PET-CT scanner characterization for PET raw data use in biomedical research.

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Computerized Medical Imaging and Graphics journal homepage: www.elsevier.com/locate/compmedimag

PET-CT scanner characterization for PET raw data use in biomedical research Chiara Gianoli a,b,∗ , Marco Riboldi b,1 , Christopher Kurz a,2 , Elisabetta De Bernardi c,3 , Julia Bauer a,2 , Giulia Fontana d,4 , Mario Ciocca e,5 , Katia Parodi a,f,6 , Guido Baroni b,7 a Heidelberg Ion Beam Therapy Center and Department of Radiation Oncology, Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120 Heidelberg, Germany b Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy c Department of Health Sciences – Tecnomed Foundation, University of Milano-Bicocca, via Cadore 48, 20090 Monza, Italy d Unità di Bioingegneria Clinica, Strada Privata Campeggi, 53, 27100 Pavia, Italy e Unità di Fisica Medica, Strada Privata Campeggi, 53, 27100 Pavia, Italy f Ludwig Maximilians University (LMU) Munich, Experimental Physics – Medical Physics, Am Coulombwall 1, 85748 Garching, Germany

a r t i c l e

i n f o

Article history: Received 18 October 2013 Received in revised form 11 March 2014 Accepted 24 March 2014 Keywords: Biomedical imaging PET imaging Data interpretation PET raw data dicom PET image

a b s t r a c t The purpose of this paper is to describe the experiments and methods that led to the geometrical interpretation of new-generation commercial PET-CT scanners, finalized to off-line PET-based treatment verification in ion beam therapy. Typically, the geometrical correspondence between the image domain (i.e., the dicom PET) and the sinogram domain (i.e., the PET raw data) is not explicitly described by scanner vendors. Hence, the proposed characterization can be applied to commercial PET-CT scanners used in biomedical research, for the development of technologies and methods requiring the use of PET raw data, without having access to confidential information from the vendors. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction The application of Positron Emission Tomography (PET) imaging to treatment verification of ion beam therapy [1–5] has been increasingly encouraged by the development of technologies and

Abbreviations: PET, Positron Emission Tomography; CT, Computed Tomography; LOR, Line of Response; 2/3D, two/three dimensional. ∗ Corresponding author at: Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, P.za Leonardo da Vinci 32, 20133, Milano, Italy. Tel.: +39 02 2399 9022. E-mail addresses: [email protected], [email protected] (C. Gianoli), [email protected] (M. Riboldi), [email protected] (C. Kurz), [email protected] (E. De Bernardi), [email protected] (J. Bauer), [email protected] (G. Fontana), [email protected] (M. Ciocca), [email protected] (K. Parodi), [email protected] (G. Baroni). 1 Tel.: +39 02 2399 9012/9021; fax: +39 02 2399 9000. 2 Tel.: +49 6221 56-36569. 3 Tel.: +39 02 6448 8288. 4 Tel.: +39 0382 078 513/512; fax: +39 0382 078 903. 5 Tel.: +39 0382 078408; fax: +39 0382 078903. 6 Tel.: +49 89 289 14085; fax: +49 89 289 14072. 7 Tel.: +39 02 2399 3349/9011; fax: +39 02 2399 3360/9000.

methods towards the improvement of PET image quality. PETbased treatment verification is applied in ion beam therapy to verify the consistency of the delivered treatment with respect to the treatment planning simulation. In ion beam therapy, the positron (␤+ ) emitters are produced via nuclear fragmentation reactions between the penetrating beam particles and the target nuclei of the tissue. The ␤+ emitter distributions can be imaged during irradiation by means of dedicated dual-head PET devices (in-beam PET) [1,6] or subsequently to irradiation by means of PET scanners installed inside the treatment room (in-room PET) [7,8] or outside the treatment room (off-line PET) [5,9,10]. Despite the issue of reduced count statistics and increased washout effects with respect to the in-beam and in-room approaches, the off-line approach is currently adopted in clinical application thanks to the reduced integration effort that is required [11,12]. The availability of technology coming from conventional PET imaging in nuclear medicine makes the installation of commercial PET-CT scanner an accessible solution for PET-based treatment verification in ion beam therapy. Posttreatment PET-CT verification relies on a comparison between the dicom PET image and a Monte Carlo prediction of the ␤+ emitter distributions typically based on rigid registration between the post-treatment dicom CT image and the treatment planning dicom CT image. The Monte Carlo simulation code statistically models

http://dx.doi.org/10.1016/j.compmedimag.2014.03.008 0895-6111/© 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Gianoli C, et al. PET-CT scanner characterization for PET raw data use in biomedical research. Comput Med Imaging Graph (2014), http://dx.doi.org/10.1016/j.compmedimag.2014.03.008

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Table 1 Information reported in the header file of the PET raw data, describing the 3D acquisition modality of the scanners Biograph True Point and Biograph mCT. Differently from the scanner Biograph True Point, the scanner Biograph mCT provides the matrix of random counts: the true counts matrix was therefore calculated by summing up the 13 time of flight (TOF) bins and subtracting the matrix of random counts.

