Laser-Doppler Blood Perfusion Flowmetry for studying Post-Occlusion Reactive Hyperaemia and Drug Administration by Iontophoresis

Transcription

1 Laser-Doppler Blood Perfusion Flowmetry for studying Post-Occlusion Reactive Hyperaemia and Drug Administration by Iontophoresis Frits F.M. de Mul Kolff Institute Dept. Biomedical Engineering University Medical Center Groningen Groningen, the Netherlands Biomedical Optics group, Department of Applied Physics, University of Twente, Enschede, the Netherlands

2 Contents: 1. Principles of Laser-Doppler Blood Perfusion Monitoring. Model for Post-Occlusion Reactive Hyperaemia (PORH) to study Peripheral Arterial Occlusive Disease (PAOD) 3. Model for Drug Administration using Iontophoresis Publications: see website: scroll to Laser Doppler.

3 LDV: Principles Principle of Laser-Doppler Blood Flow Perfusion Monitoring in Tissue A laser beam with pencil shape will be scattered by structures (particles, cells, vessels,...) in tissue. If these structures have a velocity the scattered light will get a slight Doppler frequency shift. This shift can be measured by mixing the emerging light with the original incident light. The shift is proportional to the averaged (*) particle velocity and the amount of scattering particles involved. (*) averaged : over directions and magnitudes of particle velocities 3

4 LDV: Principles Principle of laser Doppler: v : particle velocity k 0 and k s : incoming and scattered wavevectors k = π/λ ; λ = wavelength k 0 k = k s -k 0 v k s D = f D : D f D Doppler frequency ks k0 v kv sin 1 cos Normally in tissue: is small : <> < 10º approx.: k k 0, k s : only v-component k 0 measured 4

5 LDV: Types of Instruments (1) (A) Differential (Dual-beam) Laser Doppler Velocimetry Interference fringe pattern z Fringe spacing s sin Scattered intensity burst time Detection preferentially in forward direction Doppler frequency f. sin / v z 5

6 LDV: Types of Instruments () (A) Differential (Dual-beam) Laser Doppler Velocimetry 1. Original frequency [ Hz] Doppler-shifted frequency + D [ Hz] 3. Doppler frequency D [ < 0 khz] 4. Doppler intensity signal : ~ (freq.sign) 6

7 LDV: Types of Instruments (3) (B) Laser Doppler Perfusion Velocimetry laser 0 0 Averaged Doppler frequency: v detector Heterodyne mixing = - 0 laser 0 v 1 detector Homodyne mixing = 1 - Averaging by: - random velocities - (multiple) scattering in random directions 7

8 LDPV: Spectra (1) (B) Laser Doppler Perfusion Velocimetry Doppler frequency spectrum Doppler power spectrum f( D ) heterodyne peak S( D ) heterodyne homodyne 0 D 0 D Heterodyne peak: due to large amount of non-doppler shifted scattered photons. 8

9 S( D ) LDPV: Spectra () (B) Laser Doppler Perfusion Velocimetry Doppler power spectrum Larger c Larger v Power spectrum depends on: - concentration c - velocity v Moments of Power spectrum : M n ( n n. S( ) d 0 0,1,,...) 0 D Moments: M 0 : ~ concentration of moving scatterers M 1 : ~ flux of moving scatterers M 1 / M 0 : ~ velocity 9

10 LDPV (B) Laser Doppler Perfusion Velocimetry Photodiode Laser fiber 10

11 LDPV: Instruments (B) Laser Doppler Perfusion Velocimetry: Instrument design (a) laser glass fibers 0 detector (a) Glass fibers for light transport Disadvantages: motional artefacts sensitive for local variations v (b) Direct-contact velocimetry: Laser and detector in one probe probe (b) v no motional artefacts local averaging 11

12 LDPV: Signals (B) Laser Doppler Perfusion Velocimetry LD spectra of finger tip upon occlusion of upper arm 0 sec Concentration = 0 th moment Flux = 1 st moment of power spectrum occlusion heart beat noise See software package LASDOPP <velocity> = flux/concentration heart beat 1

13 LDPV: Skin Tissue (B) Laser Doppler Perfusion Velocimetry Schematic cross section of Skin tissue Needed: Data about perfusion of different layers at different depths 13

