Final Examination

1. X-ray diagnostics and planar imaging. X-ray sources and detectors; interaction of X-rays with matter; contrast mechanisms in the human body; factors affecting image quality; the evolution of CT; Hounsfield units; fan-beam reconstruction; basic concepts of projection imaging (image magnification, source magnification); the linear convolution model of projection imaging; image formation of point sources and objects; slit images; transfer functions.

2. Nuclear medicine imaging: Gamma camera and SPECT. The Anger principle; collimators; pinhole and multi-pinhole imaging; gamma-camera planar imaging in nuclear medicine; types of sources used (radiopharmaceuticals); efficiency; achievable image parameters; spatial resolution; noise sources; organs examined and clinical applications. The principles of SPECT, implementation methods, factors affecting image quality, and areas of application.

3. Nuclear medicine imaging: PET. Principles of PET and coincidence detection techniques; timing considerations; true, random and scatter coincidences; relationship between activity and count rate; noise-equivalent count rate (NEC); single rate and random rate; positron range; non-collinearity of annihilation photons; characteristics of PET detectors; factors affecting image quality; clinical and research applications.

4. Ultrasound imaging and linear transmission systems. Ultrasound sources and detectors; interaction of ultrasound with matter; tissue models; A-, B- and M-mode imaging; Doppler mode. Linear systems, shift-invariant transformations, the principle of superposition, Fourier, Laplace, Z and Walsh transforms, filtering, discrete Fourier transform, and the sampling theorem.

5. Magnetic Resonance Imaging (MRI). Basic concepts of MRI (excitation, spin, Larmor frequency, gyromagnetic ratio); spin alignment and relaxation in an external magnetic field; T1 and T2 relaxation; Bloch equations; structure and operation of MRI systems; free induction decay (FID); spin-echo and inversion-recovery sequences; three-dimensional MRI imaging.

6. Properties of diagnostic images. The concept of an image; digital images; properties of 2D images (hue, saturation, brightness); fundamental image-quality characteristics (contrast, noise, resolution); combined image-quality measures (MTF, SNR, DQE); image-recognition models and performance metrics, including the Rose model and its application to Poisson statistics, ROC analysis; elements of digital image processing; the DICOM standard.

7. Properties of the two-dimensional Radon transform and inverse Radon transform. Parameterisation of a line; transformation properties and theorems; convolution; the Central Slice/Fourier Slice Theorem; Fourier inversion formula; back-projection operator; adjoint Radon transform; Hilbert transform and its role in Radon inversion; filtered back-projection; discrete filtered back-projection; Ram-Lak, Shepp–Logan and cosine filters.

8. Iterative reconstruction methods in deterministic models and analytical image reconstruction in higher dimensions. Voxel-based Radon transform; Kaczmarz iteration; maximum-likelihood estimation; maximum a posteriori estimation; the ML-EM algorithm; E and M steps of emission tomography reconstruction; MAP-LM and OSEM reconstruction methods; higher-dimensional Radon transforms; multidimensional inversion formulas; general inversion formulas in arbitrary dimensions; ray transforms; extension of the ray transform to the complete Fourier transform; three-dimensional filtered back-projection; medical applications of CT.

1. Fundamentals of radiation physics, development of the dose concept, and characteristics of dosimeters. Radiation dose measuring instruments; structure and characteristic parameters; types of ionisation chambers, conditions of applicability, construction and calibration factors; film dosimetry; thermoluminescent dosimeters (TLDs). The role, types and principal properties of radiotherapy phantoms. The role of irradiation devices in radiation therapy; characteristics of deep-therapy X-ray units; properties and structure of cobalt units; operating principles, structure and key parameters of linear accelerators.

2. Photon and electron beam calibration. Dosimetric quantities; parameters of photon therapy; inverse square law; irradiation fields; equivalent field size; field matching; photon beam transmission through the patient; collimator factors; percentage depth dose (PDD); PDD measurements in water and air; characteristics of SSD and SAD irradiation techniques; determination and measurement of TAR, TPR and TMR; beam profiles; inhomogeneity corrections.

3. Treatment planning in photon teletherapy. Workflow of treatment planning; patient immobilisation and setup; the role of imaging modalities (PET, CT, MRI) in radiation therapy; delineation of organs at risk and target volumes; treatment-planning techniques; beam-modifying devices; evaluation of treatment plans; dose-volume histograms (DVHs) and their applications; verification of treatment plans; portal films and electronic portal imaging devices (EPIDs); types of treatment errors and available correction methods.

4. Application of electron radiation in radiotherapy. Interaction of electrons with absorbing media; clinical electron energy ranges; measurement and characteristics of depth-dose curves; inverse square law; practical range (Rp); CSDA range; electron dose gradients; electron spectra; beam quality parameters; electron-beam dosimetry; dose profile characteristics; use of applicators; requirements for clinical application.

