Challenges in (PET) tracer kinetic modelling. Dr Julian C. Matthews Division of Informatics, Imaging and Data Sciences, University of Manchester

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1 Challenges in (PET) tracer kinetic modelling Dr Julian C. Matthews Division of Informatics, Imaging and Data Sciences, University of Manchester

2 Outline of presentation Give an overview of my perception on some the remaining challenges of tracer kinetic modelling Input function measurements Ill-conditioned models Model selection Model fitting v parameter estimation Discuss the potential benefit of PET-MR technology for tracer kinetic modelling Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 2

3 What is the purpose of kinetic modelling? Sometimes the biological process that we are interested in is related to changes in concentrations of a radiotracer. Absolute concentrations, at a given time point, are also affected by other processes that are not of interest (nuisance variable) Such processes could add biological variability to our comparison of interest (false negative) Such processes could be altered by some disease or intervention that we are investigating (false positive) Quantitation Particularly important when we want to compare across modalities So the aim is to locate a parameter which is specific to the biological process that we are interest in and desirably is quantifiable Time lapse movie of the radioactivity concentrations of [ 11 C]SB in the human brain. Gee, A.D. et al., Current Radiopharmaceuticals. 1(2): p , 2008 Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 3

4 Compartmental modelling with an arterial input function Fick principle established by Adolph Fick in the 1870 s and states that the rate of radiotracer uptake is equal to the product of Blood flow/perfusion (F) The concentration of the radiotracer in arterial blood (C a t ) From this a series of compartmental models have been proposed for modelling different radiotracers Reversible Irreversible but we need an input function in order to fit these models to our data Examples of reversible compartmental models from: Gunn, R.N., S.R. Gunn, and V.J. Cunningham,. Journal of Cerebral Blood Flow and Metabolism, (6): p Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 4

5 Gold standard: Discrete/continuous arterial blood sampling Arterial blood radioactivity concentrations can be obtained with High temporal resolution (every second) A good signal-to-noise ratio even at low doses Excellent repeatability SwissTrace makes an MR compatible system Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 5

6 Arterial blood sampling issues Logistical/ethical The insertion of an arterial line can effect recruitment and has potential risks Limitations of reinsertion of cannula on multiple occasions Requires a suitably skilled person to insert the line (and care for it whilst the line is inserted) Can result in a large volume of blood being withdrawn Rate of 5 ml min -1 Often switch to discrete sampling after minutes Even more limiting for preclinical PET scanning due to low volumes of blood that can be extracted Scientific The withdrawal of blood through tubing results in a temporal blurring (Iida, H., et al., J Cereb Blood Flow Metab, (5): p ) This can be very variable between patients Some radiotracers can stick to the tubing causing errors in the measurements PFTE tubing may be required Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 6

7 Image derived input functions (IDIF) Possible to obtain reliable activity concentration from sampling large blood vessels such as the aorta For smaller vessels correction for partial volume and spill-in are needed Can also extract input functions from the kinetics in non arterial areas IDIF suffer from Limited temporal sampling Potential bias within the images due to reconstruction limitations Poor signal-to-noise ratio Where blood vessels are smaller such as in the brain (carotid arterial) it is more difficult For the estimation of CMRglc values using an IDIF in [ 18 F]FDG PET brain studies, a reliable absolute blood-sample-free procedure is not available yet. from: Zanotti- Fregonara P, et al. J. Cereb. Blood Flow Metab , 2009 Even more challenging in small animals although this has been attempted by a number of groups Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 7

8 Population input function For some tracers such as [ 18 F]FDG this can work surprisingly well The shape of input functions are very similar Even apparently robust to conditions such as diabetes (Eberl S et al. Eur. J. Nucl. Med , 1997) However there is still a need to scale the magnitude using a discrete sample Unpublished data collected by Cathryn Brock at Hammersmith MRC cyclotron unit, London Insert: Published data from Wakita et al, J. Nucl. Med. 41: ,2000 Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 8

9 Population input function Using such an approach it is possible to accurate quantify K i values to within 5-10% of values with arterial sampling Takikawa et al, Radiology 188: , 1993 Arterial and arterialised scaling samples ( min) + autoradiographic and 3K model 0.2+/-2.9% (arterial) -1.0+/-2.7% (art. ven.) Phillips et al, J. Nucl. Med. 36: , 1995 Arterial scaling + autoradiographic (up to 6 samples) Eberl et al, Eur. J. Nucl. Med. 24: , 1997 Autorad + 10/45 min arterial scaling (averaging + Feng) inc. patients with high fasting blood glucose Also possible to use late venous samples for scaling Takagi et al, Ann. Nucl. Med. 18: , 2004 Wakita et al, J. Nucl. Med. 41: ,2000 Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 9

