Basic perfusion theory

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1 Basic perfusion theory January 24 th 2012 by Henrik BW Larsson Functional Imaging Unit, Diagnostic Department

2 Outline What is perfusion Why measure perfusion Measures The easy part: What to do and why The complicated part: Formalism and models The really complicated part: Deconvolution Conclusion

3 What is perfusion? Large vessels : flow ½ mm Perfusion: related to the microvascular system ~ the capillaries

4 The vascular system of the brain and perfusion Venules: capacity vessels 50% Veins 20% Artery:conductance vessels 30% Capillaries: exchange vessels ~ transport~diffusion Arteriole:resistance vessels

5 Perfusion : ml/100g/min ½ mm

6 Perfusion : ml/100g/min ½ mm

7 Perfusion metrics in imaging: ml/min/ 100g or ml/min/100ml ½ mm

8 Number of transport (ml) vehicles entering 100 ml tissue pr. time unit:: ml/min/100 ml tissue volume

9 Important metrics Perfusion: f [ml/min/100g] or [ ml/min/100ml ] Brain Perfusion ( flow ) : Cerebral blood flow CBF [ml/100g/min] Cerebral blood volume: CBV [ml/100g] ½ mm Volume of Distibution: V d [ml/100g] or [ml/100ml] Mean transit time: MTT [s] Blood brain permeability: PS product [ml/100g/min]

10 Important metrics Perfusion: f [ml/min/100g] or [ ml/min/100ml ] Brain Perfusion ( flow ) : Cerebral blood flow CBF [ml/100g/min] Cerebral blood volume: CBV [ml/100g] ½ mm Mean transit time: MTT [s] Blood brain permeability: PS product [ml/100g/min]

11 Blood flow changes and energy metabolism in brain and skeletal muscle 5 30 % Brain Muscle Activation Increases up to 30 x Rest

12 Why measure brain perfusion? It intimately related to brain activation Govern oxygen delivery and CMRO 2 : CMRO 2 =CBF x (Ca Cv) = CBF x Ca x OEF Is profoundly changed in nearly all brain diseases either primarily or secondary or in a more subtle way

14 Non-invasive perfusion: What to do and the easy part

15 Measuring perfusion by an external registration: CT,SPECT,PET,MRI detector artery f vein f: perfusion in [ml/min /100g]

16 How can it be measured? Add a contrast agent carried by the blood to the tissue

17 Bolus of tracer or contrast

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40 Bolus of tracer or contrast

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42 Bolus of tracer or contrast

43 Bolus of tracer or contrast

44 Bolus of tracer or contrast

45 Bolus of tracer or contrast

46 Bolus of tracer or contrast

47 Bolus of tracer or contrast

48 Bolus of tracer or contrast

49 Bolus of tracer or contrast

50 Bolus of tracer or contrast

51 Bolus of tracer or contrast

52 Bolus of tracer or contrast

53 Bolus of tracer or contrast

54 Bolus of tracer or contrast

55 Bolus of tracer or contrast

56 Bolus of tracer or contrast

57 Bolus of tracer or contrast

58 Bolus of tracer or contrast

59 Bolus of tracer or contrast

60 Bolus of tracer or contrast

61 How can it be measured? Add a contrast agent carried by the blood to the tissue Contrast agent exogent endogent

62 The complicated part: Single bolus injection and external registration

63 The complicated part: Single bolus injection and external registration

64 time

65 Perfusion (f) = ml/min vehicles/min x Signal C tis (0) : f C a (0) Conc (C a ) = mmol/ml the cargo they carry time

66 C tis (t) = f C a (0) Δt RF(t) C tis (0) = : f C a (0) Δt flux dose MTT RF(t) =1 for t < MTT RF(t) =0 for t > MTT time

67 C tis (t) = f C a (0) Δt RF(t) C tis (0) = f C a (0) Δt time

68 Summing up: direct short bolus Measure the tissue conc Measure the input conc i.e. input function Scanner signal : C tis (t) = f C a (0) Δt RF(t) Estimate f and RF(t)

69 Summing up Measure the tissue conc Measure the input conc i.e. input function Scanner signal : C tis (t) = f C a (0) Δt RF(t) Estimate f and RF(t) RF(t) by model free methods, or assume a model e.g. RF(t) =e -k2t

