Kyle J. Myers, Ph.D. NIBIB/CDRH Laboratory for the Assessment of Medical Imaging Systems

1. Image Acquisition Issues in Quantitation Tasks Kyle J. Myers, Ph.D. NIBIB/CDRH Laboratory for the Assessment of Medical Imaging Systems

2. Knowledge of the is critical for solving an forward problem Description of the data for a known object Inference about an underlying object from an image inverse problem

3. Knowledge of the forward problem Description of the data for a known object • Provides a description of images/data • Noise, resolution, artifacts,… • Optimal classification and estimation depend on likelihood of data given underlying object

4. Acoustic reflectance Medical ultrasound Concentration Nuclear medicine MRI (spin density) MRS Field strength Biomagnetic imaging Attenuation Film densitometry Transmission x-ray Scattering properties Medical ultrasound Electric, magnetic properties Impedance tomography MRI (magnetization MRI (spin relaxation) Source strength Fluorescence microscopy Index of refraction Phase-contrast microscopy Gene expression DNA chips, microarrays Object property being imaged

5. Image acquisition: a mapping from object space to data space • g= data ( ) • H =the imaging process (mapping) • f = tumor/object/patient (what we want to ) • Which H is best? What more can we do with possible improvements in H ? given find

6. Need models/measures of H to characterize the data

7. Singular Value Decomposition (SVD): Tool for understanding the forward problem • Basis functions are found by eigenanalysis of HtH • Continuous-Continuous (CC) system • Linear, shift-invariant (LSIV) • Fourier theory: Basis functions are wavefunctions • MTF describes resolution • NPS describes noise • Continuous-Discrete (CD) system • H is shift-variant • Resolution and noise depend on location • Basis functions may be “natural pixels,” tubes or cones (projection imaging)

8. Measure the mapping… When the object is a point source f (r) = d(r - r0) , The image is thedetector sensitivity function = a component of the mapping H.

9. Measuring H on FASTSPECT II at U. of AZ

10. Eigenfunctions of an octagonal SPECT system Barrett et al., IPMI (1991).

11. Null space: Hfnull = 0 • If f1 and f2 differ by a null function: Hf1 – Hf2 = 0  no difference in the image • CC system: where MTF has zeros • CD system examples: finite sampling • Limited-angle tomography • Temporal sampling • Spatial sampling (pixel binning) • All digital systems have null functions • Can’t recover object uniquely from image

12. Null functions cause artifacts Reconstruction of a brain phantom by filtered backprojection. (Courtesy of C.K. Abbey)

13. Image reconstruction • Regularization can reduce objectionable artifacts • Can’t put back what’s lost due to null functions • Makes noise nonlocal – contributions from entire image Sequence of reconstructions of a brain phantom by the MLEM algorithm after 10, 20, 50, 100, 200, and 400 iterations. (Courtesy of D.W. Wilson.)

14. Knowing the forward problem means knowing the null space Barrett et al., IPMI (1991).

15. Classification tasks: Ideal (Bayesian) observer • Optimal classifier is based on the likelihood ratio: • Performance is determined by statistics of the likelihood ratio • ROC analysis Disease present) Disease present)

16. Estimation • Tumor volume • Requires delineation of border • Tracer uptake • Total or specific activity • Angiogenesis • Vessel tortuosity Bullitt et al., IEEE TMI (2003).

17. Estimation: Basic concepts • q is P –D vector of object parameters • pr(q) is prior probability density; describes underlying randomness in the parameters • pr(g|q) = mapping from parameters to data = likelihood of data given q • q(g)= estimate of parameter vector ^

18. Estimability • pr(g|q1) = pr(g|q2)impliesq1=q2 • Closely linked to null functions • Estimates of pixel values run into problems of estimability • See Barrett and Myers, 2004

19. Figures of merit • Bias, variance • Mean-square error • Overall fluctuation in the estimate for particularq • Requires gold standard = true value of parameter • Only meaningful for estimable parameters • Limited by measurement noise, anatomical variation, form of the estimator

20. Figures of merit – cont’d • Ensemble MSE (EMSE) • Need to know prior on q • Prior information can be statistical or model-based • Makes problem well-posed

21. Courtesy Miguel Eckstein, UCSB Family of possible tumors • Tumor = t(qt) • Location • Size • Shape • Density • Some unknowns are nuisance parameters • Estimate or marginalize • Key to tractability is knowledge of pr(qt)

22. Inhomogeneous backgrounds can mask tumor/margins • Additional source of variability in the data • Degrades tumor detectability, estimation of tumor parameters • Reduced noise, increased resolution may not improve task performance • Many models for pr(qb) to describe random backgrounds

23. Hoppin et al., IEEE TMI (2002). No-gold standard estimation • Use at least 2 modalities to estimate q OR • Use at least 2 estimators for same data • Regress the estimates from all sources • Requires model for parameter q, knowledge of pr(g|q)

24. Optimal acquisition system is task-dependent Estimation results Detection results Kupinski et al., SPIE 2003

25. Drug response studies using clinical (human) readers • Beware of reader variability TPF vs FPF for 108 US radiologists in study by Beam et al., (1996).

26. Drug response studies using clinical (human) readers • Adds to sources of variability in the study • Need more cases to power the study • Analyzed via random-effects or multivariate ROC analysis • Multi-reader multi-case (MRMC) ROC methodology is commonly used in CDRH for determining contribution of variability due to range of reader skill, reader threshold, and case difficulty

27. IMAGE ACQUISITION Filtration Object Digital detector (indirect) X-ray generation Why consider display image quality? Image Processing PACS Display Processing • Poor display quality can: • reduce effectiveness of diagnostic or screening test • lead to misdiagnosis • cause inconsistent clinical decisions The diagnostic imaging chain is as effective as its weakest component! Courtesy Aldo Badano, CDRH

28. Choice of image acquisition system and settings will depend on the answers to these questions: • What information about the object is desired from the image? • How will that information be extracted? • What objects/patients will be imaged? • What measure of performance will be used?

29. Summary • The future: Knowledge of the forward problem will enable well-characterized, patient-specific image-acquisition choices and processing/estimation methods • For now: • Make sure the problem is well-posed and the parameters are estimable • Avoid pixel-based techniques • Use model-based (low-dimensional) methods • Try to keep the human out of the loop • Validate, validate, validate!