Basic Principles of Tracer Kinetic Modelling

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The Spectrum of Medical Imaging Basic Principles of Tracer

Lammertsma Structure X-ray/CT/MRI Physiology US, SPECT, PET,

pathways PET Molecular targets PET, SPECT Department of

Center, Amsterdam, The Netherlands Email: aa.lammertsma@vumc.

Diagnosis [ 11 C]PIB Uptake Inject Scan 1.4 Control 1.4 AD 1.

2 Increased uptake: Increased binding Increased flow and/or

0 Qualitative PET sufficient for diagnosis

monitoring disease progression and response to therapy Data

1 The Spectrum of Medical Imaging Basic Principles of Tracer Kinetic Modelling Adriaan A. Lammertsma Structure X-ray/CT/MRI Physiology US, SPECT, PET, MRI/S Metabolism PET, MRS Drug distribution PET Molecular pathways PET Molecular targets PET, SPECT Department of Nuclear Medicine & PET Research, VU University Medical Center, Amsterdam, The Netherlands PET: Quantitative Picomolar Sensitivity Jones, 1996 PET Diagnosis [ 11 C]PIB Uptake Inject Scan 1.4 Control 1.4 AD Wait Increased uptake: Increased binding Increased flow and/or extraction Increased delivery Qualitative PET sufficient for diagnosis (sensitivity/specificity) Quantitative PET needed for monitoring disease progression and response to therapy Data Tolboom, Ossenkoppele, et al. [ 11 C]R116301: NK1 Receptor Ligand Principles of Modelling base-line post-aprepitant Summed image BP ND = / Data Wolfensberger et al.

2 Tracer Model PET scanner Measurement Radioactivity Principles of Modelling Tracer Model Quantitative Evaluation Physiological Parameter Tracer Kinetic Modelling Compartment Models Tracer Model: Purpose: Method: Mathematical description of the fate of the tracer in the human body, in particular in the organ under study To quantify functional entities given the distribution of radioactivity Divide possible distribution of tracer in a limited number of discrete compartments volume tracer Free Bound Glucose metabolism Receptor ligand flow tracer scanning Delivery through arterial blood Input function Nomenclature Consensus nomenclature for in vivo imaging of reversibly binding radioligands Flow Innis RB, Cunningham VJ, Delforge J, Fujita M, Gjedde A, Gunn RN, Holden J, Houle S, Huang SC, Ichise M, Iida H, Ito H, Kimura Y, Koeppe RA, Knudsen GM, Knuuti J, Lammertsma AA, Laruelle M, Logan J, Maguire RP, Mintun MA, Morris ED, Parsey R, Price JC, Slifstein M, Sossi V, Suhara T, Votaw JR, Wong DF, Carson RE J Cereb Flow Metab (2007) 27: 33 39

H 2 O as Perfusion Tracer Single Compartment Model Advantages Freely diffusible Metabolically inert Simple kinetics Short half life (2 min) Repeat measurements Disadvantages Short half life On-site

F/V T d /dt = F C A -(F/V T ) Solution: (t) = F C A (t) e -(F/V T)t History Delay and dispersion Lammertsma et al. (1990) J Cereb Flow Metab 10: 675-686.

3 H 2 O as Perfusion Tracer Single Compartment Model Advantages Freely diffusible Metabolically inert Simple kinetics Short half life (2 min) Repeat measurements Disadvantages Short half life On-site cyclotron C A d /dt = C A - = E F; H 2 O: E = 1 = F V T = / = /V T ; H 2 O: =F/V T H 2 O Compartment Model H 2 O Time-Activity Curves C A F F/V T C A F (t) = F C A(t) e -(F/VT)t Non-linear regression F/V T d /dt = F C A -(F/V T ) Solution: (t) = F C A (t) e -(F/V T)t History Delay and dispersion Lammertsma et al. (1990) J Cereb Flow Metab 10: Parametric Images Volume of Distribution CBF Equilibrium - partition coefficient d (t)/dt = 0; dc P (t)/dt=0 V T = /C P Non-equilibrium V T = / C P C P d/dt = C P V T Single tissue compartment model d (t)/dt = C P (t) - (t) At equilibrium: C P (t) - (t) = 0 V T = /C P = / Data Rijbroek, Boellaard, et al.

