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

Size: px

Start display at page:

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

Joan Hensley
6 years ago
Views:

1 Using mathematical models & approaches to quantify BRAIN (dynamic) Positron Emission Tomography (PET) data Imaging Seminars Series Stony Brook University, Health Science Center Stony Brook, NY - January 29 th, 2013 Francesca Zanderigo, PhD

The role of modeling in PET [ 11 C]DASB [

2 The role of modeling in PET [ 11 C]DASB [ 11 C]PIB [ 18 F]FDG [ 11 C]WAY [ 11 C]CUMI [ 11 C]PE2I [ 11 C] ABP... RECONSTRUCTION CO-REGISTRATION MOTION CORRECTION MDDs PTSDs ADs... Application of mathematical models & approaches to PET data (Time Activity Curves - TACs) to estimate PET OUTCOMES of interest STATS (e.g., GROUP ANALYSIS)

3 The importance of quantification in PET To be useful in clinical investigations, PET needs to be quantitatively correct: the information collected by the camera (i.e., the pictures of the radioligand distribution in the brain) must be translated into numbers that relate to well-defined biologic entities. Short of a validated quantitative analysis, the information is of little value for clinical investigations. Laruelle M, Slifstein M, Huang Y (2003) Relationships between Radiotracer Properties and Image Quality in Molecular Imaging of the Brain with Positron Emission Tomography. Molecular Imaging and Biology 5(6):

4 What is a mathematical model? MODEL = a representation that includes only some relevant aspects of reality REALITY = a biological/physiological system, whose complexity and (indirect) measurements issues (e.g., in vivo) make the use of models appealing MATHEMATICAL MODEL = set of mathematical equations describing the relationships existing between the variables of the real system Answers for X Answers from M X SYSTEM M MODEL Questions about X Questions about M To DESCRIBE - QUANTIFY - INTERPRET - PREDICT

5 The system under investigation in brain PET A INPUT OUTPUT B C

6 The system under investigation in brain PET A INPUT OUTPUT B C RADIOLIGAND IN BRAIN TISSUE THAT INTERACTS WITH THE RECEPTORS

7 PET the Region Of Interest (ROI) level PET images tn t2 t1 TISSUE ROI TAC activity/concentration [µci/cm 3 ] time [min] MODEL ESTIMATES blood flow, glucose uptake, potential binding... NUMBERS!!!

8 PET the voxel level PET images tn t2 t1 TISSUE VOXEL TAC activity/concentration [µci/cm 3 ] time [min] ESTIMATES blood flow, glucose uptake, potential binding... PARAMETRIC MAPS!!! MODEL

9 ROI vs. voxel ROI voxel High Signal-to-Noise Ratio (SNR) Limited number (< 100) of ROIs: computationally-demanding analysis can be applied Original spatial resolution lost Affected by the methods used for ROIs delineation, PET-MRI coregistration etc. Heterogeneity issue Low SNR Elevated number (~10 5 ) of voxels: need for faster & simpler methods of analysis Original spatial resolution preserved Exploratory analysis (in absence of a priori hypothesis on ROIs) Heterogeneity issue lessens

10 The system under investigation in brain PET A INPUT OUTPUT B C RADIOLIGAND IN ARTERIAL PLASMA AVAILABLE TO BIND RADIOLIGAND IN BRAIN TISSUE THAT INTERACTS WITH THE RECEPTORS

11 Input Function (IF) & metabolites IF & metabolites-corrected IF (cif) metabolites metabolites correction

12 Input Function (IF) & metabolites

13 Invasive PET Full arterial & metabolites analysis Gold-standard : to measure how much radioligand is supplied to the brain tissue to properly quantify the uptake amount Arterial sampling: invasive, costly, time-consuming, risky & uncomfortable for subjects, unfeasible in clinical practice - tends to deter subjects participation - requires highly specialized medical staff & labs (blood analysis) (tech note) Mathematical problems related to the presence of noise in the measured arterial data

14 The system under investigation in brain PET A INPUT OUTPUT B C RADIOLIGAND IN ARTERIAL PLASMA AVAILABLE TO BIND RADIOLIGAND IN BRAIN TISSUE THAT INTERACTS WITH THE RECEPTORS