5. Brachytherapy. Brachytherapy techniques; characteristics of brachytherapy sources; afterloading treatments; structure and quality assurance of HDR systems; use of applicators and dose-prescription methods; definitions of dose-rate quantities; beta-emitting isotopes; dosimetry of interstitial brachytherapy.

6. Advanced radiation therapy techniques. Fundamentals of intensity-modulated radiation therapy (IMRT); characteristics of inverse treatment planning; IMRT delivery techniques; operating principles of tomotherapy systems and CyberKnife systems; dosimetric verification of IMRT plans; technical possibilities of image-guided radiation therapy (IGRT); patient setup uncertainties; systematic and random errors; fundamentals of radiosurgery; physical principles of proton therapy.

7. Quality assurance in radiation therapy. Basic concepts of quality assurance; quality control of treatment machines; quality assurance of treatment-planning systems; the significance of international protocols; familiarity with IAEA TRS-398 and TRS-430 protocols.

8. Radiation protection and radiobiology in radiation therapy. Natural and artificial radiation sources; temporal development of biological effects; direct and indirect effects; free-radical formation; LET, RBE and BED concepts; biological effects of radiation; factors influencing radiation response; dose limits for the public and occupationally exposed workers; the linear-quadratic (LQ) model; fractionated radiotherapy; BED calculations in teletherapy, brachytherapy and proton therapy; radiation protection tasks in radiation therapy centres.

1. Scintillation materials and detectors. Comparison of the main properties of scintillation materials, including detection efficiency and afterglow time. Principles of operation and types of photomultiplier tubes (PMTs), quantum efficiency, signal shape and temporal characteristics. Avalanche photodiodes (APDs), silicon photomultipliers (SiPMs/GAPDs), position-sensitive PMTs (PS-PMTs), and the applicability of CZT detectors.

2. Implementation of gamma-camera systems. Operating principle of the Anger camera, analogue and digital cameras, statistical position estimation. Collimation techniques, applied radiopharmaceuticals, efficiency, attainable imaging parameters, spatial resolution, noise sources, organs examined, clinical objectives, image corrections and calibration procedures.

3. Single Photon Emission Computed Tomography (SPECT). Principles of SPECT, implementation methods, factors influencing image quality and fields of application. Analytical and ML-EM reconstruction methods, conjugate projections, compensation for scatter and attenuation within the body, and calibration procedures for SPECT systems.

4. Positron Emission Tomography (PET). Fundamental concepts including true, random and scatter coincidences, line of response (LOR), the relationship between activity and count rate, noise-equivalent count rate (NEC), single rate and random rate, pile-up, dead time, intrinsic activity of lutetium-containing detectors, positron range, and non-collinearity of annihilation photons.

5. Production and preparation of radionuclides for PET. Production of PET isotopes in particle accelerators and preparation for clinical use. Radiation protection in radiopharmaceutical production. Patient dose and dose monitoring. Dose estimation in PET/CT and SPECT/CT examinations. Radiation protection aspects of nuclear medicine diagnostics.

6. Hybrid imaging systems. Integration of SPECT and PET with CT; motivation for hybrid imaging; attenuation correction using CT-derived attenuation maps; advantages and clinical significance of SPECT/CT and PET/CT; integration with MRI.

7. Image noise and filtering methods. Sources of image noise, noise reduction strategies, hardware- and software-based noise suppression techniques, low-pass filters, and Butterworth filtering.

I. Planar Imaging and Linear Systems

1. Digital imaging. Concept and generation of digital images; properties of 2D images (hue, saturation, brightness); 2D and 3D images; fundamental image-quality metrics (contrast, noise, spatial resolution); noise characteristics; combined image-quality indicators (MTF, SNR, DQE); image-recognition models and performance measures, including the Rose model and ROC analysis.

2. Linear systems. Linear systems, shift-invariant transformations, the principle of superposition, Fourier transform, filters, discrete Fourier transform, sampling theorem, and the generation of Fourier-space artefacts.

3. Digital image processing. Grayscale transformations (contrast enhancement, inversion, histogram equalisation, histogram matching); spatial-domain filtering (linear filters, convolution, smoothing, digital derivatives, sharpening, unsharp masking); image enhancement in the frequency domain.

4. Planar imaging as a linear system. Basic concepts of projection imaging (image magnification and source magnification); linear convolution model of projection imaging; image formation of a point source, point object and slit; transfer functions.

5. DICOM file format and communication. Structure of DICOM files, separation of image and textual information, DICOM tags, data representation, and the DICOM coordinate system.

II. Tomography

6. Properties of the two-dimensional Radon transform. Parameterisation of lines, line integrals, transformation properties and theorems (symmetry, linearity, rotation, translation, scaling), convolution, image of a point source, sinogram representation of a line source, and digital Radon transforms.