Format Bytes per pixel Matrix size

Scale factor

Projection View Plane mm/pixel (projection) Degree/pixel (view) mm/pixel (plane)

Number of extracted matrix Number of rings Maximum ring difference Axial compression, span Number of segments Segment table (plane)

the nuclear interaction between projectiles and the target nuclei of the irradiated tissue, as a function of the energy and fluence of the ion beam, the stopping properties of the elementary tissue volumes (i.e., the CT voxel) and the internal (for carbon ions) or experimental (for protons) cross-sections of nuclear reactions [13,14]. A Gaussian filter is in general applied to the simulated ␤+ distribution to take into consideration the effects of positron range, the intrinsic physical spatial resolution of the scanner and image reconstruction, thus enabling PET prediction to be compared directly to the dicom PET image provided by the scanner [10,14]. The accuracy of PET-based treatment verification is strongly limited by the extremely low count statistics characterizing the acquired PET image, which are orders of magnitude below that in conventional nuclear medicine applications. Such a poor statistics adds up to well-known PET imaging drawbacks, such as the limited spatial resolution and the need of multiple corrections to achieve optimal image quality. The rationale of our research, that motivated this study on commercial PET-CT scanners, is to provide quantitative tools for the off-line PET-based treatment verification in ion beam therapy, making the most of PET raw data extracted from commercial scanners. The investigation of alternative reconstruction strategies, specifically developed to increase the robustness to noise in PET-based treatment verification [15–18], requires the establishment of the geometrical relationship between the acquired PET raw data and the dicom PET-CT images. Dedicated software tools simulating PET imaging systems have been developed to provide controlled environments for testing novel methods [19–21]. Commercial scanner performances can be accurately reproduced by modelling the scanner design and the physical properties of the scanner components, in addition to the computational procedures adopted to discretise and organize the physical projections in the PET raw data matrix. These software tools could be successfully used to understand the geometrical relationship between sinogram and image domains in the corresponding real scanner. Nevertheless, due to limited access to proprietary vendor information, they do not cover most of the new-generation PET-CT scanners such as those adopted for our applications. This paper describes the experimental and methodological framework that provides the geometrical interpretation of newgeneration commercial PET-CT scanners, finalized to the use of PET raw data in biomedical research. Specifically, the presented methodology allows one to define the geometrical correspondence between the PET raw data and the dicom PET-CT image provided by arbitrary PET-CT scanner.

Biograph True Point

Biograph mCT

Signed integer 2 336 336 313 2.005 0.5357 2.025 1 (net trues) 41 27 11 5 81;69;47

Signed integer 2 400 168 621 2.005 1.0714 2.027 14 (13 TOF + randoms) 55 49 11 9 109;97;75;53;31

2. Materials and methods 2.1. PET-CT scanners The Biograph mCT PET-CT scanner (Siemens Medical Solutions USA, Inc.) is installed at Heidelberg Ion Beam Therapy Center (HIT, Germany) and is currently used for off-line PET-based treatment delivery verification in clinical practice [10,14,22]. The Biograph True Point PET-CT scanner (Siemens Medical Solutions USA, Inc.) is installed at Centro Nazionale di Adroterapia Oncologica (CNAO, Pavia) for conventional treatment planning in the ongoing clinical activities. 2.2. PET raw data The header file of the PET raw data contains information that describes the 3D acquisition modality in histogram-mode (i.e., sinogram) of the scanner (Table 1). PET raw data are not corrected for random, scatter, attenuation and normalization (i.e., crystal efficiency correction), and the time of flight localization is not taken into account. According to parameters reported in Table 1, the PET raw data files were imported in Matlab (The MathWorks, Inc., Natick, MA). In 3D acquisition modality, the PET raw data are organized in the sinogram plane (direct or oblique planes) as a function of the polar angle ϕs , defined by the connection between two different detector rings. Sinogram planes are classified in segments, according to the number of rings, the maximum ring difference and the span [23]. The transverse sinogram is identified across two adjacent detector rings, thus increasing the number of sinogram planes (doubling the axial sampling). For each azimuthal angle ϑs , parallel projections (coplanar only for ϕs = 0) are organized along the coordinate ps . In the following, a set of parallel projections for any azimuthal angle ϑs and polar angle ϕs will be referred as view, corresponding to the 3D Radon transform in a mathematical description. The sinogram frame is therefore described in terms of projections, azimuthal angle and sinogram plane (ϑ/2 coordinates). 2.3. Reference frame definition The dicom PET image frame is chosen as the reference frame. The dicom PET-CT data were read in Matlab (The MathWorks, Inc., Natick, MA) by means of the Matlab embedded function dicomread. By exploiting the co-registration in the scanner frame, the dicom CT image was registered to the dicom PET image and sampled to the dicom PET image grid, thus referring to a unique image frame. Slices corresponding to ascending values of Image Position Patient




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Fig. 1. The reference frame (left panel), the corresponding physical system frame (central panel) and the sinogram frame (right panel). Please note that the origin of the physical system frame does not coincide with the isocenter of the scanner as defined in dicom data (i.e., the scanner frame). The Head First Supine convention is assumed, as described by patient feet model.

were stored as a function of increasing values of the slice number n. As a consequence, the reference frame was described in terms of rows, columns and slices (r, c, n coordinates) as depicted in Fig. 1. The definition of an image frame in which a certain object is physically expressed is required. A physical system frame is therefore introduced. For simplicity, the physical system frame is just centred in the reference frame and expressed in millimetres, according to the following equations:

