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Lääketieteellisen fysiikan ja tekniikan yhdistys (LFTY) Finnish Society for Medical Physics and Medical Engineering |
LFT-päivä 12.2.2015, Tampereen teknillinen yliopisto
Posterikilpailuun osallistuneet
1. Mikael Eriksson, Aalto yliopistoComparison of five methods for deformable, multimodal image registration in prostate and pelvic area
2. Matti Kortelainen, Itä-Suomen yliopisto
Development of respiratory motion compensation for gated myocardial perfusion single-photon emission computed tomography
3. Mari Lehti-Polojärvi, Tampereen teknillinen yliopisto
Electrical impedance tomography applied to stem cells in hydrogel scaffold
4. Kalle Lehto, Tampereen teknillinen yliopisto
Pre-clinical 3D-imaging of eye using contrast enhanced x-ray microtomography
5. Simo Ojanen, Itä-Suomen yliopisto
Finite-Difference Time-Domain Modelling of Ultrasound Transit Time Spectrum in Two Component Material
6. Minna Pitkänen, Aalto-yliopisto
Mapping of cortical hand representations using navigated transcranial magnetic stimulation and functional imaging
7. Ari Ronkainen, Itä-Suomen yliopisto
Site-dependent biomechanical chondrocyte responses and mechanical properties of rabbit knee joint cartilage
8. Ilmari Tamminen, Tampereen teknillinen yliopisto
BAckground and specific contrast enhancements for imaging biological samples with uCT
9. Jenni Tick, Itä-Suomen yliopisto
Reconstruction of ultrasound field in Schlieren tomography
11. Amalia Moreno Galera, Tampereen teknillinen yliopisto
Methods and Models for Biological Sig- nals and Images (M2oBSI) research group, at the Department of Signal Processing
Postereiden abstraktit
Comparison of five methods for deformable, multimodal image registration in prostate and pelvic areaMikael Eriksson, Aalto yliopisto
MOTIVATION: Radiation therapy planning in prostate cancer typically uses both CT images and T2-weighted MR images, for dose calculations and treatment volume delineation, respectively. By using mDixon MR images to generate synthetic attenuation maps, CT imaging can be discarded from the planning process, and dose delivery uncertainties due to e.g. errors in the CT-MR image registration decrease. Despite the improvement in initial image alignment an MR-only radiotherapy workflow provides, multimodal image registration of mDixon and T2-weighted images may still be needed. The aim of this Thesis was to compare five deformable registration algorithms for use in this workflow; diffeomorphic Demons, B-spline registration, fast elastic image registration (FEIR), and a locally affine hierarchical and a locally rigid hierarchical method. METHODS: The registration methods were evaluated qualitatively (visual assessment) and quantitatively for 19 cases. In the quantitative analysis anatomical landmark accuracy, normalised cross-correlation of gradient images and the Dice similarity coefficient (DSC) of the bladder, prostate and seminal vesicles were used as evaluation metrics. The imaging sessions were set up such that initial image misalignment of both minimal and substantial magnitudes could be analysed. Furthermore, a bladder-filling experiment was conducted to investigate large internal organ deformations. Multivariate analysis of variance was used to investigate whether the registration method performances differed statistically significantly, and further statistical analysis provided additional insight into performance on a metric-by-metric basis. RESULTS: The results showed that in cases following the normal MR-only radiation therapy workflow, image alignment was good even with no registration, but was improved with registration. When intentional patient movement impaired the initial alignment, the benefit of image registration increased. FEIR was the best method in terms of visual assessment, quantitative evaluation and computational speed, with among other highlights a landmark accuracy of sub-voxel resolution (2.4 mm). B-spline registration and registration using diffeomorphic Demons also performed well, while the locally affine and locally rigid hierarchical methods were more inconsistent and error-prone. Accurate registration of the bladder was a relative weakness for all methods even with minimal bladder deformations, and none of the methods managed to deal with the larger deformations seen in the bladder-filling experiment. CONCLUSIONS: FEIR performed very well on all accounts and seems well-suited for use in the MR-only radiotherapy work-flow for prostate cancer. However, the initial misalignment between mDixon and T2-weighted images in this workflow was small enough (typically 13 mm, approaching sub-voxel resolution) that deformable image registration might not be necessary in MR-only radiation therapy.