14 LDPV: Instruments (B) Laser Doppler Perfusion Velocimetry: Instrument design Depth sensitive sensor use detectors at different distances from the light source (see fig.) use different colors (red light probes deeper than green) 14

15 Contents: 1. Principles of Laser-Doppler Blood Perfusion Monitoring. Model for Post-Occlusion Reactive Hyperaemia (PORH) to study Peripheral Arterial Occlusive Disease (PAOD) 3. Model for Drug Administration using Iontophoresis

16 A model for PORH (Post-Occlusion Reactive Hyperemia), as measured with Laser-Doppler Perfusion Monitoring Frits F.M. de Mul Fernando Morales Ruiz Andries J. Smit Reindert Graaff Jan Aarnoudse

17 Microcirculation: PORH-model blood flow through microvasculature ( < 1 mm diameter) Regulation of microcirculation: controlled by musculature of the arterioles based on ambient temperature and/or concentration of metabolism-related substances (O, CO, NO ) operating through vasodilatation Peripheral Arterial Occlusive Disease (PAOD): stenoses in proximal arteries. decrease of available pressure level in arterioles vasodilatation impaired or delayed 17

18 PORH-model Post-Occlusive Reactive Hyperemia (PORH)-test: to assess microvascular functioning Procedure of PORH: arterial occlusion upstream in artery to extremity before, during and after arterial occlusion: local blood perfusion measured at distal extremity as function of time 18

19 Blood perfusion PORH-model PORH-test procedure Maximum overshoot Half-maximum flux Resting flux Occlusion Biological zero Cuff release: zero time point t RF t MF t HF time Characteristic times: t RF, t MF, t HF 19

20 perfusion (p.u.) Perfusion [a.u.] 60 Measured data (typical) PORH-model (all measurements by F. Morales) 40 healthy 0 PAOD time (sec) Time [sec] Healthy PAOD: Response to occlusion: Slower and lower 0

21 Perfusion flux PORH-model MF Healthy RF: Resting Flux HF OC: Occlusion. PAOD BZ: Biological Zero time MF = maximum, HF = half decrease time between maximum and resting flux, t RF = time of cross point with RF. 1

22 PORH-model PAOD vs. Healthy: Longer time scales Rise time and Decrease time tend to become equal Decreased overshoot maximum Similar behaviour for Diabetes patients

23 PORH-model Building blocks for the flow model: I : Flow [m 3 /s] V : Pressure [Pa = N/m = J/m 3 ] Electrical analogon I : Current [C/s = A] V : Voltage [V = J/C] Block Symbol Units Flow resistance R Compliance C Inertance L Electrical analogon Pa.s/m 3 V/A = Vs/C m 3 /Pa Pa.s / (m 3 /s) C/V V.s / A Expression 8l R R C L 4 0 3R 0 l Eh 9l 4R 3 0 μ = viscosity [Ns/m ] l = tube length [m] R 0 = tube radius [m] E = Young s elasticity modulus [N/m ] h = tube wall thickness [m] ρ = density [kg/m 3 ]

24 Model: PORH-model Two sub-models: arterial and capillary Arterial part: flow resistance + compliance Capillary part: time-dependent flow resistance R 1 V 0 C 1 V 1 Arterial system R leak I (flow) R cap (t) Capillary system V 0 = driving pressure (battery) supply tank R = resistance narrow tube C = compliance (capacitor) storage vessel I is the flow measured by LDF R leak accounts for possible flow leakage passing capillary system 4

25 PORH-model Model with details: Two sub-models: arterial and capillary R 1 I (flow) V 0 C 1 V 1 R leak R cap (t) Arterial system Capillary system R s are resistances (narrow tubes) C s are compliances (storage vessels) 5

26 PORH-model Model with details: Two sub-models: arterial and capillary R 1 I (flow) R V 0 C 1 V 1 R 4 C R 3 Arterial system Capillary system Normally R 4 >> R, R 3. Small times: C small impedance R cap R flow I large Large times: C large impedance R cap R + R 3 flow I small 6

27 PORH-model R 1 I (flow) Model: V 0 C 1 V 1 R R 4 C R 3 Arterial system Capillary system Jump response after pressure return upon cuff release after occlusion: (Electrical: sudden voltage V 0 ) I a0 1a1 exp( p1t ) (1 a1) exp( pt) with a 0 a1, p1, p f R1, R, R3, R4, C1,, C NB. Two exponentials, both decreasing in time.