D D ⎧ im im ⎪ ⎨ (x, y) = c − 2 + 0.5 , r − 2 + 0.5 · pixel spacing ⎪ ⎩ z = n − Nslice + 0.5 · slice thickness 2

(1)

Where pixel spacing and slice thickness are reported in the header file of dicom PET data, Dim is the image size (parameterized in row number r and column number c) and Nslice is the total number of dicom PET data, or image slices (parameterized in slice number n). In general, the geometrical correspondence between the image domain (r, c, n) and the sinogram domain (ps , ϑs , ϕs ) is not explicitly described. The object representation is analyzed in both image and sinogram domains in order to map the PET raw data onto the dicom PET image, according to the defined physical system frame. In Fig. 1 the image and the sinogram domains are depicted and the corresponding frames are described.

2.4. Experimental framework for geometrical characterization The proposed characterization was based on a set of acquisitions that were expected to outline how the physical projections are discretized and organized in the PET raw data matrix. This goal will be referred to in the following as geometrical characterization. The cylindrical uniform phantom and the rod sources, as available from scanner vendors for periodic calibration and quality control, were acquired in pre-defined positions within the Field of View (FOV) of the scanner. For the Biograph mCT, point sources bought from manufacturer were used instead the rod sources. The object was placed at the isocenter of the scanner with the use of positioning laser lines, and was moved along the y and z directions by means of the bed shifts and along the x translation by moving manually the object itself (Fig. 1). The performed acquisitions used for data analysis are summarized in Table 2.

The geometrical characterization can be summarized in the following steps:

i. Extract the geometrical parameters of the considered acquisitions by fitting a sinogram model expressed in the sinogram frame (ps , ϑs , ϕs ) and convert them in physical coordinates; ii. Extract the coordinates from the reference frame (r, c, n) and map them onto the physical system frame (x, y, z), according to the defined physical frame; iii. Find the geometrical correspondence between the sinogram frame and the reference frame through the physical coordinates. iv. In other words, with reference to the adopted physical system frame defined in Fig. 1, the sinogram frame (ps , ϑs , ϕs ) was mapped onto the reference frame (r, c, n). Due to the complex 3D geometry of the problem, the study was divided into axial and trans-axial components.

2.5. Axial geometrical characterization 2.5.1. Direct sinogram planes: axial mapping The acquisitions of point and rod sources (this latter placed parallel to the x direction in the physical system frame), axially shifted along the z direction with respected to the scanner isocenter, were used to identify the axial correspondence between the sinogram and image frames. The sinogram planes characterized by ϕ = 0 (the first part of the PET raw data matrix, identified by the first segment table in the header file of PET raw data) were considered, thus their axial identifier ϕs in the sinogram frame will be referred to as zs coordinate. The number of counts for each sinogram plane was calculated. The peak value was extrapolated from Gaussian interpolation of the resulting profile as a function of the identifier zs . The identifier of the sinogram plane representing the axial position of the source in the sinogram frame was expressed in physical coordinates according to: zp = zs · scale factor

mm pixel

(2)

The axial coordinate zp was associated to the axial coordinate detected in the image domain and expressed in the physical system frame z. Similar to the sinogram frame, the geometrical parameter was extracted from the dicom PET image by searching the peak value in the number of counts (i.e., the measured activity) reported in the image slices. The axial mapping equation was therefore derived by finding the relationship between zp and z.


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Fig. 2. Simulated sinogram planes for the Biograph True Point (panel A) and the Biograph mCT (panel B): absence of arc-correction (left); presence of arc-correction (right). The four images cover the area identified by the scanner diameter (Dscanner = 842 mm, according to scanner specifications in Table 3) and purple lines indicate the borders of the area included in the FOV (DFOV = 673.68 mm for the Biograph True Point and DFOV = 802.00 mm for the Biograph mCT, according to the PET raw data matrix dimension and the trans-axial scale factor reported in Table 1).

2.5.2. Oblique sinogram planes: data organization Each segment was stored in a defined portion of the PET raw data matrix reported as segment table in the header file of PET raw data, indicating the number of sinogram planes for each segment. In order to identify the sinogram frame in the oblique sinogram planes (the remaining part of PET raw data matrix, identified by the other segment table values in the header file of PET raw data), point and rod sources shifted alternatively along the y and x directions with respect to the isocenter of the scanner, were acquired. Differently from direct sinogram planes where projections laid on a trans-axial plane of the FOV, the oblique sinogram planes split the ring into two parts at different axial positions. The projections are therefore divided into two segments connecting opposite semi circumference of the rings (i.e., segments ±ϕ). The split was hypothesized to occur alternatively around the x or y axis, as rotational axis of the oblique sinogram planes (in Fig. 1, a split around the y axis is assumed). The number of counts on each sinogram plane was analyzed for both the shifted acquisitions, showing the appearance of the source as a function of the sinogram plane identifier ϕs . If the source shifted along the y direction appears at the same axial position for the two segments, the y axis coincides to the assumed rotational axis of the oblique plane. Conversely, if the source shifted along the y direction appears at different axial positions, the axis of rotation is x. In order to identify the succession of the two segments 1 · 105 , the considered source acquisition is shifted perpendicularly with respect to the identified rotation axis (i.e., shift along x if the rotation axis is y). According to the physical system frame reported in Fig. 1, the oblique sinogram plane where the source appears firstly would belong to the segment −ϕ, if the source position is placed along the positive part of the axis. Viceversa, the sinogram plane would belong to the segment +ϕ as