Development of respiratory motion compensation for gated myocardial perfusion single-photon emission computed tomography
Matti Kortelainen, Itä-Suomen yliopisto
Introduction Single-photon emission computed tomography (SPECT) myocardial perfusion imaging (MPI) examination is performed to assess circulation of blood within left ventricular (LV) myocardium. Electrocardiogram (ECG) based cardiac-gating enables quantification of LV wall motion, wall thickening and mechanical dyssynchrony of myocardial contraction, which provide relevant clinical information about the state of the heart. Due to long image acquisition time, SPECT studies are susceptible to motion artifacts, which degrade image quality and affect the quantification of LV function. Especially respiratory motion is still a challenge in clinical environment, and it has been shown to cause overestimation of LV wall motion and wall thickening. However, the effect of respiratory motion on the quantification of LV mechanical dyssynchrony has not been studied. The aim of this thesis is to develop a respiratory motion compensation method for gated myocardial perfusion SPECT examinations. In addition, the clinical significance of the method in evaluation of LV wall motion, wall thickening and mechanical dyssynchrony is studied. Materials and Methods Fourteen patients referred to MPI examinations were imaged at rest using Philips Precedence SPECT/CT system. The emission data was acquired in list-mode format to enable flexible retrospective data processing. A custom-made MATLAB algorithm was developed to form planar projection images from the emission data. During imaging, ECG and thoracic bioimpedance signals of the patients were measured. ECG was utilized to divide the emission data to 16 cardiac frames describing an average cardiac contraction cycle. Bioimpedance signal was utilized to perform respiratory gating with a novel approach named as projection-wise quiescent period gating (P-QPG). In P-QPG, emission data acquired at expiratory phase of respiration is used in image formation while ensuring similar emission photon statistics between different SPECT projection angles. 3D images were reconstructed with ordered subsets expectation maximization algorithm (Hybrid Recon Cardiology; Hermes Medical Solutions). The 3D images were analyzed for LV wall motion, wall thickening and mechanical dyssynchrony (Quantitative Gated SPECT; Cedars-Sinai Medical Center). Dyssynchrony parameters of interest were phase histogram bandwidth, standard deviation and entropy. The dual-gated (respiratory and cardiac gating) images were compared with standard cardiac-gated images to evaluate clinical significance of respiratory gating. Statistical significance was evaluated with Wilcoxon signed-rank test. Results Respiratory gating was found capable of reducing motion blur by increasing contrast between myocardium and LV lumen. Differences in LV wall motion and wall thickening were non-significant between cardiac-gated and dual-gated images (p > 0.05). Statistically significant (p < 0.05) increases were observed in global phase histogram bandwidth (49.3° vs. 65.1°) and global phase histogram standard deviation (12.3° vs. 15.9°) when respiratory gating was applied. In addition, phase histogram bandwidth and phase histogram standard deviation increased in LV lateral wall (39.0° vs. 47.6° and 9.4° vs. 13.6°, respectively) and LV anterior wall (30.0° vs. 34.7° and 7.1° vs. 9.4°, respectively). Conclusions The novel respiratory gating method has potential to reduce motion blur in myocardial perfusion SPECT images. Respiratory motion compensation has effect on LV mechanical dyssynchrony parameters and may affect clinical decision making. However, further studies are required to evaluate the effects caused by lower signal-to-noise ratio which is inherent in dual-gated images. In addition, the dependence of the results on respiratory motion amplitude needs to be studied.