15 The third component INPUT OUTPUT RESPONSE FUNCTION RESPONSE FUNCTION =

16 How can we describe the response of a system? A INPUT OUTPUT B C DATA MODELS (IN-OUT or BLACK BOX) SYSTEM MODELS (STRUCTURAL or WHITE BOX)

17 Compartmental models: basics They provide a description of the system internal mechanisms, based on physical principles or structural hypotheses (e.g., mass balance & conservation) COMPARTMENT: a quantity of matter homogeneously behaving in the system (e.g., the same substance in different physical spaces OR two different substances in the same physical space) A COMPARTMENTAL MODEL: a set of compartments connected to each other B C CONNECTION: substance flow, controlling/regulatory signal (e.g., transport between two sites OR chemical transformation in one site)

18 2-Tissue Compartment (2TC) model K1 k3 Cp(t) Cf+ns(t) Cs(t) k2 k4 RADIOLIGAND CONCENTRATION IN THE ARTERIAL PLASMA CORRECTED FOR METABOLITES TISSUE CONCENTRATION OF THE SPECIFICALLY BOUND RADIOLIGAND TISSUE CONCENTRATION OF THE FREE + NON-SPECIFICALLY BOUND RADIOLIGAND Mintun et al. (1984) A quantitative model for the in vivo assessment of drug binding sites with positron emission tomography. Ann Neurol. 15(3):

19 in vitro in vivo In vitro BOUND RADIOLIGAND-RECEPTOR COMPLEX RECEPTORS FREE RADIOLIGAND In vivo k 3 k on Michaelis equilibrium k 4 = k off DISSOCIATION CONSTANT DENSITY OF RECEPTORS

20 Innis et al. (2007) Review Article. Consensus nomenclature for in vivo imaging of reversibly binding radioligands. JCBF&Met 27:

21 Matching data & model TISSUE ROI TAC activity/concentration [µci/cm 3 ] time [min] Cp(t) K1 k2 Cf+ns(t) k3 k4 Cs(t)

22 Fitting dpu TACs vst dca cer functions of cif & model rate constants time

23 1-Tissue Compartment (1TC) model K1 Cp(t) Ct(t) k2 RADIOLIGAND CONCENTRATION IN THE ARTERIAL PLASMA CORRECTED FOR METABOLITES TISSUE CONCENTRATION OF THE FREE + NON-SPECIFICALLY + (SPECIFICALLY) BOUND RADIOLIGAND Mintun et al. (1984) A quantitative model for the in vivo assessment of drug binding sites with positron emission tomography. Ann Neurol. 15(3):

24 Matching data & model TISSUE ROI TAC TISSUE ROI TAC activity/concentration [µci/cm 3 ] time [min] activity/concentration [µci/cm 3 ] time [min] Cp(t) K1 k2 Cf+ns(t) k3 k4 Cs(t) Cp(t) K1 k2 Ct(t)

25 Kinetic analysis GOLD-STANDARD MICRO-PARAMETERS (k i ) MACRO-PARAMETRES (V T, BP f ) RADIOLIGAND SPECIFIC 2TC irreversible (e.g., [ 18 F]FDG) 2TC constrained (e.g., [ 11 C]WAY) IN VIVO IN VITRO OPTIMIZATION NON-LINEARITY NON IDENTIFIABILITY NON STABILITY CONVERGING ISSUES COMPUTATIONAL DEMAND NOT VOXEL-ANALYSIS FRIENDLY push towards simpler (but less informative) analysis

26 Graphical Analysis (GA) PATLAK PLOT Patlak et al. (1983) Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. J Cereb Blood Flow Metab 3(1): 1-7 LOGAN PLOT Logan et al. (1990) Graphical analysis of reversible radioligand binding from time-activity measurements applied to [N- 11 C-methyl]-(-)-cocaine PET studies in human subjects. J Cereb Blood Flow Metab 10(5): MANIPULATIONS OF THE MODEL EQUATIONS TRANSFORMATIONS OF THE DATA

27 Patlak plot [ 18 F]FDG in the brain slope FRACTIONAL IRREVERSIBLE METABOLIC RATE OF THE RADIOLIGAND (= how many milliliters of radioligand present in the plasma are metabolized for each gram of tissue every minute)