70 Different perfusion tracers behaves differently

71 C tis (t) = f C a (0) RF(t) C tis (0) = f C a (0) Δt time (s)

72 C tis (t) = f C a (0) Δt RF(t) C tis (0) = f C a (0) Δt RF(t) = e -k2t 1 2 time (s)

73 C tis (t) = f C a (0) Δt RF(t) C tis (0) = f C a (0) Δt RF(t) = e -k2t time (s)

74 C tis (t) = f C a (0) RF(t) C tis (0) = f C a (0) Δt RF(t) = e -k2t time (s)

75 C tis (t) = f C a (0) Δt RF(t) C tis (0) = f C a (0) Δt RF(t) = e -k2t + e -k3t time (s)

76 The residue impulse response function RF(t) RF(t) : the fraction of the injected dose remaining in the tissue (voxel) as a function of time Mean transit time : MTT MTT = RF(t) 0

77 Mean transit time : MTT RF(t) 1 MTT t 1 MTT = RF(t)dt 0 RF(t) MTT t n N 1 MTT= RF(t) n N t t MTT

78 Perfusion: f Distribution vol: V d Mean transit time: MTT Generally f = V d MTT For an intravascular contrast agent, the case in brain MRI we have: Brain perfusion: CBF Brain blood volume: CBV Mean transit time: MTT CBF = CBV MTT

79 Generally For an intravascular contrast agent, the case in brain perfusion MRI we have: Brain perfusion: CBF Brain blood volume: CBV Mean transit time: MTT CBF = CBV MTT

80 The really complicated part: Deconvolution

81 We cannot apply a bolus directly in the tissue!

82 Input : C a (t) Tissue enhancement : C tis (t) = f C a (τ) RF(t- τ) dτ 0 tissue Deconvolution : find f RF(t) f time

83 Input : C a (t) Tissue enhancement : C tis (t) =? tissue

84 Input : C a (t) Tissue enhancement : C tis (t) = f C a (0) RF(t) Δt tissue

85 Input : C a (t) Tissue enhancement : C tis (t) =? tissue

86 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) =? tissue If the linearity of the system exist

87 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (0) RF(t - 0) Δτ tissue 0 0

88 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (1) RF(t - 1) Δτ tissue 1 1

89 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (2) RF(t - 2) Δτ tissue 2 2

90 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (3) RF(t - 3) Δτ tissue 3 3

91 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (4) RF(t - 4) Δτ tissue 4 4

92 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (5) RF(t - 5) Δτ tissue 5 5

93 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (6) RF(t - 6) Δτ tissue 6 6

94 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (7) RF(t - 7) Δτ tissue 7 7

95 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (8) RF(t - 8) Δτ tissue 8 8

96 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (9) RF(t - 9) Δτ tissue 9 9

97 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (10) RF(t - 10) Δτ tissue 10 10

98 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (11) RF(t - 11) Δτ tissue 11 11

99 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (12) RF(t - 12) Δτ tissue 12 12

100 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (13) RF(t - 13) Δτ tissue 13 13

101 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (14) RF(t - 14) Δτ tissue 14 14

102 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (15) RF(t - 15) Δτ tissue 15 15

103 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (16) RF(t - 16) Δτ tissue 16 16

104 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (17) RF(t - 17) Δτ tissue 17 17

105 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (18) RF(t - 18) Δτ tissue 18 18

106 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (19) RF(t - 19) Δτ tissue 19 19

107 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (20) RF(t - 20) Δτ tissue 20 20

108 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (21) RF(t - 21) Δτ tissue 21 21

109 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (22) RF(t - 22) Δτ tissue 22 22

110 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (23) RF(t - 23) Δτ tissue 23 23

111 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (24) RF(t - 24) Δτ tissue 24 24

112 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (25) RF(t - 25) Δτ tissue 25 25

113 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (26) RF(t - 26) Δτ tissue 26 26

114 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (27) RF(t - 27) Δτ tissue 27 27

115 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (28) RF(t - 28) Δτ tissue 28 28

116 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (29) RF(t - 29) Δτ tissue 29 29

117 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (30) RF(t - 30) Δτ tissue 30 30

