Radiolabelled Molecules for Brain Imaging with PET and SPECT

Positron emission tomography (PET) and single-photon emission computed tomography (SPECT) are in vivo molecular imaging methods which are widely used in nuclear medicine for diagnosis and treatment follow-up of many major diseases. These methods use target-specific molecules as probes, which are labeled with radionuclides of short half-lives that are synthesized prior to the imaging studies. These probes are called radiopharmaceuticals. The use of PET and SPECT for brain imaging is of special significance since the brain controls all the body’s functions by processing information from the whole body and the outside world. It is the source of thoughts, intelligence, memory, speech, creativity, emotion, sensory functions, motion control, and other important body functions. Protected by the skull and the blood–brain barrier, the brain is somehow a privileged organ with regard to nutrient supply, immune response, and accessibility for diagnostic and therapeutic measures. Invasive procedures are rather limited for the latter purposes. Therefore, noninvasive imaging with PET and SPECT has gained high importance for a great variety of brain diseases, including neurodegenerative diseases, motor dysfunctions, stroke, epilepsy, psychiatric diseases, and brain tumors. This Special Issue focuses on radiolabeled molecules that are used for these purposes, with special emphasis on neurodegenerative diseases and brain tumors

Spherical radon transforms and mathematical problems of thermoacoustic tomography

The spherical Radon transform (SRT) integrates a function over the set of all spheres with a given set of centers. Such transforms play an important role in some newly developing types of tomography as well as in several areas of mathematics including approximation theory, integral geometry, inverse problems for PDEs, etc. In Chapter I we give a brief description of thermoacoustic tomography (TAT or TCT) and introduce the SRT. In Chapter II we consider the injectivity problem for SRT. A major breakthrough in the 2D case was made several years ago by M. Agranovsky and E. T. Quinto. Their techniques involved microlocal analysis and known geometric properties of zeros of harmonic polynomials in the plane. Since then there has been an active search for alternative methods, which would be less restrictive in more general situations. We provide some new results obtained by PDE techniques that essentially involve only the finite speed of propagation and domain dependence for the wave equation. In Chapter III we consider the transform that integrates a function supported in the unit disk on the plane over circles centered at the boundary of this disk. As is common for transforms of the Radon type, its range has an in finite co-dimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography, for instance when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. In Chapter IV we investigate implementation of the recently discovered exact backprojection type inversion formulas for the case of spherical acquisition in 3D and approximate inversion formulas in 2D. A numerical simulation of the data acquisition with subsequent reconstructions is made for the Defrise phantom as well as for some other phantoms. Both full and partial scan situations are considered

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

3D fusion of histology to multi-parametric MRI for prostate cancer imaging evaluation and lesion-targeted treatment planning