Electrical impedance tomography applied to stem cells in hydrogel scaffold
Mari Lehti-Polojärvi, Tampereen teknillinen yliopisto
There is a great need for new imaging methods for monitoring cell growth in the fields of tissue engineering and regenerative medicine. Electrical impedance tomography (EIT) could provide a label free, non-invasive and fast method for cell culture monitoring. This work is a feasibility study on what kind of results EIT may provide when cells are cultured in a 3D hydrogel scaffold and how the novel EIT setup is optimally built. This work is divided into two parts: (1) electrical impedance spectroscopy (EIS) measurements and (2) computer modelling of the EIT setup. In the EIS study part, several different gellan gum (GG) hydrogels, with and without encapsulated stem cells are measured using the impedance spectroscope HF2IS device (Zurich Instruments AG, Switzerland). EIS measurements are done to samples with different adipose stem cell concentrations and the effect of cell viability is also measured. In the second study part, two dimensional EIT computer models are done in COMSOL Multiphysics. The sensitivity field of EIT setup is simulated in order to find the optimal electrode locations and resistivity values for the aqueous solution used between electrodes and the sample. The EIS experiments indicate that the measured impedance is dependent on the concentration and viability of the cells. Impedance increases as the amount of cells increases. The average impedance for 0.5 million cells in 1 ml of GG hydrogel incubated in 1 ml of cell culture medium drops 13 % after samples are exposed to lethal 43 °C temperature for 2 hours. The results suggest that impedance measurements can be used as a tool for assessing cells encapsulated in 3D hydrogel scaffold. Optimal electrod.e configuration and resistivity values are obtained by the EIT model and these parameters can be used in the future EIT measurements
PRE-CLINICAL 3D IMAGING OF EYE USING CONTRAST ENHANCED X-RAY MICROTOMOGRAPHY
Kalle Lehto, Tampereen teknillinen yliopisto
Objective: Degenerative retinal diseases cause irreversible vision loss for millions of people annually. In the development of new therapies for these vision threatening diseases, experimental animal models have an important role. Present methods for pre-clinical imaging of animal retina are mostly limited to only a part of the eye. Previously, non-destructive high-resolution X-ray microtomography (?CT) has proven its feasibility in pre-clinical studies of soft tissue morphology. In this master`s thesis, contrast enhanced ?CT methodology is further developed for ex-vivo eye imaging and used for assessment of retinal structures in healthy control and RCS rat eyes having inherited light-sensitive photoreceptor layer degradation. Methods: In the preliminary study, control mouse and rat eyes were used for optimizing the staining and imaging parameters. The fixed set of imaging parameters was applied to control (n=5) and dystrophic RCS (n=5) rat eyes. The eyes were post-mortem enucleated, fixed in Davidson's solution and dehydrated in rising alcohol series. Before the imaging, the eyes were immersed in 15 ml of absolute ethanol augmented with 1% w/v iodine (I2E). The whole eyes were then imaged by µCT with 4X magnification resulting in 3.2 µm voxel size. Reconstructed 3D image stacks were post-processed, segmented and thicknesses of the retinal layers were calculated. Results: The results indicate that contrast enhanced µCT allows high-resolution imaging, visualization and morphological analysis of most of the eye tissues. Seven anatomical layers of the control and four layers of the RCS retina were visually identified and dystrophic changes in the retina could be clearly assessed from the images. The average thickness of the retina was 10% lower in the RCS eye. Conclusions: This thesis shows, for the first time, that ?CT can be used for ex-vivo 3D histology of soft tissues such as retina that consist of various neuronal cell layers. The morphology of the eye structures can be assessed quantitatively in 3D using ?CT. The acquired image sets can be used for 3D histology without physically sectioning the sample; the whole eye 3D image can be virtually sectioned in-silico in any orientation with high resolution.
Finite-Difference Time-Domain Modelling of Ultrasound Transit Time Spectrum in Two Component Material
Simo Ojanen, Itä-Suomen yliopisto
Laajakaistaisen ultraäänen vaimenemisen (Broadband Ultrasound Attenuation, BUA) avulla voidaan tarkastella luun tiheyttä sekä esitutkia mahdollista luukatoa eli osteoporoosia. Ultraäänitutkimuksissa suurena ongelmana on ultraäänikentän vaihesammuminen, joka johtuu yksittäiselle ultraäänikiteelle saapuvista erivaiheisista ultraääniaalloista. Tämän takia mitatusta ultraäänisignaalista katoaa olennaista tietoa. Onkin ehdotettu, että ultraääniaalto voidaan mallintaa samansuuntaisina rinnakkain etenevinä ultraäänisäteinä. Näin ollen kunkin ultraäänisäteen kulkuaika riippuu vahvasti siitä, kuinka pitkän matkan se kulkee luussa ja luuytimessä. Tämän teorian nojalla mitatusta ultraäänisignaalista voidaan muodostaa kulkuaikaspektri (Transit Time Spectrum, TTS), jossa esitetään näytteen