10 Population input function limitations However although reliable values of K i can be obtained this is not true for microparameters (K 1,k 2,k 3,k 4 ) This is because there are difference in the peak of the input function possible from variations in injection and first pass kinetics This does not work as well for other tracers Some tracers with clear additional sources of variability (e.g. [ 11 C]DASB with SSRI) Tracers which metabolise extensively tend to have input functions which vary Others are not fully investigated Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 10

11 Other limitation of IDIF and Population IF Whole blood or blood plasma concentration? The input function should consist of the radioactivity which is able to cross into tissue through one pass If the kinetics between whole blood and plasma are rapid then this should be whole blood (e.g. [ 15 O]water) If the kinetics are slow then this should be the activity in plasma (e.g. [ 18 F]FDG For many tracers the ratio of activity in plasma to whole blood changes of time (PoB ratio) Hence measurement of whole blood activity is not sufficient Chemical form of radioactivity Similarly many tracers are metabolised and have circulating radiolabelled metabolites If only the parent radiochemical is able to cross into the tissue then the input function should be parent in plasma/blood In the brain polar metabolites are often unable to cross the BBB but this may not be the case with pathologies and outside of the brain Need for complex models with multiple input functions (e.g. [ 11 C]Thymidine with [ 11 C]bicarbonate) Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 11

12 Additional solutions and challenges Reference tissue model The practical limitations of the measurement of reliable input functions has led to the use of reference tissue model Require a suitable reference tissue (similar/identical to the tissue of interest except for the biological process of interest) A suitable reference tissue may not be available or change in the reference tissue could be misinterpreted as changes in the tissue of interest. Additional complexities With the body there are organs for which and arterial input function is not appropriate Lung Liver Distribution of radiotracers can occur through other mechanism other that blood supply Urinary excretion Biliary elimination Bowels In summary: The measurement and use of appropriate inputs functions is still a significant practical challenge, particularly if we want methods to translate into the clinic Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 12

13 Model selection For a radiotracer need to select the model which best fits the data Numerous ways of doing this Akaike information criteria (AIC) F-test Example Simulated [ 18 F]FDG data for grey matter using a 4k model with blood volume Apply different levels of noise each with 100 realisations Fit the 3k and 4k models and determine which is the preferred model based of AIC and F-test Noise limits the complexity of the model that the data can support Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 13

14 Parameter estimation The model which best fits the data is not necessarily the model which is give the best parameter estimates Dependent on the application but we are often wanting to establish differences Example continued Simulate normal and -10% [ 18 F]FDG in grey matter Plot mean +/- standard deviation using the 3k and 4k model to estimate K i Use of the 3k model results in better precision but at the expense of bias Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 14

15 Model selection v Parameter estimation Parameter estimation Greater ability of the 3k model to separate K i differences Model selection but for lower noise levels in this region the 4k model results in better model fits Both models can adequately determine differences. Probably prefer the 4k model as it may be less sensitive to nuisance variables Both models equally poor at determining differences in K i In this example the 3k model should be the preferred model to estimate K i even when the 4k model results in a better fit to the data Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 15

16 Background: Deep Brain Stimulation in patients with de-afferentation pain De-afferentation pain Chronic pain condition cause by damage to nerves Phantom limb pain Anaesthesia dolorosa Treatment options typically ineffective Deep Brain Stimulation (DBS) Electrodes placed into the brain and selectively stimulate certain regions Peri-aqueductal gray (PAG) Experimental use of this approach has shown benefit However the mechanism is not understood Hypothesis: That DBS of the PAG results in the release of endogenous opiates Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 16

17 [ 11 C]diprenorphine PET [ 11 C]diprenorphine (DPN) is a PET radiotracer which binds to mu, kappa and delta opiate receptors within the brain High concentrations in: many cortical areas; striatum; thalamus; posterior regions of the brain stem. Low concentrations in the occipital cortex Data acquisition dynamic PET data for 90 minutes arterial blood sampling Release of endogenous opiates should reduce the available receptor concentration and the signal measured using [ 11 C]DPN. PET images of [ 11 C]DPN from minutes post injection. Data collected on the HRRT, RM-OP- OSEM reconstruction (12 iterations), post smoothed (6mm FWHM) Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 17

18 Modelling: Spectral Analysis De-convolution operation Estimation of kinetic parameters Time activity curve Input function Rate of uptake of activity from arterial blood into brain regions Steady state ratio of activity in brain regions to blood and is proportional to opiate receptor concentration Impulse response function (decay corrected) iii t = α j e β jt ; α j 0 Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) j 18

19 Spectral Analysis: Effect of noise Spectra and impulse response function Estimated parameters of interest Pile up at edges of spectra Wagging tail of IRF Skew distribution Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 19