Multi-parametric magnetic resonance imaging (mpMRI) of localized prostate cancer has the potential to support detection, staging and localization of tumors, as well as selection, delivery and monitoring of treatments. Delineating prostate cancer tumors on imaging could potentially further support the clinical workflow by enabling precise monitoring of tumor burden in active-surveillance patients, optimized targeting of image-guided biopsies, and targeted delivery of treatments to decrease morbidity and improve outcomes. Evaluating the performance of mpMRI for prostate cancer imaging and delineation ideally includes comparison to an accurately registered reference standard, such as prostatectomy histology, for the locations of tumor boundaries on mpMRI. There are key gaps in knowledge regarding how to accurately register histological reference standards to imaging, and consequently further gaps in knowledge regarding the suitability of mpMRI for tasks, such as tumor delineation, that require such reference standards for evaluation. To obtain an understanding of the magnitude of the mpMRI-histology registration problem, we quantified the position, orientation and deformation of whole-mount histology sections relative to the formalin-fixed tissue slices from which they were cut. We found that (1) modeling isotropic scaling accounted for the majority of the deformation with a further small but statistically significant improvement from modeling affine transformation, and (2) due to the depth (mean±standard deviation (SD) 1.1±0.4 mm) and orientation (mean±SD 1.5±0.9°) of the sectioning, the assumption that histology sections are cut from the front faces of tissue slices, common in previous approaches, introduced a mean error of 0.7 mm. To determine the potential consequences of seemingly small registration errors such as described above, we investigated the impact of registration accuracy on the statistical power of imaging validation studies using a co-registered spatial reference standard (e.g. histology images) by deriving novel statistical power formulae that incorporate registration error. We illustrated, through a case study modeled on a prostate cancer imaging trial at our centre, that submillimeter differences in registration error can have a substantial impact on the required sample sizes (and therefore also the study cost) for studies aiming to detect mpMRI signal differences due to 0.5 – 2.0 cm3 prostate tumors. With the aim of achieving highly accurate mpMRI-histology registrations without disrupting the clinical pathology workflow, we developed a three-stage method for accurately registering 2D whole-mount histology images to pre-prostatectomy mpMRI that allowed flexible placement of cuts during slicing for pathology and avoided the assumption that histology sections are cut from the front faces of tissue slices. The method comprised a 3D reconstruction of histology images, followed by 3D–3D ex vivo–in vivo and in vivo–in vivo image transformations. The 3D reconstruction method minimized fiducial registration error between cross-sections of non-disruptive histology- and ex-vivo-MRI-visible strand-shaped fiducials to reconstruct histology images into the coordinate system of an ex vivo MR image. We quantified the mean±standard deviation target registration error of the reconstruction to be 0.7±0.4 mm, based on the post-reconstruction misalignment of intrinsic landmark pairs. We also compared our fiducial-based reconstruction to an alternative reconstruction based on mutual-information-based registration, an established method for multi-modality registration. We found that the mean target registration error for the fiducial-based method (0.7 mm) was lower than that for the mutual-information-based method (1.2 mm), and that the mutual-information-based method was less robust to initialization error due to multiple sources of error, including the optimizer and the mutual information similarity metric. The second stage of the histology–mpMRI registration used interactively defined 3D–3D deformable thin-plate-spline transformations to align ex vivo to in vivo MR images to compensate for deformation due to endorectal MR coil positioning, surgical resection and formalin fixation. The third stage used interactively defined 3D–3D rigid or thin-plate-spline transformations to co-register in vivo mpMRI images to compensate for patient motion and image distortion. The combined mean registration error of the histology–mpMRI registration was quantified to be 2 mm using manually identified intrinsic landmark pairs. Our data set, comprising mpMRI, target volumes contoured by four observers and co-registered contoured and graded histology images, was used to quantify the positive predictive values and variability of observer scoring of lesions following the Prostate Imaging Reporting and Data System (PI-RADS) guidelines, the variability of target volume contouring, and appropriate expansion margins from target volumes to achieve coverage of histologically defined cancer. The analysis of lesion scoring showed that a PI-RADS overall cancer likelihood of 5, denoting “highly likely cancer”, had a positive predictive value of 85% for Gleason 7 cancer (and 93% for lesions with volumes \u3e0.5 cm3 measured on mpMRI) and that PI-RADS scores were positively correlated with histological grade (ρ=0.6). However, the analysis also showed interobserver differences in PI-RADS score of 0.6 to 1.2 (on a 5-point scale) and an agreement kappa value of only 0.30. The analysis of target volume contouring showed that target volume contours with suitable margins can achieve near-complete histological coverage for detected lesions, despite the presence of high interobserver spatial variability in target volumes. Prostate cancer imaging and delineation have the potential to support multiple stages in the management of localized prostate cancer. Targeted biopsy procedures with optimized targeting based on tumor delineation may help distinguish patients who need treatment from those who need active surveillance. Ongoing monitoring of tumor burden based on delineation in patients undergoing active surveillance may help identify those who need to progress to therapy early while the cancer is still curable. Preferentially targeting therapies at delineated target volumes may lower the morbidity associated with aggressive cancer treatment and improve outcomes in low-intermediate-risk patients. Measurements of the accuracy and variability of lesion scoring and target volume contouring on mpMRI will clarify its value in supporting these roles