läpäisevien ultraäänisäteiden kulkuajat sekä niiden suhteelliset osuudet mitatusta ultraäänisignaalista. Tutkimushypoteesi on, että komposiittimateriaalin karakterisointi on mahdollista lateraalisesta epähomogeenisuudesta riippuvan kulkuaikaspektrin avulla ja sitä voidaan mallintaa aikatason differenssimenetelmällä. Työssä tarkasteltiin kulkuaikaspektroskopian mallintamista numeerisesti aikatason differenssimenetelmän avulla (Finite-Difference Time-Domain, FDTD) 1 ja 5 MHz:n ultraäänilähteillä sekä verrattiin ulostulosignaaleja ja kulkuaikaspektrejä kokeellisesti tehtyihin mittauksiin. Kokeelliset mittaukset tehtiin Queenslandin teknillisessä yliopistossa, Brisbanessa, Australiassa. Kokeelliset mittaukset tehtiin perinteisellä läpäisymittauksella. Mallinnus suoritettiin kaupallisella Wave 3000 plus (Cyberlogic Inc., NY, USA) ohjelmalla. Mallien mittausasetelma oli oleellisesti sama kuin kokeellisissa mittauksissa. Malleissa tarkasteltiin neljää vesihauteessa olevaa akryylilieriötä, joissa oli erilaiset porrasmaiset geometriat. Ulostulosignaalit kussakin mittauksessa ja simulaatiossa vastasivat muodoltaan toisiaan. Toisaalta simulaatioissa ulostulosignaaleissa havaittiin viivettä verrattuna kokeellisiin mittauksiin. Tämä johtuu kokeellisten mittausten sekä simulaatioissa käytettyjen materiaalien ominaisuuksien eroista. Ulostulosignaaleista muodostetut kulkuaikaspektrit kussakin geometriassa vastasivat myös toisiaan lukuun ottamatta jo mainittua viivettä. Kulkuaikaspektreistä oli selvästi havaittavissa mittausgeometrioiden porraskohtien aiheuttamat kulkuaika erot. Laajakaistaisen ultraäänen vaimenemisen avulla voidaan tarkastella halutun kappaleen tiheyttä sekä arvioida sen koostumusta ja rakennetta. Kulkuaikaspektroskopia pyrkii havainnollistamaan ultraäänen etenemistä monimutkaisissa huokoisissa komposiittimateriaaleissa, kuten luussa. Kulkuaikaspektroskopia on suhteellisen uusi käsite, joten se vaatii huomattavan paljon lisätutkimuksia esimerkiksi monimutkaisemmilla geometrioilla sekä fantomeilla tai kliinisillä malleilla. Tässä työssä havaittiin, että FDTD-simulaatioiden ja kokeellisten mittausten kulkuaikaspektrit vastasivat toisiaan. Lisäksi komposiittimateriaalin karakterisointi lateraalisesta epähomogeenisuudesta riippuvan kulkuaikaspektrin avulla voidaan mallintaa aikatason differenssimallilla.
Mapping of cortical hand representations using navigated transcranial magnetic stimulation and functional imaging
Minna Pitkänen, Aalto yliopisto
a) Objectives
Navigated transcranial magnetic stimulation (nTMS) combines magnetic stimulation of the brain and neuronavigation. nTMS of the motor cortex can result in muscle responses, such as motor evoked potentials (MEPs) and silent periods (SPs), which can be detected in electromyogram (EMG). The MEP is a peak in the EMG signal and it measures the excitability of the motor cortex. The SP, on the other hand, can be seen as a ceasing of the EMG during voluntary muscle action and it is a measure of inhibition. Prior to brain surgery, often the MEPs are used to map motor representations. This is not, however, always possible and the SPs might be mapped instead of MEPs. Previous studies have utilized non-navigated TMS which may, however, severely decrease the resolution of the areas. The purpose of the thesis was to characterize and compare MEP and SP representations using nTMS, to evaluate the potential use of SPs in the mappings, and to compare the map center of gravities (CoGs) with the local maxima locations obtained using blood-oxygen-level dependent (BOLD) functional magnetic resonance imaging (fMRI) and arterial spin labeling (ASL) fMRI. The measurements were performed on ten healthy right-handed volunteers. The MEP and SP areas were mapped for three small hand muscles using nTMS with and without a stimulation grid. The sizes and the CoGs of the representations were calculated using spline interpolation. The differences in the MEP and SP maps were analyzed and the CoGs were compared with the local maxima in the motor cortex obtained using fMRI and ASL. The effects of the stimulation grid, the muscle-of-interest, and the stimulated hemisphere on the sizes and CoGs were also investigated. The MEP area was larger on the dominant than on the non-dominant side (p=0.002) and the representation sizes of the muscles differed (p=0.004). The MEP CoGs were significantly more medial (p=0.025) and anterior (p=0.011) than the SP CoGs. The CoGs of the muscles differed in the anterior-posterior direction (p=0.003). The grid or the hemisphere did not affect the sizes (p=0.656, p=0.331) or the CoGs (anterior-posterior: p=0.885, p=0.058; medial-lateral: p=0.521, p=0.710). Furthermore, the nTMS CoGs were located significantly more anterior than the BOLD (p<0.001) and ASL (p<0.001) local maxima. The results might be due to different neural processes between the excitatory and inhibitory motor functions as well as between the involuntary activation of the muscles during nTMS and voluntary activation during ASL and BOLD fMRI. In the future, the mapping of the representation areas could involve also the SPs, instead of only MEPs; the SPs could give additional information about the motor representations and plasticity of the motor cortex.