28 PORH-model I a0 1a1 exp( p1t ) (1 a1) exp( pt) at time t = 0: I = a 0 [1 - a 1 - (1 - a 1 )] = 0 at time t : I a 0 [ ] = a 0 1 I total ~ exp(-t/τ 1 ) ~ exp(-t/τ ) a 0 With p 1 = 1/τ 1 and p = 1/τ : τ 1 and τ : characteristic times If τ 1 < τ : see figure 0 1 time

29 PORH-model Approximation: Arterial much faster than capillary Two separate submodels: arterial and capillary R 4 R 1 V 0 C 1 V 1 Arterial system R R C 4 I (flow) Capillary system R 3 V 1 V0 1 e t / 1 1 R1C 1 arterial V 1 I 1 R R3 R R 3 e t / I total capillary C RR3 R R 3 1 time

30 Approximation: 1 R1C 1 C RR3 R R From flow physics: RC if or or or or 3 8l R l E h R R l. Eh (viscosity ) (tube (wall (wall (tube length) radius) PORH-model 1l EhR elasticity ) thickness ) R 1 V 0 C 1 V 1 0 Arterial system I 1 R R C 4 total I (flow) Capillary system arterial capillary time R 3

31 PORH-model R 1 I (flow) Model approximation: V 0 C 1 V 1 R R 4 C R 3 V 1 V0 1 e t / 1 Arterial system Capillary system V 1 R I 1 R R3 R Even better approx.: 3 e t / V 1 R I 1 R1 R R3 R Question: when can we use the approximation? 3 e t / I total 1 arterial capillary time

32 PORH-model R 1 I (flow) Model: V 0 C 1 V 1 R R 4 C R 3 Arterial system Capillary system arterial I total capillary Examples of fitting: program LASDOP: 1 time

33 perfusion (a.u.) PORH-model Model fitting : two examples: Healthy person (upper) and PAOD-patient (lower; down shifted -0) healthy Measurement Resting flux Fit 0 10 PAOD time (sec) Lower figure includes sine-approx. of vasomotion

34 Model fits: PORH-model Model parameters for recordings of a typical healthy person and a typical PAOD-patient Person Model 1 (sec) (sec) Exact Healthy Approx I total arterial capillary PAOD Exact Approx Healthy persons: exact model and approximation coincide; and render similar parameter values: indication for: arterial part faster than capillary part. 1 time PAOD-persons: models have very different parameters; Both arterial part and capillary part are slow.

35 Char. time (s) ; Area ratio (%) PORH-model PAOD diabetes M. I total arterial capillary 00 healthy 1 time PORH 50 RF 0 tau1 tau trf tmf thf Area Oc Area : Ratio of areas between measured data and extrapolated resting flux RF, for Reactive Hyperemia period (PORH) vs. Occlusion period (Oc). Indicates compensation of oxygen debt from Occlusion period in the PORH period. 35

36 PORH-model Model fits: Signal strengths Ratio of maximum flux vs. resting flux: no significant differences between healthy, Diabetes M. and PAOD: 3.1 ± 0.6 for PAOD-group (N=7) 5.8 ± 4.8 for Diabetes M.-group (N=9) 3. ±.7 for healthy group (N=8) Overall signal strength: No significant differences

37 PORH-model Conclusions from model fitting: 1. Exact model fits all measurements. Approximate model fits healthy group only 3. Response time: a. Arterial part : Healthy group faster than Diabetes-M.-group and much faster than PAOD-group b. Capillary part : similar response time for all 4. Signal strengths (resting flux and maximum flux) : no significant differences between groups 5. Area ratio between (PORH-RF) and (Occl.-RF) signals < 1 (aver. 0.6; healthy pers.) and >1 (aver. 1.5; POAD (Indicates compensation of oxygen debt from occlusion period)

38 Contents: 1. Principles of Laser-Doppler Blood Perfusion Monitoring. Model for Post-Occlusion Reactive Hyperaemia (PORH) to study Peripheral Arterial Occlusive Disease (PAOD) 3. Model for Drug Administration using Iontophoresis