the source position is placed along the negative part of the axis. Once established the geometrical relationship between sinogram plane identifiers ϕs and physical system frame, each stack of oblique sinograms was assigned to the corresponding segment. 2.6. Trans-axial geometrical characterization 2.6.1. Data organization Due to the cylindrical nature of the scanner, the physical projections measured along each LOR (Line of Response) are more closely spaced towards the edges of the FOV. In order to correct for this non-uniform sampling, projections on each view are interpolated according to a strategy known as arc-correction. Therefore, the eventual absence of arc-correction would modify the object representation in the sinogram domain, by stretching the object size in the corresponding view. This would result in a distorted reconstruction of the object, especially if significantly displaced from the scanner isocenter. By using visual inspection, the arc-correction does not clearly appear in the sinogram plane: the acquired objects cover the central area of the FOV where the non-uniform sampling can hardly be observed. The investigation was finalized to the definition of the projections geometry and to the identification of projection gaps associated to two adjacent detector blocks, in order to correct for count reduction in the sinogram planes (i.e., crystal geometry correction). To investigate the presence or absence of arc-correction, the typical diamond-shaped pattern on sinogram planes associated to the transverse gap between blocks was analyzed [24]. The pattern of gaps in the sinogram plane was simulated by accounting for and neglecting the arc-correction in the discretization of projections along each view: two sinogram models were therefore

Table 2 Cylindrical uniform phantom and rod/point sources acquisitions expressed in the scanner frame for the Biograph True Point and the Biograph mCT. Translations are expressed in millimetres with respect to the scanner isocenter. The x and y directions are defined in Fig. 1. Biograph True Point

Biograph mCT

Cylindrical uniform phantom

Rod source

Cylindrical uniform phantom

Point source

y (mm)

x (mm)

z (mm)

y (mm)

x (mm)

z (mm)

0 −50 +47

0 0 −100

0 +30 0

0 −37 +37

0 0 +100

0 +50 0




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Table 3 Geometrical scanner specifications (identical for Biograph True Point and Biograph mCT). Number of detector blocks Nblock Number of crystals per block Ctan × Cax = Cblock × Cblock Scanner diameter (mm) Dscanner Crystal dimension (mm3 ) dtan × dax × drad

48 13 × 13 842 4 × 4 × 20

implemented. Gaps were represented as unitary pixels placed along the scanner circumference. According to scanner specifications reported in Table 3 [25], the azimuthal angle defined by two adjacent gaps or the angular amplitude of each detector block is defined by ˛ = 2/Nblock . The pixel size and projection angle adopted in the sinogram simulation were set equal to the trans-axial scale factor reported in the header file of PET raw data. In the arc-corrected simulation the physical LOR spacing was neglected and projections were discretized according to the pixel size, thus generating the arc-corrected sinogram. The physical projections appeared shrunk according to sin (ϑrel ), where ϑrel is the azimuthal angle relative to the considered view. The absence of arc-correction was simulated by interpolating each view of the arc-corrected sinogram onto a grid defined by cos (ϑrel ). The function reassigned an equal number of samples to each detector block, independently of the relative azimuthal angle ϑrel , reproducing a dense LOR sampling at the edges of the FOV and an almost uniform sampling in the centre of the FOV. When observing the gaps pattern as a function of the projection angle ϑs , the arc-correction simulation generated a sinusoidal pattern on the sinogram plane according to cos (ϑs ), whereas the absence of the arc-correction led to a linear pattern, as reported in Fig. 2. In both cases, the pattern of gaps appeared as symmetric lines crossing the sinogram plane, spaced by the dimension of the detector block projection (with arc-correction) or by the dimension of the detector block itself (without arc-correction). In order to discriminate the presence or the absence of arc-correction on PET raw data, the gap pattern was hypothesized invariant within segments, neglecting the effect of different photon-crystal interaction angle (i.e., parallax or cross-talk errors). The sinogram representing the gap pattern on PET raw data was generated by summing up all sinogram planes of the three acquisitions of the cylindrical uniform phantom, thus obtaining a high count statistics representation of gaps, covering at the most the FOV. In the following these sinograms will be referred to as average sinograms. The diamond-shaped pattern was identified by searching the higher correlation between the average sinogram and the two binary patterns obtained from sinogram simulations in presence and in absence of arc-correction. Correlation peaks were found by shifting a sinusoidal line (presence of arc-correction) and an inclined straight line (absence of arc-correction) at a resolution of ϑ/2 (i.e., half of the elementary projection angle of the scanner). The shape of the correlation peak revealed the presence or the absence of arc-correction while the positions of correlation peaks highlighted the structure of gaps pattern, useful to determine the configuration of detector blocks and the dimension of the gap in terms of fraction of elementary crystal (Cgap ). The correlation peaks highlighted the position of the first gap, thus determining the true configuration of the detector block in the scanner. Hypothesizing a symmetric structure for the PET scanner, two configurations of detector blocks could be distinguished according to the first gap found at ϑs = 0◦ or at ϑs = ˛/2, as depicted in Fig. 3. 2.6.2. Trans-axial mapping The trans-axial sinogram model, parameterized in ps and ϑs , has to take into consideration whatever arc-correction is applied on PET raw data. In case of not arc-corrected sinograms, the adoption of this sinogram model would require the interpolation strategy