Site-dependent biomechanical chondrocyte responses and mechanical properties of rabbit knee joint cartilage
Ari Ronkainen, Itä-Suomen yliopisto
Aim: It is not known how in situ chondrocytes from various cartilage surface sites within a knee joint respond to compressive loading. The aim of this current study is to determine the biomechanical response of superficial zone articular cartilage chondrocytes, which are imaged at varying locations within the rabbit knee joint. In addition to the cell-level parameters, equilibrium and dynamic modulus of these different articular cartilage locations are determined. Materials and Methods: A confocal laser scanning microscope combined with a custom indentation system was utilized to image superficial zone chondrocyte responses to compressive loading in their native environment. Experiments were performed on patella, groove, femoral condyles and tibial plateaus from sacrificed female New Zealand White rabbits (13 ± 1 month). Image stacks (210 µm x 210 µm, pixel size 0.41 µm) of cartilage were acquired with 0.5 µm increments into the tissue depth up to 60 µms. Chondrocytes (N = 90-100 / site) were cropped and reconstructed from the image stacks, and their volumes and dimensions (i.e. cell height, width and depth) were determined for each tissue site before and after compression (2 MPa, 20 mins). Global, local axial and transverse tissue strains and equilibrium and dynamic moduli were also determined for each site. Results: When comparing matching sites to each other, it was noticed that chondrocytes from patella underwent a greater volume decrease (compared to femoral groove cells; p < 0.05) primarily due to a greater decrease in cell height (p < 0.05). This was consistent with greater levels of both global and local axial strains in the patellae (p < 0.05), and with lower equilibrium moduli of patellae (p < 0.05). Lateral condyle cells underwent a greater volume decrease (compared to lateral plateau cells; p < 0.05) primarily due to a greater decrease in cell height, which was consistent with greater levels of tissue strains (p < 0.05) and lower equilibrium moduli (p < 0.05) of lateral condyles. On the other hand, medial condyle cells underwent a smaller volume decrease (compared to medial plateau cells; p < 0.05) primarily due to an elevated cell expansion in the depth direction and lesser expansion in width direction. This was consistent with the levels of major and minor strains and the equilibrium moduli. Conclusions: Chondrocyte biomechanical responses in the rabbit knee joint articular cartilage and mechanical properties of these tissues were site-dependent. The volume decreases of chondrocytes due to deformation were always driven by cell height decreases, which were always larger than cell expansion in lateral directions. Cell expansion in lateral directions was anisotropic, implying that local tissue structure causes the cells to deform in a preferred way. In addition to these findings, the cell height changes were inversely proportional to the equilibrium moduli of cartilage, implying that stiffness of tissue affects the cell height change under loading. These findings suggest that site-dependent loading of the joint affects the mechanobiological responses of chondrocytes, which may drive cartilage adaptation in site-specific manner.