118 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (31) RF(t - 31) Δτ tissue 31 31

119 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (32) RF(t - 32) Δτ tissue 32 32

120 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (32) RF(t - 32) Δτ tissue 32 32

121 Input : C a (t) composed of many small input Tissue enhancement : C tis (t) = f C a (33) RF(t - 33) Δτ tissue 33 33

122 Tissue enhancement : f C a (τ) RF(t - τ ) Δτ ; τ = 0:33 τ:

123 Total tissue enhancement : C tis (t)= f C a (τ) RF(t - τ ) Δτ ; τ = 0:33 τ:

124 Total tissue concentration: t C tis (t)= f C a (τ) RF(t - τ ) dτ 0 The convolution integral τ:

125 Input : C a (t) Tissue enhancement : C tis (t) = f C a (τ) RF(t- τ) dτ tissue Deconvolution : find f and RF(t) f time

126 Conclusion Measure the tissue conc Measure the input conc i.e. input function Bolus input : C tis (t) = f C a (0) Δt RF(t) Estimate f and RF(t) Veneous injection : C tis (t) = f C a (τ) RF(t- τ) dτ

127 Deconvolution ~ Modelbased Use a model e.g.: Monoexponentiel, biexponentiel, Optimise the free parameters by least square fit to tissue enhancement curve It is robust Relative insensitive to noise Incorrect if the model is inappropriately chosen

128 Deconvolution ~ Modelfree No model a priory Very flexible: many of free parameters A projection Very sensitive to noise Incorrect if not regularized rigoriously Fourier transform, SVD, GSVD, Tikhonov, GPD

129 The story can begin

130 DCE T1 perfusion and blood brain barrier: Methodological considerations and applications January by Henrik BW Larsson Functional Imaging Unit, Diagnostic Department

131 Acute MS lesions T1 T1-Gd

132 Paramagnetic Contrast, Gd-DTPA Decreases homogeneity in molecular environment Increases relaxation speed!

133 Acute MS lesions T1 T1-Gd

134 BBB permeability : PS / K trans / K i

135 Dynamic Contrast Enhanced Heart Perfusion, normal MR signal blood tissue time

136 Dynamic Contrast Enhanced Heart Perfusion, normal MR signal blood tissue time

137 Rest scan : healthy subject

138 Stress scan: healthy subject

139 Gadolinium-DTPA as perfusion CA T1w MR-signal T2*w MR-signal extravascular intravascular Time to peak bolus time bolus time

140 Gadolinium-DTPA as perfusion CA T1w MR-signal T2*w MR-signal extravascular intravascular Time to peak bolus time bolus time

141 Dynamic T1 weighted contrast enhanced perfusion MRI in brain at 1.5 tesla F = 83 ml/100/min Larsson at al MRM 2001, p272

142 Dynamic T1 weighted contrast enhanced perfusion MRI in brain at 3 tesla Time resolution: 5 slices pr. 1.24s

143 Dynamic T1 weighted contrast enhanced perfusion MRI in brain at 3 tesla Time resolution: 5 slices pr. 1.24s

144 Gd gives shorter T 1 = faster recovery Short range works only in same compartment Increased signal in blood and tissue on T1W images Normally BBB - K trans Now perfusion - CBF

145 MRI Perfusion Measurement Procedure, Gd: Intravenous injection of Gd-DTPA Rapid imaging using T1W FFE (SR TurboFLASH) Conversion of signal units to concentration via relaxation rate units Data analysis: deconvolution approach

146 From MR signal to concentration of contrast agent R1 = 1/T1 MR signal Concentration C tis C a callibration by external phantoms

147 R 1 Gd+ - R 1 Gd- = relaxivity C ΔR 1 (t) = relaxivity C(t)

148 Conversion of MR signal to tracer concentration Measured MR signal Equilibrium magnetization Flip angle Saturation recovery delay Tissue R 1 before bolus Change of tissue R 1 due to Gd bolus s(t) = M 0 sin(α)[1-exp(-td(r 1 +ΔR 1 (t)))], ΔR 1 (t) = r 1 c(t) Saturation recovery equation Relaxivity of contrast agent M 0 sin(α) s(td) Tracer concentration 1/R 1 TD