Fig. 3. The configuration of detector blocks can find the first gap at ϑs = 0◦ (upper) or alternatively at ϑs = ˛/2 (lower).

described in the previous paragraph (limited to the FOV defined by purple lines in Fig. 2). In the following, the sinogram model description is given for arc-corrected sinograms. The trans-axial geometrical characterization requires the acquisition of reference objects shifted along x and y directions with respect to the scanner isocenter. Quantitative analysis was performed on the three acquisitions of the cylindrical uniform phantom shifted along the y directions by means of the bed shift, that were more reliable than the x direction applied by moving manually the object (point and rod sources as reported in Table 2). The choice of cylindrical uniform phantoms, instead point and rod sources, was motivated by the availability of two sinusoidal curves on each sinogram plane, repeated for multiple sinogram planes. The border of phantom strips in the sinogram domain was extracted in each sinogram plane by setting a threshold corresponding to 40% of the maximum value of the sinogram plane. In order to exclude the noisy sinogram planes at the edges of the FOV, the strip segmentation was applied only if the number of counts on the sinogram plane was higher than 1 · 105 counts. This exclusion was introduced by observing considerable irregularities on the phantom profiles segmented according to the 40% of the maximum, due to low count statistics on oblique sinogram planes at the edge of the FOV. In principle this could be avoided by prolonging the PET acquisition time. Two sinusoidal curves f (ϑs ) were defined by the two border pixels along each view, as a function of the projection angle ϑs . The sinogram patterns clearly demonstrated that the angular coverage was equal to and that the first projection view was roughly assumed as equal to 0◦ , as depicted in Fig. 4. Accordingly, the projection angle variable was set equal to ϑs = (0, ϑ, . . ., − ϑ). By placing the origin of the sinogram frame in correspondence of the middle of the view, the profiles in the sinogram domain can be modelled according to the following equation: f (ϑs ) = xs · cos (ϑs ) + ys · sin (ϑs ) + bs

(3)

Where xs and ys are the shifts detected in the sinogram frame, and bs is the average integral value of the 2-periodic curve. These parameters were calculated by fitting the curve f (ϑs ) with the trust-region algorithm in a non-linear least square method, being ϑs the independent variable. The offset value bs depended


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Fig. 4. In the trans-axial FOV of the scanner, shifts along x and y directions with respect to the scanner isocenter determine specific sinogram features according to the first projection view.

on the threshold set to identify the phantom strip perimeters. The parameters xs and ys , extracted from sinogram domain, were expressed in physical coordinates according to:

y directions, in order to refine the first projection view with a resolution superior to the elementary projection angle ϑ. Equation (3) was therefore modified as follows:

(xp , yp ) = (xs , ys ) · transaxial scale factor

˜ + ys · sin (ϑs + ϑ) ˜ + bs f (ϑs ) = xs · cos (ϑs + ϑ)

mm pixel

(4)

To extract the phantom centroids from the dicom PET image, a segmentation strategy was implemented by setting a threshold corresponding to 1% of the maximum value of the image slice. The calculated centroids were expressed in the physical system frame (x, y) and associated to the corresponding shift values extracted from the sinogram domain and expressed in physical coordinates (xp , yp ). Shift and centroid values detected in the sinogram and image domain were associated to the corresponding axial coordinate in the physical system frame, coming from the axial mapping. The difference values, corresponding to offset values for the transaxial mapping, were calculated for the three acquisitions of the cylindrical uniform phantom. The median value of the statistical distribution was identified and the mapping equation was therefore derived. 2.6.3. Refined identification of the first projection angle Expression (3) is based on the assumption that the first projection angle corresponds to 0◦ and accordingly the second projection angle corresponds to ϑs = ϑ, being this latter the elementary projection angle reported as trans-axial scale factor in Table 1. This assumption was questioned by considering that the first projection angle may fall within the range of the elementary projection ˜ − ϑ ∩ ϑ ˜ ≤ ϑ) due to possible presence of angle itself (i.e., ϑ≥ the gap at ϑs = 0◦ (Fig. 3) or due to interleaving strategies adopted by the scanner vendors. For such a reason, the first projection angle ˜ was identified according to a specific strategy based on the three ϑ acquisitions of the cylindrical uniform phantom shifted along the

(5)