Quantitative PET Study Injection of positron emitting tracer Measurement of time-activity curves Input: plasma (C P

4 Receptor Ligand Uptake Receptor Studies Three Compartment Model Two Compartment Model C P C F C S metabolites k 5 k 6 metabolites Whole blood C NS PET PET Exchange between C F and C NS fast C ND = C F + C NS Receptor Ligand Model Quantitative PET Study Injection of positron emitting tracer Measurement of time-activity curves Input: plasma (C P ) + whole blood (C WB ) Response: Ideal: tissue ( ) Actual: PET (C PET ) Solution C PET = f (C P, C WB, parameters)

5 PET Receptor Studies PET Receptor Studies PET measurement C PET (t) = (1-V B ) (t) + V B C WB (t) (t) = C ND (t) + C S (t) Relationship with pharmacological parameters = f ND k on (B avail -C S (t)/sa) = k off Note: B avail = B max -B occ (e.g. endogenous ligand) Differential equations V B dc ND (t)/dt = C P (t) - C ND (t) - C ND (t) + C S (t) dc S (t)/dt = C ND (t) - C S (t) Tracer alone = f ND k on B avail = k off K D = k off /k on BP ND = / =f ND B avail /K D Receptor Studies Receptor Studies Parameter of interest Binding Potential: BP ND = / Parameters of interest Tracer alone BP ND = f ND B avail / K D Multiple studies in same subject Separate assessment B avail and K D Binding Potential: BP ND = / Reflects specific binding Tracer alone: BP ND = f ND B avail /K D Volume of distribution: V T = / (1+ / ) Contains non-displaceable component Volume of Distribution Single tissue compartment model At equilibrium: V T = /C P = / C P d/dt = C P Two tissue compartment model At equilibrium: dc ND (t)/dt = dc S (t)/dt = 0 dc S /dt = C ND - C S = 0 C S = ( / ) C ND V T = /C P = (C ND +C S )/C P =(1+ / ) C ND /C P dc ND /dt+dc S /dt = C P - C ND = 0 C ND = ( / ) C P V T = / (1+ / ) Binding Potential input model Direct BP ND = / But: often unstable Indirect Target tissue: V T = / (1+ / ) Reference tissue: V T ' = '/ ' = / BP ND = (V T -V T ')/V T But: reference tissue required Reference tissue model

6 Time after injection (min) Binding Potential Definitions Relative to non-displaceable concentration: BP ND = f ND B avail /K D = (V T -V ND )/V ND = / Overview Kinetic Analysis Process Relative to total plasma concentration: BP P = f P B avail /K D = V T -V ND = / Relative to free plasma concentration: BP F = B avail /K D = (V T -V ND )/f P = /f P Overview kinetic analysis Dynamic PET scan Kinetic model Activity (kbq/ml) Input function Limitations V B Fitting routine time-activity curve Ac (kbq/cc) Tijd (min) Kinetic parameters Limitations Tracer Procedures Model Simplifications Theoretical Model simplifications Complexity physiological process Practical Performance scanner Imperfect implementation Complexity procedure Measurement of blood volume using C O sample: 100% blood, concentration C A PET scanner: tissue concentration concentration is constant: tissue BV = / C A

7 Model Simplifications Pathophysiology C O is a red cell marker Capillary haematocrit < large vessel hematocrit Whole blood concentration is not constant Correction for haematocrit difference required Separate haematocrit measurement Alternative: fixed haematocrit ratio Assumed haematocrit ratio to be checked in pathology A tracer procedure should be reassessed for each new pathophysiological condition Possible breakdown of the model should be considered in interpreting clinical data Limitations Tracer Procedures Complexity Physiological Process Theoretical Model simplifications Complexity physiological process Practical Performance scanner Imperfect implementation Complexity procedure Tracer Metabolite Questions

Using mathematical models & approaches to quantify BRAIN (dynamic) Positron Emission Tomography (PET) data

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