7. Analytical inverse Radon transform. Central/Fourier Slice Theorem, Fourier inversion formula, back-projection operator, adjoint Radon transform, Hilbert transform and its role in inversion, filtered back-projection, discrete filtered back-projection, Ram-Lak, Shepp–Logan and cosine filters, and inversion using orthogonal polynomial systems.

8. Analytical image reconstruction in higher dimensions. Higher-dimensional Radon transforms, multidimensional inversion formulas, general inversion formulas in arbitrary dimensions using Riesz potentials, ray transforms, completion of ray transforms to the full Fourier transform, filtered back-projection on the Orlov sphere.

9. Iterative reconstruction in deterministic models. Voxel-based Radon transform, linearised systems of equations, generalised inverse as an L² minimum solution, calculation of the generalised inverse, and Kaczmarz iteration.

10. Iterative reconstruction in probabilistic models. Maximum Likelihood estimation, Maximum A Posteriori estimation, Poisson models for particle detection, ML-EM algorithms, E and M steps in emission and transmission tomography, MAP-LM and OSEM reconstruction methods.

1. True random numbers and pseudorandom numbers; physical and algorithmic random-number generators; generation of uniformly distributed random numbers; middle-square, middle-product, multiplicative and mixed congruential methods; periodicity and aperiodic sections of random-number sequences.

2. Statistical tests of random-number sequences: goodness-of-fit tests, χ² tests, tests for uniformity and independence, one- and multidimensional frequency tests, digit-frequency, poker, gap, run, and subsequence tests.

3. Monte Carlo sampling of discrete probability distributions and acceleration techniques for sampling.

4. Various methods for sampling continuous random variables defined by a probability density function. The inverse cumulative distribution function (inverse transform) method and the von Neumann acceptance–rejection (rejection sampling) method. The efficiency of rejection sampling and techniques for improving its efficiency. The composition method and its application to the efficient sampling of approximately uniform random variables. Tabular sampling methods and the evaluation of the approximations they provide based on their analogy with the inverse cumulative distribution function method.

5. Generalised rejection methods and exact sampling of normal distributions; approximate sampling of normal distributions using sums of canonical random variables.

6. Sampling isotropic directional distributions in three-dimensional space by various methods: (1) based on the theorem concerning the partitioning of a sphere into slices by equidistant parallel planes; (2) using normally distributed directional components; (3) by applying rejection sampling to points uniformly distributed within the cube circumscribing the unit sphere, rejecting those falling outside the sphere; and (4) using Marsaglia’s method. Sampling a cosine-weighted directional distribution with respect to the normal vector of a plane.

7. Sampling isotropic directional distributions in two-dimensional space and acceleration of rejection methods using double-angle techniques.

8. Monte Carlo simulation of particle transport; analogue and non-analogue simulations; particle-associated Monte Carlo parameters; main components of particle transport codes; collision routines and post-collision direction sampling.

9. Modelling free path length in homogeneous, piecewise homogeneous and heterogeneous media; Woodcock method.

10. Monte Carlo modelling of Compton scattering; transformation of the Klein–Nishina angular distribution; Carlson, Kahn and Koblinger methods.

11. Variance-reduction techniques in particle transport simulation; statistical weights, spatial importance, Russian roulette and trajectory splitting methods.

12. Monte Carlo interpolation of multivariable functions.

1. Dynamics of magnetic moments: classical and quantum-mechanical descriptions.

2. The MR signal: induction, demodulation and basic experiments.

3. Spatial encoding and image formation: gradients, k-space, gradient echo and spin echo techniques, two-dimensional imaging.

4. Sampling: properties of the Fourier transform, FFT, effects of sampling and relaxation processes.

5. Signal-to-noise ratio and image contrast.

6. Steady-state imaging: coherent and incoherent cases, contrast mechanisms and stimulated echoes.

7. Advanced acceleration techniques.

8. Technical background: magnets, gradient systems, amplifiers and radiofrequency (RF) systems.

1. Fundamentals of external beam radiotherapy treatment planning and its dosimetric verification (2D, 3D conformal radiotherapy and IMRT).

2. Fundamentals of brachytherapy and advanced brachytherapy techniques.

3. Advanced radiation therapy techniques, including tomotherapy systems, CyberKnife, radiosurgery and the physical principles of proton therapy.

4. Quality assurance in radiation therapy: basic concepts of quality assurance, quality control of treatment units, quality assurance of treatment-planning systems, and the significance of international protocols, including IAEA TRS-398 and TRS-430.

5. Radiation protection tasks in radiation therapy centres and radiobiology

6. Measurement techniques in radiation therapy: ionisation chambers, semiconductor detectors, TLDs, OSLDs and dosimetric measurement protocols.