˜ is the first projection angle to be identified, thus resultWhere ϑ ing dependent on the identified shifts in sinogram domain (i.e., the xs and ys parameters). The curve f (ϑs ) was fitted making use of the same algorithm and method adopted above. A quantitative analysis ˜ was based on the statistical distribution of the extracted values of ϑ performed and the median value was identified as first projection angle. 2.7. Implementation of the geometrical characterization By exploiting the outcomes of the axial geometrical characterization, oblique sinograms were projected onto the direct planes according to the Fourier rebinning algorithm (FORE) [23,26] in order to increase the sinogram count statistics and reduce the dimension of the reconstruction problem. The polar angles of different segments were determined by considering that the scanner diameter reported in Table 3 does not coincide with the effective detection system diameter, which was derived from the detection system perimeter. The latter was determined according to the physical dimension of the crystal ring, being known the number of blocks, the number of crystals per block and the tangential crystal dimension, as reported in Table 3. The mapping equations enabled the dicom PET image FOV identification on the sinogram domain. Subsequently, the rebinned sinograms were interpolated onto the dicom PET image grid. The 2D geometrical system matrix expressing the area of intersection between the mapped projections and the pixels of the dicom PET image was therefore calculated, accounting for the presence




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Fig. 5. Counts profile as a function of the sinogram plane identifier ϕs for the Biograph mCT scanner. The succession of nine segments was observed.

or absence of arc-correction and for the identified first projection angle. Relying on the trans-axial geometrical characterization, the projection gaps associated to two adjacent detector blocks were corrected in order to account for count reduction due to these gaps

in each sinogram plane (i.e., crystal geometry correction). The correct trans-axial sinogram model was used to identify the gap path and the missing projections in correspondence to the gap were estimated by means of linear interpolation, independently for each projection angle. The axial PET raw data combination described by

Fig. 6. The average sinograms generated by using all the three acquisitions of the cylindrical uniform phantom for the Biograph True Point (panel A) and the Biograph mCT (panel B).


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Fig. 7. 2D correlation values calculated between the average sinogram and the binary patterns for the arc-corrected and not arc-corrected sinogram models (i.e., the sinusoidal line and inclined straight line, respectively) for the Biograph mCT. Absolute values of the 2D correlation depended to the thickness of the binary pattern. The sinusoidal lines were shifted by ϑ/2 and ϑ with respect to the identified angle of the first correlation peak (ϑs = 0◦ ) in order to support results for the first projection angle identification.

Fig. 8. Image centroids and sinogram shifts expressed in the physical system frame for the cylindrical uniform phantom placed at the isocenter of the scanner Biograph mCT. The variability appears higher for the sinogram shifts, in agreement with the noise level (i.e., the count statistics) affecting the segmentation of the sinogram planes. The slope of the lines indicates misalignments along the axial dimension introduced by object positioning. The offset between parallel lines coincides with the offset identified in the trans-axial mapping equation. Samples at the edges of the FOV for the sinogram shifts are missing because the threshold excluded the corresponding sinogram planes. Only one of the four samples is missed because of the different axial FOV extension.


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Table 4 Offsets detected as median difference values between shift and centroid: xoffset = (x − xp ) and yoffset = (y − yp ). Shifts are estimated by fitting the sinogram model, independently applied on the border of phantom strips f (ϑs ) a function of ϑs , thus leading to the upper and lower sinusoidal curves for each phantom. An overall median difference values between shift and centroid was obtained by considering the upper and lower sinusoidal curves of all the three acquisitions of the cylindrical uniform phantom. f (ϑs ) upper

Biograph mCT

Biograph True Point

Biograph mCT Biograph True Point

f (ϑs ) lower

y bed

xoffset (mm)

yoffset (mm)

xoffset (mm)

yoffset (mm)

0 −37 +37 0 −50 +47

−0.96 −0.63 −1.02 −0.77 −0.42 −0.97 xoffset (mm) −0.99 −0.61

−1.68 −2.32 −0.65 −0.98 −2.40 −0.58

−1.07 −0.90 −1.15 −0.53 −0.34 −0.60 yoffset (mm) −1.17 −0.96

−1.13 −1.40 0.01 −1.26 −0.88 1.31

Overall Overall

the michelogram scheme, including blind rings (i.e., axial gaps), was taken into account [27]. The overall processing enabled the reconstruction of the transformed (i.e., mapped) PET raw data matrix consistent to the dicom PET image. 3. Results and discussions 3.1. Axial geometrical characterization 3.1.1. Direct sinogram planes: axial mapping The correspondence between the point and rod sources positions calculated in image and sinogram domains and converted into physical coordinates zp and z was described by the following expression:

z = −zp + 0.5 +

Nsino 2

(6)

Where Nsino is the number of sinogram planes for the segment characterized by ϕ = 0◦ . The residual absolute difference between the positions identified into the different domains was always inferior to 0.22 mm within the considered acquisitions (Table 2). The difference in millimetres between the axial FOV covered by the dicom PET image and the axial FOV covered by the Nsino sinogram planes was therefore computed. The physical system frame, centred by definition in the axial FOV covered by the dicom PET image, was therefore centred also in the axial FOV covered by the sinogram. 3.1.2. Oblique sinogram planes: data organization As observable in the counts profile as a function of the sinogram plane identifier ϕs (Fig. 5), the first stack of sinogram plane corresponded to the segment characterized by ϕ = 0◦ , then segments succeeded according to increasing inclinations due to a broader connection among rings. For each segment, the two sinogram plane stacks symmetrically connecting the detector rings and characterized by opposite polar angles (one at −ϕ, the other at +ϕ) were stored nearby, in agreement with the segment table reported in the header file of PET raw data. The two segments characterized by opposite polar angles were localized within the PET raw data matrix. The point source shifted along the y coordinate appeared at the same sinogram plane identifier ϕs of the source placed at the isocenter. The rotational axis of sinogram planes splitting the rings in two parts was therefore identified in correspondence of the y axis. The point source shifted along the negative direction of the x coordinate, appeared first in the second stack of sinogram planes of equal inclination. Due to the inverted correspondence between the coordinates zs and z reported in (6), the segment −ϕ was therefore attributed to the second stack

of sinogram planes, being the positive rotation +ϕ defined by the z axis approaching the x axis (Fig. 1).