149 T1 measurement s(t) = M 0 sin(α)[1-exp(-td R 1 )] T 1 = 1.23 s (frontal gray matter) R 1 M 0

150 Favorite brain arteries for AIF Middle Cerebral Artery (MCA) ICA Internal Carotid Artery (ICA)

151 Slice position in DCE

152 Dynamic T1 weighted contrast enhanced perfusion MRI in brain at Sat-Recovey: TI = 120ms TR= 4 ms TE= 2 ms Angle = 30 o Voxel = 3x3x6 mm Time resolution: 5 slices pr. 1.24s 3 tesla Dose: Magnevist/ Dotarem 0.05mmol/kg

153 Dynamic T1 weighted contrast enhanced perfusion MRI in brain at 3 tesla Sat-Recovey: TI = 120ms TR= 4 ms TE= 2 ms Angle = 30 o Voxel = 3x3x6 mm Time resolution: 5 slices pr. 1.24s Dose: Magnevist/ Dotarem 0.05mmol/kg

154 Deconvolution approach to quantitative perfusion measurement tissue curve arterial input tissue response c t (t) (mm) c a (t) (mm) = F RF(t) t (s) t (s) t (s) C t (t) = F C a (t) RF(t) = F C a (t ) RF(t-t ) dt t 0 MTT = RF(t)dt CBV = F MTT

155 Dynamic T1w contrast enhanced MRIperfusion CBF map

156 Deconvolution methods c t (t) = F c a (t) RF(t) gray matter ROI arterial input RF(t): monoexp tissue curve RF(t): deconvolution with SVD RF(t): deconvolution with Tikhonov

157 The residue impulse response function gray matter ROI arterial input tissue curve RF(t): deconvolution with SVD RF(t): deconvolution with Tikhonov

158 Tikhonov s deconvolution or Generalized SVD large small Larsson at al JMRI 2008, p754

159 Examples of CBF maps ml/100g/min We found perfusion value for ROI s to be 62 ml/100g/min in gray matter and 21 ml/100g/min in white matter in 7 patients with acute optic neuritis.

160 ml/100g/min Combined Anatomical and Functional MRI: Anatomy & perfusion of the brain

161 Two patients with stroke (one week old) T 2 - w image DWI CBF ml/100g/min Larsson at al JMRI 2008, p754

162 CBV ml/100g MTT s Larsson at al JMRI 2008, p

163 Perfusion in clinical desicision making Assesment of cerebral ischemia Assesment of reversible versus irreversible tissue damage before treatement

164 Comparison of MR perfusion methods: Carotic flow measurement (PCM) DCE ASL PET ( 15 H 2 O) Otto Henriksen at al JMRI 2012, in press

165

166 17 healthy subjects, years Performed twice - Variation: Within persons method variation Between persons variation

167 Table 1. Cerebral blood flow measurements by different modalities Mean Bias * p- value ** s betw s with CV betw CV with Global CBF PCM % 7.4% ASL % 4.8% DCE % 15.1% PET % 11.9% Gray matter CBF ASL % 6.1% DCE % 15.3% PET % 11.8% White matter CBF ASL % 4.9% DCE % 15.8% PET % 12.4%

168 Table 1. Cerebral blood flow measurements by different modalities Mean Bias * p- value ** s betw s with CV betw CV with Global CBF PCM % 7.4% ASL % 4.8% DCE % 15.1% PET % 11.9% Gray matter CBF ASL % 6.1% DCE % 15.3% PET % 11.8% White matter CBF ASL % 4.9% DCE % 15.8% PET % 12.4%

169 Comparison of MR perfusion methods: Otto Henriksen at al JMRI 2012, in press

170 Conclusion Large inter-individual variability all methods Same mean global CBF across ASL, DCE, PET PCM global flow > global ASL, DCE, PET No correlation between methods, except A (weak) correlation between PCM and DCE Existence of significant subject-method interaction

171 Does it works if BBB is leaky? Can we still estimate CBF? Can we estimate PS (K i or K trans )? Can we estimate CBV? Can we differentiate between V d and CBV?