39 A Diffusion Model for Drug Administration by Iontophoresis, as measured with Laser-Doppler Perfusion Flowmetry Frits F.M. de Mul, Judith Blaauw, Jan Aarnoudse

40 LD - Diffusion model for Iontophoresis Goal of the project: Model to characterise Iontophoresis, As measured with Laser-Doppler blood perfusion flowmetry in capillaries in extremities, Application: preeclampsia, Characteristics: 1-dim. Diffusion of concentration Decay term (removal) Saturation with subsequent iontophoretic shots. 40

41 LD - Diffusion model for Iontophoresis Perfusion signal Typical iontophoresis recording End of Iontophoresis shots Resting flux Start iontophoresis time occlusion ( occlusion performed to measure biological zero level) 41

42 LD - Diffusion model for Iontophoresis Laser-Doppler probe for Iontophoresis } Glass fibers probe } to/from electrodes Sponge material with drug to administer; electrically conductive; ionic transport tissue Typical dimensions: probe: diameter 10-0 mm, height 5-10 mm; fiber separation 50 m. The diffusion can be considered as mono-dimensional (in depth direction). 4

43 LD - Diffusion model for Iontophoresis The model: 1. 1-Dimensional diffusion. Decay (removal) 3. Saturation with subsequent shots. 43

44 LD - Diffusion model for Iontophoresis The model: 1. 1-Dimensional diffusion. Decay 3. Saturation by subsequent shots., 1. 1-Dimensional diffusion c t D z c t = time [s] z = depth [m] c = concentration [kg/m 3 ] D = diffusion coefficient [m /s] c = f (z, t) Start (boundary condition) for c (z,t) : concentration pulse at z=0 and t=0. c( 0,0) c 0, with 0 c ( z, t) dz Q for all t, including t = 0. Q ~ total amount of administered molecules

45 LD - Diffusion model for Iontophoresis c t D z c c / t = increase of c in time c / z = increase of c in space (slope) c/ z = / z ( c/ z ) = change in slope Example: c = children on a slide: No change in slope No increase of # children in time Change in slope present. Increase of # children in time D is proportionality constant 45

46 conc LD - Diffusion model for Iontophoresis The model: 1. 1-Dimensional diffusion. Decay 3. Saturation by subsequent shots. 1-Dimensional diffusion : solution c t D z c c( z, t) Q Dt exp{ z } 4Dt, time Q = amount of injected molecules Parameter in fig.: depth z Constants in fig.: D = Q = 1 Drawback: decrease by diffusion only is too slow But : decrease by leakage (sideways) will also be present 46

47 conc conc LD - Diffusion model for Iontophoresis The model: 1. 1-Dimensional diffusion. Decay 3. Saturation by subsequent shots.. Experiments show: Decrease in time too slow: Add decay term: - c c t D z c c c( z, t) Q Dt exp{ z 4Dt t}, if D 0 : c( t) c(0).exp( t) Without decay With decay Parameter: depth 0 Constants: D = ; Q = 1 ; = time time

48 LD - Diffusion model for Iontophoresis The model: 1. 1-Dimensional diffusion. Decay 3. Saturation by subsequent shots. Assume: excess (*) flow F(t) ~ concentration (*) = above resting flux level. c( z, t) Q Dt exp{ z 4Dt t} F( t) Q0 z exp Dt 4Dt t, Assume: N shots with interval t exp[-(n-1).s] F( t) t n N n1 t ( n 1) t exp ( n 1) s Q Dt n exp z 4Dt s = shot saturation constant; if s = 0: all shots contribute equally (exp=1) if s >>1: only first shot contributes (n=1 only) 0 n t n n s=0 s=0.5 s=1

49 LD - Diffusion model for Iontophoresis, t n t t t Dt z Dt Q s n t F n n n n N n 1) ( 4 exp 1) ( exp ) ( 0 1 Final model: Notation in program: 1 ; 4 ; ~ ; ) exp( 1) ( exp D z D Q C t t t C s n F n n n N n 1 = diffusion time constant = decay time constant (both: if larger, then process slower) The model: 1. 1-Dimensional diffusion. Decay 3. Saturation by subsequent shots. 49