3.2. Trans-axial geometrical characterization 3.2.1. Data organization For both for the Biograph True Point and the Biograph mCT scanners, the correlation analysis of the diamond-shaped pattern on the average sinograms reported in Fig. 6 demonstrated that the PET raw data are corrected for the non-uniform sampling of the view due to the arc shape of the scanner (i.e., the arc-correction). The binary patterns used to identify the correlation peaks with the average sinogram showed distinct correlation peaks for the arc-corrected sinogram model (Fig. 7). Fig. 7 demonstrated also that the position of the first correlation peak was found in correspondence of 0◦ , and also in correspondence of ϑ/2 but not in correspondence of ϑ as relevant for the first projection angle identification. This suggested that the configuration of detector blocks can be reasonably localized at ϑs = 0◦ (Fig. 3). Correlation peaks were repeated at a multiple of ˛/ϑ, equal to 14 for the Biograph True Point and 7 for the Biograph mCT, demonstrating that ϑ is an integer multiple of ˛ in agreement to the number of crystals per block that was equal to 13 for both scanners. Accordingly, the dimension of the gap was equal to one crystal such that each gap contributed to one fake crystal (Cgap = 1). It was reasonable to assume that the Biograph mCT scanner combines in a single projection the counts detected by two couples of adjacent crystals.

3.2.2. Trans-axial mapping The acquisition of the cylindrical uniform phantom shifted along the y direction generated a sin (ϑ) curve shape in the sinogram domain, indicating that the first projection view corresponded to 0◦ in the adopted physical system frame, as depicted in Fig. 4. Positive shifts along the x and y directions resulted in positive values along the xs and xs coordinates (Fig. 4). The analytical estimation of xs and xs revealed misalignments along the axial dimension due to object positioning (Fig. 8). By displaying the shifts xp and xp as a function of the sinogram planes identifier ϕs , linear trends consistent within different segments could be observed. Fig. 8 reports the comparison of the centroids extracted from the dicom PET image (x and y) and the shifts extracted from the sinogram (xp and xp ) as a function of the axial coordinate z in the physical system frame. Inaccuracies identified in image and sinogram domains were in agreement, as proved by parallel trends showed by fitting the parameters for each spatial component of the trans-axial FOV. Table 4 summarizes the statistical analysis on the three acquisitions of the cylindrical uniform phantom for the Biograph True


G Model CMIG-1251; No. of Pages 11 10


Point and for the Biograph mCT, demonstrating that the mapping equation implies an offset. The correspondence between the phantom shifts analytically estimated in the sinogram domain and the phantom centroids calculated in the image domain, both converted into physical coordinates (xp , yp ) and (x, y), was therefore described by the following expression: (x, y) = (xp , yp ) + (xoffset , yoffset )

(7)

Where xoffset , yoffset are the identified offset values (Table 4). Differently from the axial FOV, the physical system frame turned out to be shifted in the trans-axial FOV covered by the sinogram. 3.2.3. Refined identification of the first projection angle The first projection angle refinement was based on three different acquisitions of the cylindrical uniform phantom shifted along the y direction. The median values of the statistical distribution of ˜ values resulted equal to 0.24◦ and 0.20◦ , being ϑ = the extracted ϑ 180◦ /336 = 0.5357◦ and ϑ = 180◦ /168 = 1.0714◦ the elementary projection angles for the Biograph True Point and the Biograph mCT scanners, respectively. In both cases, the 25th and 75th percentile values of the distribution differed considerably less than the elementary projection angle (the interquartile ranges were equal to 0.25◦ and 0.35◦ , respectively). According to the obtained results, we ˜ can be assumed equal to concluded that the first projection angle ϑ ϑ /2 = 0.2679◦ for both scanners. In such a way, the projecmin tion angle ϑs falls in the middle of the crystal, in agreement to the first gap found in correspondence of ϑs = 0◦ and to the correlation peaks found both in correspondence of 0◦ and ϑ/2, as depicted in Fig. 7 for the Biograph mCT. 4. Conclusions The proposed experimental and methodological framework led to the definition of a reliable geometrical correspondence between the PET raw data and the dicom PET-CT image, as provided by the PET-CT scanner. The described scanner characterization procedure enabled us to make use of PET raw data exported from commercial PET-CT scanners, such to define the projection model to be used for PET raw data reconstruction, coherently with the dicom PET image. The reliability of the geometrical correspondence between the PET raw data and the dicom PET image was verified on additional rod/point sources acquisitions. The reconstruction of the mapped PET raw data resulted co-registered and directly comparable to the dicom PET image. The projection model can be used to test alternative reconstruction strategies on patient data, subsequently to the transformation (i.e., mapping) of the extracted PET raw data matrix. In order to fully exploit the information provided by the scanner, time of flight localization of the Biograph mCT scanner is expected to be taken into account [28–30]. In this work, the 13 time of flight bins were summed up together and treated as the FOV was not partitioned. Hypothesizing circular symmetry of FOV partitioning, points sources placed along the scanner diameter (y direction for simplicity) would be acquired. An extensive dataset of point sources acquisitions would be therefore required, in opposition to the reduced amount of experimental data adopted in this work for scanner characterization. The number of counts in each bin, normalized by the total amount of counts, would be analyzed as a function of the radial position of the source. A probability model describing the fuzzy FOV partitioning could be considered. The system matrix would be provided with the resulting probability map for each time of flight bin, expressing a weighting factor for each point (i.e., voxel) of the FOV to be reconstructed. The proposed geometrical characterization, in combination with time of flight information, would be used to test on clinical

