelet morphology Maximum surface coverage Rocking or submersion testing Rate of platelet activation due to the surface

67 Example Fit to Experimental Data of Wagner and Hubbell

68 Cellular Transport Models

69 Transport Models Challenge: Large Number of Parameters Cannot be determined from Fully- Developed, Steady-State State flows

70 Channel Flow Experiments Vary flow rate to help isolate lift forces Vary plasma viscosity to isolate drag forces Get RBC concentration in a 3-Dimensional 3 field Get RBC velocity and plasma velocity

71 Experiments Complex Channel Flow Plasma with additives Track the concentration of RBC, while varying the plasma density Concentrated RBC suspension

72 Cell Scale Models

73 Experiments Still taking suggestions Cell settling and wall interactions Cell-Cell interactions (dilute interactions) Cell-Cell interactions (dense suspensions) Effect of changing internal pressure

74 HemoGlide Bearing Test 75mm FLOW CHAMBER ROTOMETER DIRECTION OF FLOW 30 o Pressure Taps PRESSURE TAPS CENTRIFUGAL PUMP Test Section LC SENSOR TEST SECTION ROI Y (a) X FLOW STRAIGHTENER 100mm (b) Z X 74

75 Web Site

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