50 LD - Diffusion model for Iontophoresis Experiments: (by J. Blaauw) Periflux 4000 laser Doppler system (Perimed), Periflux tissue heater set to 31 C (PF4005, Peritemp), Perfusion probe: Laser beam (wavelength 780 nm),, Iontophoresis probe (PF481-, Perimed, Sweden) containing a thermostatic probeholder, Iontophoresis controller (PeriIont 38, Perimed), Position: dorsal side of middle phalanx of third finger, Subjects sitting, forearms on soft pillow at heart level, Temperature-controlled room (T=3.4 ± 0,5 C) 50

51 LD - Diffusion model for Iontophoresis Laser-Doppler perfusion monitor: measures 0th and 1st moment of power spectrum of Doppler signal, M n n. S( ). d ; n 1 0,1 M 0 ~ concentration of moving (red) blood cells M 1 ~ perfusion flux (flow) M 1 / M 0 ~ averaged velocity of blood cells Practical limits: 1 = 0 Hz ; = 1 khz 51

52 LD - Diffusion model for Iontophoresis Experiments: Administered drugs: 1. ACh: acetylcholine,. SNP: sodium nitroprusside Expected: SNP has dilatation effect on vessels and capillaries; this will lead to a higher perfusion. 5

53 LD - Diffusion model for Iontophoresis Subjects for experiments, using in testing the model: code ACh SNP Subjects: - Pre-eclampsia patients (Post partum) - Controls (healthy) (Post partum) PPP PPC N= 18 N=1 0, Experimental settings: Resting flow measurement, duration (s) ( 1 ) Shot duration (s) Current (ma), anodal (A) or cathodal (C) Nr. of shots Shot interval (s) A C 9 90 ( 1 ): in some cases 100 or 00 s See LASDOP program

54 perfusion (a.u.) LD - Diffusion model for Iontophoresis Fit results ( Pre-eclampsia patients; SNP-administration): 9 shots; 90 sec. apart , time (sec) Parameters: χ red = 1.15; 1 = 76 ± 10 s ; = 408 ± 30 s ; s = 0.09 ± χ red = 1.90; 1 = 65 ± 1 s ; = 5 ± 30 s ; s = ±

55 parameter value LD - Diffusion model for Iontophoresis E E E+03 tau1 tau s max/frest red. chi-sq. Group: Pre-eclampsia patients; Post-partum; SNP-administration, E E E E E-0 Time constants: 1 : diffusion : decay Shot saturation constant: s s = 0: all shots contribute; s : first shot only E subject nr. Reduced : = 1 for optimum fit. 55

56 LD - Diffusion model for Iontophoresis Overall results for post-partum patients (PPP) and post-partum controls (PPC) 4 groups: PPC-ACh, PPC-SNP, PPP-ACh, PPP-SNP, Excluded subjects from calculations, due to off-limit values ( s >= 10 6 or >= 10 5 s ): 6 of 80 ; max. 3 of. : decay negligible s = 0 : all shots contribute equally s : first shot contributes only

57 LD - Diffusion model for Iontophoresis Overall results for post-partum patients (PPP) and controls (PPC) , PPP-ACH PPC-ACH PPP-SNP PPC-SNP 0 red. chi-sq.* 100 tau1 (s) tau/10 (s) s * 500 tm-t0 (s) max/rest*100 57

58 LD - Diffusion model for Iontophoresis Conclusions: PPP = post-partum patients PPC = post-partum controls 1 ~ 1/D : sign. higher in PPP s (ACh and SNP); slower diffusion PPP-ACH ~ T 1/ : sign. higher in ACh s (PPP and PPC); slower decay PPC-ACH PPP-SNP PPC-SNP, s : shot saturation constant: sign. higher in ACh s (PPC and PPP); first shot(s) dominate(s) t M : sign. higher in SNP s (PPC and PPP); see max / resting flux : sign lower in PPC-ACh. 0 red. chi-sq.* 100 tau1 (s) tau/10 (s) s * 500 tm-t0 (s) max/rest*100 diffusion coefficients (with z = 1 mm resp. 10 µm): 10 4 resp. 1 x not-electrically sustained values. 58

59 Contents: 1. Principles of Laser-Doppler Blood Perfusion Monitoring. Model for Post-Occlusion Reactive Hyperaemia (PORH) to study Peripheral Arterial Occlusive Disease (POAD) 3. Model for Drug Administration by Iontophoresis Publications: see website: scroll to Laser Doppler. the end