28 Logan plot brain reversible radioligand slope RADIOLIGAND DISTRIBUTION VOLUME (= ratio between the radioligand concentration inside the tissue & in the steady state)

29 Patlak & Logan PROs CONs Only 1 macro-parameter estimated (no info on micro-parameters) Small computational time No need for a compartmental model defined in details Easy implementation Patlak works only for irreversible radioligand Logan estimates are affected by bias The choice of the linearity time window can be not trivial & impact the results

30 From bloody to bloodless A INPUT OUTPUT B C RADIOLIGAND IN ARTERIAL PLASMA AVAILABLE TO BIND INPUT is common to all brain regions/voxels

31 Reference Region Approaches (RRAs) A TARGET REGION INPUT B C activity/concentration time [min] INPUT B A activity/concentration REFERENCE REGION time [min]

32 Ideal Reference Region K1 Cp(t) Ct(t) k2 activity/concentration [µci/cm 3 ] REFERENCE REGION (RR) time [min] devoid of specific binding invariant between groups independent of treatment effect

33 Full Reference Tissue Model (FRTM) K1 k3 Cf+ns(t) Cs(t) ANY TARGET REGION k2 k4 Cp(t) K1 k2 CRR(t) FRTM RELIES ON THE PRESENCE OF A REGION WITHOUT SPECIFIC BINDING THAT CAN BE USED AS RR FOR ALL THE OTHERS INPUT is COMMON to both target region & RR Lammertsma et al. (1996) Comparison of methods for analysis of clinical [ 11 C]raclopride studies. J. Cereb. Blood Flow Metab. 16: 42 52

34 Simplified Reference Tissue Model (SRTM) K1 Ci(t) ANY TARGET REGION k2 Cp(t) K1 k2 CRR(t) SRTM RELIES ON THE PRESENCE OF A REGION WITHOUT SPECIFIC BINDING THAT CAN BE USED AS RR FOR ALL THE OTHERS INPUT is COMMON to both target region & RR Lammertsma AA, Hume SP (1996) Simplified Reference Tissue Model for PET Receptor Studies. Neuroimage 4: 153 8

35 Bloodless GA: Logan plot with a RR brain reversible radioligand The non-displaceable binding potential (BP ND ) is related to the slope slope Logan et al. (1996) Distribution volume ratios without blood sampling from graphical analysis of PET data. J Cereb Blood Flow Metab. 16(5):

36 RRAs PROs CONs Do not require arterial sampling Require RR (devoid of receptors of inte re st & invar iant between groups), not available for many radioligands Easy implementation Cheap Only the non-displaceable binding potential (BP ND ), only linearly related to B available & K D Different degrees of BP ND BIAS compared to cif-based analysis* *Zanderigo et al. Reference region approaches in PET: a comparative study on multiple radioligands. In submission with JCBF&Met (third review)

37 A custom-built software: BrainFit

38 Other alternatives 1. Bolus + infusion protocols 2. Pseudo-equilibrium methods 3. Auto-radiographic protocols 4. Semi-quantitative analysis (e.g., Standard Uptake Value, SUV - Time To Peak, TTP)

39 1. Bolus + infusion protocols Other alternatives Carson et al., (1997) Quantification of Amphetamine-Induced Changes in [ 11 C]Raclopride Binding with Continuous Infusion. Journal of Cerebral Blood Flow and Metabolism 17:

40 2. Pseudo-equilibrium methods Other alternatives Farde et al., (1989) Kinetic Analysis of Central [ ll C]Raclopride Binding to D2-Dopamine Receptors Studied by PET-A Comparison to the Equilibrium Analysis. Journal of Cerebral Blood Flow and Metabolism 9:

41 Other alternatives 3. Auto-radiographic protocols 4. Semi-quantitative analysis (e.g., Standard Uptake Value, SUV - Time To Peak, TTP) Thie (2004) Understanding the Standardized Uptake Value, Its Methods, and Implications for Usage. Journal of Nuclear Medicine, 45(9):

42 THANKS FOR YOUR ATTENTION! :-)

Basic Principles of Tracer Kinetic Modelling

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