172 Before CA Blood brain barrier defect in brain tumors After CA Tikonov: CBF = 53ml/100g/min 90 Gray matter Tikonov: CBF = 157 ml/100g/min 300 Tumor lesion Concentration a.u Concentration a.u time (sec) time (sec)

173 Before CA Blood brain barrier defect in brain tumors After CA Tikonov: CBF = 53ml/100g/min 90 Gray matter Tikonov: CBF = 157 ml/100g/min 300 Tumor lesion Concentration a.u Concentration a.u time (sec) time (sec)

174 Permeability - surface area map ml/100g/min

175 Measurement of Brain Perfusion, Blood Brain Barrier Permeability using Dynamic Contrast Enhanced T1- Weighted MRI at 3 T Larsson at al MRM 2009, p1270

176 Compartment model BBB arteries C a (t) veins F F blood C b (t) V b K i K i (1-Hct) C e (t) V e tissue Intracellular space V tis V d

177 BBB arteries C a (t) veins F F blood C b (t) V b K i K i (1-Hct) C e (t) V e tissue Intracellula r space V tis, C tis V d Tissue voxel

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181 Patlak & Gjedde method

182 Calculation of BBB permeability Patlak & Gjedde method or two-compartment model & Tikhonov CBF estimation

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186 Gray matter Tumor Tumor

187 Does it works if BBB is leaky? Can we still estimate CBF? yes Can we estimate PS (K i or K trans )? yes Can we estimate CBV? yes Can we differentiate between V d and CBV? yes In the relevant range!

188 F (ml/100g/min) 120 K i (ml/100g/min) Anatomy, T2w V d (ml/100g) 0 CBV 20 V b (ml/100g)

189 F (ml/100g/min) 100 K i (ml/100g/min) Anatomy, T2w T2 w TSE V d (ml/100g) CBV 20 V b (ml/100g)

190 DCE in evaluation of tumor recurrence versus radiation necrosis FDG-PET as referene Vibeke A Larsen et al Submitted

191 Tumor recurrence Tumor recurrence Radiation necrosis

192 Recurence versus necrosis

193 Recurence versus necrosis

194 DCE in evaluation of tumor recurrence versus radiation necrosis FDG-PET as referene: CBV from DCE seems a sensible parameter Larsen VA at al Submitted

195 Pivotal for all measurement The input function Partial volume effect on the arterial input function in T1-weighted perfusion imaging and limitations of the multiplicative rescaling approach Adam E Hansen et al. MRM 2009, p1055

196 Effect of partial volume on the arterial input function high in-plane resolution: (1.15mm) 2 voxel

197 Point spread function of input function

198

199 Future directions The feasibility at 7 T? Incorporation of water exchange, i.e. water permeability Larsson at al MRM 2001, p272

200 T1 versus T2 Gd based perfusion Advantage T1 No image distortion (no susceptibility) Input function clearly defined No bias due to defect BBB Half of normal clinical dose Disadvantage T1 Fewer slices Lower S/N for tissue conc time function Necessitate high field strength 3 tesla Injection of contrast agent Can only be repeated a few times Many slices Advantage T2 High S/N for the tissue conc time function Input function cannot be defined clearly Perfusion is estimated to high MR signal to conc is problematic Perfusion is bias when BBB is defect Injection of contrast agent Repeatable? Disadvantage T2

201 Conclusion It is possible to generate CBF maps using DCE T1 weighted MRI at 3 T Perfusion values are consistent with literature Tikhonov s method is best suited for deconvolution DCE T1 weighted MRI appears promising for distinguishing tumor recurrence and radiation necrosis employing CBV Easy identification of vasculature with DCE T1 weighted MRI allows to study details of input function

202 Thanks to Egill Rostrup, Adam E Hansen, Otto Henriksen, Glostrup Hospital Bente Sonne Møller, Helle Juhl Simonsen, Marjut Lindhart, Glostrup Hospital Olav Haraldseth, Trondheim Vibeke Andrée Larsen, Ian Law, Julie M Grüner, RH Frederic Courivaud, Philips Clinical Scientist Lundbeck Centre for Neurovascular Signaling Thank you for your attention!

Dynamic Contrast Enhance (DCE)-MRI

Dynamic Contrast Enhance (DCE)-MRI contrast enhancement in ASL: labeling of blood (endogenous) for this technique: usage of a exogenous contras agent typically based on gadolinium molecules packed inside