BAckground and specific contrast enhancements for imaging biological samples with uCT
Ilmari Tamminen, Tampereen teknillinen yliopisto
Background and aims: Typically, an X-ray image forms as the applied ray becomes attenuated by the imaged sample. In biological and biomaterial samples, the common imaging issue is the low density and its homogeneous distribution. Without externally supplied heavy elements, studied features may not be visible at all, or the µCT-imaging may take unreasonable amount of time resources. The goal of this study was to test and optimize different background and specific contrast enhancement methods for overcoming these imaging issues. Materials and methods: The used background contrasting methods were based on iodine and phosphotungstic acid. Each staining method were iterated until satisfactory contrasting results were gained for examining the three dimensional anatomy of adult zebra fish. The ethanol based iodine was also used for studying the structural dissimilarities between dystrophic and healthy rat retinas. Stem cell monolayer samples were specifically stained by antibodies which were used for localizing metallic silver in the immediate proximity of the examined antigens. Results: During the research it was shown that all of the used contrasting methods were capable for enhancing the studied features in the treated samples. All of the background contrasting methods successfully enhanced the anatomical features of the adult zebra fish. Furthermore, the ethanol based iodine staining preserved the general morphology of the rat eyes and made possible for distinguishing clear structural dissimilarities between dystrophic and control retinas. The specific contrasting method enhanced successfully the target actin and lamin antigens in the examined stem cell samples. Conclusions: The used contrasting methods gave good and comprehensive base for the following research for studying wide variety of biological samples with µCT.
Reconstruction of ultrasound field in Schlieren tomography
Jenni Tick, Itä-Suomen yliopisto
Aims of the research: The acoustic output of ultrasonic transducers has traditionally been analyzed with a hydrophone. The analysis of the ultrasound field can be performed faster by using Schlieren imaging, especially Schlieren tomography. In Schlieren tomography, reconstruction of the ultrasound field is ordinarily formed by using inverse Radon transform. The inverse Radon transform has continuity assumptions and it is ill-posed, thus noise and finite number of projection angles can cause errors in the reconstructions. In this work, it is investigated whether application of least squares minimization based approaches can provide better reconstruction than the inverse Radon transform. Methods: Pressure fields of a focused and planar transducers are reconstructed from Schlieren images. The reconstructions are performed by using the inverse Radon transform and two least squares minimization approaches: Tikhonov regularization and Fourier basis approach. The reconstructed pressure fields are compared to pressure fields obtained by hydrophone measurements and theoretically computed pressure fields. Results: All three reconstruction methods gave similar results and the reconstructions were similar in comparison to the hydrophone measurements and the theoretical pressure fields. Furthermore, the Tikhonov regularization and the Fourier basis approach provided similar, or better, reconstructions than the inverse Radon transform. Conclusions: The results show that the least squares based approaches can provide similar, or better, reconstructions than the traditionally used inverse Radon transform. However, computationally the inverse Radon transform was faster than the Tikhonov regularization or the Fourier basis approach. In the future, information about different error sources, or advanced prior information of the ultrasound transducer, could be included in to the regularization approaches to attempt to further improve the reconstructions.
Methods and Models for Biological Sig- nals and Images (M2oBSI) research group, at the Department of Signal Processing
Amalia Moreno Galera, Tampereen teknillinen yliopisto
Positron Emission Tomography (PET) scanner is a medical device that uses an imaging technique, which allows the acquisition of internal body processes. In the next generation of PET scanners the scintillator crystals will be placed axially along the Field Of View (FOV), instead of radially in the tomograph. Within this new structure, the axial resolution and sensitivity increases. This thesis aims to present a Data Processing Toolbox that will be used to process and reconstruct the information acquired by previous and future versions of PET scanners. The developed Toolbox has three processes that can be independently performed or following this order: generate realistic list-mode files, histogram list- mode data sets and reconstruct sinograms into 3D images. The first process uses numerical phantoms for producing list-mode data. Moreover, the list-mode data has a realistic appearance due to the utilization of bootstrapping and shuffling tools. The second process is used for histograming different PET scanners list-mode data, which is possible within the Radon transform dependence with scanners geometry. Thirdly, the last process produces 3D images from sinograms that are corrected, rebined and reconstructed. The manipulation of the sinograms is described on this research work. In order to test the Toolbox performance, presented thesis work experiments use numerical simulations and data from real PET scanners (Inveon and COMPET). In addition a study about the optimal MLEM number of iterations according with the SNR has been evaluated. In addition, a study about the parameter dependency with the executing time determines the efficiency of the Toolbox In conclusion, this thesis presents the design and evaluation of a Toolbox, which is useful for different commercial PET scannes. The reconstruction of the sinogramsproves the high resolution of the applyed methods.!