20 Spectral analysis and [ 11 C]diprenorphine Application for [ 11 C]diprenorphine This is a particular problem for ligands with slow kinetics such as [ 11 C]diprenorphine Normal solution is to impose a constraint on the range of β values Rate constant of carbon-11 decay, λ s -1 Proposed values of β mmm = = s 1 β mmm = = s 1 β mmm = = s 1 Literature Neuroimage , 2007 Our main findings were that DPN test retest differences were lowest, and reliability highest, for parametric images of either VD or IRF 60 using the more restricted range of exponential bases. One of the most surprising findings was the comparatively poor test retest variability of the VOI-derived VDs. Initial analysis conducted using: β mmm = & with regions of interest applied to spectral analysis generated parametric maps but initial results disappointing Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 20

21 Effect of spectral constraint β mmm = β mmm = β mmm = Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 21

22 V T estimation with V T decrease Cerebellum Insula For the cerebellum: Decrease in estimated V T observed Distribution broadens with a long positive tail as the beta limit approaches the halflife of carbon-11 For insula: For the widest spectrum a decrease is observed with a broad distribution For narrower spectrums the estimated values are biased with a loss of separation of the two distributions Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 22

23 Final result: Displacement observed in the PAG Sims-Williams, H., et al., Deep brain stimulation of the periaqueductal gray releases endogenous opioids in humans. NeuroImage (2016), e Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 23

24 Benefits of PET-MR: Movement A pre-requite for good tracer kinetic modelling is that the kinetics relate to a common piece of tissue Between frame motion alters time activity curves Within frame motion reduces contrast and quantification Errors in the time activity curves will result in errors in the estimated kinetic parameters of interest Potentially much larger errors due the ill-conditioned nature of model fitting and the inability of the model to describe the time activity curves correction PET-MR offers new opportunities for motion correction Ability to characterise complex deformable motion using the MRI Ability to monitor motion using the MRI or alternative motion trigger but this comes with the potential cost of losing the dual PET-MR acquisition advantages Can we design our PET-MR acquisition to enable motion correction without compromising MR data acquisition? Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 24

25 Benefits of PET-MR: Improved The current PET-MR scanners have longer (25cm) axial fields of view compared to a typical value of ~15cm for a PET-CT Other advances in detector design have resulted in additional improvements (Compton scatter recovery) NEMA NU2 Siemens mct (9-10 kcps/mbq) Siemens mmr (~14-15 kcps/mbq) GE Signa PET-MR (~23 kcps/mbq) More counts generally will result in images with better signal-tonoise Although the quality of the counts is also important sensitivity Sensitivity profile of Siemens mct from: Jakoby et al Phys. Med. Biol , 2011 Sensitivity profile of Siemens mmr from: Delso et al. J Nucl Med , 2011 Sensitivity profile of GE Signa PET- MR from: Levin et al. IEEE Trans. Med. Imag , 2016 Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 25

26 Benefits of PET-MR: Additional improvements in SNR Time-of-flight (TOF) The GE Signa has TOF with a timing resolution of < 400ps (c.f. Siemens mct with a timing resolution of ps) For the mct, the use of TOF equates to a 30-40% reduction in the dose for comparable images (Armstrong I. et al. Nucl. Med. Commun , 2015) Image reconstruction Huge potential for synergistic PET-MR reconstruction where the radiotracer distribution Collaborative Computational Project in Positron Emission Tomography and Magnetic Resonance imaging ( British chapter ISMRM meeting in Leeds ( 37) Together there is the potential for significant improvement in signal-ti-noise ratio (SNR) which could enable more complex models to be explored and/or greater precision in estimated parameters Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 26

27 Benefits of PET-MR Image derived input functions The greater axial length (25cm) gives more opportunities to have both the area of interest and a large artery within the field of view The MRI enables identification and verification of anatomy Arterial or venous Size of vessel for partial volume correction Signal-to-noise improvements Synergistic kinetic modelling PET radiotracers and MRI contrast agents distribution are partly governed by common processes MR methods to measure these processes without a contrast agents (Arterial spin labelling) Kinetics of delivery Blood volume Blood flow/perfusion Kinetics of distribution LBM (Jochimsen T H, et al., Lean body mass correction of standardized uptake value in simultaneous wholebody positron emission tomography and magnetic resonance imaging Phys. Med. Biol , 2015) Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 27

28 Summary Challenges Input functions Still a problem and prevents translation of methods to research and clinical practice Model selection Important to enable detection of changes The methods that we use for model selection are not necessarily appropriate Potential benefits of PET-MR Motion correction Improved signal-to-noise ratio of image radioactivity measurements More opportunities for image derived input functions (IDIF) Synergistic kinetic model using both PET and MR data Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 28

29 Acknowledgements and questions Deep Brain Stimulation in patients with de-afferentation pain University of Bristol Nik Patel Hugh Sims-Williams Tony Pickering University of Manchester Peter Talbot The staff and facilities at the Wolfson Molecular imaging centre (WMIC) Questions Dr Julian C. Matthews UCL PET/MRI Methodology Symposium (23 rd Sep 2016) 29