data unconventional reconstruction strategies for noise robust quantification in off-line PET-based treatment verification in ion beam therapy. Acknowledgments This work was supported by the project European Union’s Seventh Framework ENVISION, GA 241851. Authors would like to thank Dr. Maurizio Conti from Siemens for the technical support. References [1] Enghardt W, Debus J, Haberer T, Hasch BG, Hasch BG, Hinz R, et al. Positron emission tomography for quality assurance of cancer therapy with light ion beams. A Nucl Phys 1999;654(1 Suppl. 1):1047c–50c. [2] Enghardt W, Crespo P, Fiedler F, Hinz R, Parodi K, Pawelke J, et al. Charged hadron tumour therapy monitoring by means of PET. Nucl Instrum Methods Phys Res A 2004;525:284–8. [3] Enghardt W, Parodi K, Crespo P, Fiedler F, Pawelke J, Pönisch F. Dose quantification from in-beam positron emission tomography. Radiother Oncol 2004;73(Suppl. 2):S96–8. [4] Parodi K, Paganetti H, Cascio E, Flanz JB, Bonab AA, Alpert NM, et al. PET/CT imaging for treatment verification after proton therapy: a study with plastic phantoms and metallic implants. Med Phys 2007;34(2):419–35. [5] Parodi K, Paganetti H, Shih HA, Michaud S, Loeffler JS, DeLaney TF, et al. Patient study of in vivo verification of beam delivery and range, using positron emission tomography and computed tomography imaging after proton therapy. Int J Radiat Oncol Biol Phys 2007;68(3):920–34. [6] Pawelke J, Enghardt W, Haberer T, Hasch BG, Hinz R, Kramer M, et al. In-beam PET imaging for the control of heavy-ion tumour therapy. IEEE Trans Nucl Sci 1997;44(4):1492–8. ˜ S, Daartz J, Liebsch N, Ouyang J, Paganetti H, et al. Moni[7] Zhu X, Espana toring proton radiation therapy with in-room PET imaging. Phys Med Biol 2011;56(13):4041–57. [8] Min CH, Zhu X, Winey BA, Grogg K, Testa M, El Fakhri G, et al. Clinical application of in-room positron emission tomography for in vivo treatment monitoring in proton radiation therapy. Int J Radiat Oncol Biol Phys 2013;86(1):183–9. [9] Hishikawa Y, Kagawa K, Murakami M, Sakai H, Akagi T, Abe M. Usefulness of positron-emission tomographic images after proton therapy. Int J Radiat Oncol Biol Phys 2002;53(5):1388–91. [10] Bauer J, Unholtz D, Sommerer F, Kurz C, Haberer T, Herfarth K, et al. Implementation and initial clinical experience of offline PET/CT-based verification of scanned carbon ion treatment. Radiother Oncol 2013;107(2):218–26. [11] Parodi K, Bortfeld T, Haberer T. Comparison between in-beam and offline positron emission tomography imaging of proton and carbon ion therapeutic irradiation at synchrotron- and cyclotron-based facilities. Int J Radiat Oncol Biol Phys 2008;71(3):945–56. [12] Shakirin G, Braess H, Fiedler F, Kunath D, Laube K, Parodi K, et al. Implementation and workflow for PET monitoring of therapeutic ion irradiation: a comparison of in-beam, in-room, and off-line techniques. Phys Med Biol 2011;56(5):1281–98. [13] Parodi K, Ferrari A, Sommerer F, Paganetti H. Clinical CT-based calculations of dose and positron emitter distributions in proton therapy using the FLUKA Monte Carlo code. Phys Med Biol 2007;52(12):3369–87. [14] Bauer J, Unholtz D, Kurz C, Parodi K. An experimental approach to improve the Monte Carlo modelling of offline PET/CT-imaging of positron emitters induced by scanned proton beams. Phys Med Biol 2013;58(15):5193–213. [15] De Bernardi E, Faggiano E, Zito F, Gerundini P, Baselli G. Lesion quantification in oncological positron emission tomography: a maximum likelihood partial volume correction strategy. Med Phys 2009;36(7):3040–9. [16] Zito F, De Bernardi E, Soffientini C, Canzi C, Casati R, Gerundini P, et al. The use of zeolites to generate PET phantoms for the validation of quantification strategies in oncology. Med Phys 2012;39(9):5353–61. [17] Gianoli C, De Bernardi E, Riboldi M, Baselli G, Bauer J, Parodi K, et al. PET-based dosimetry in particle therapy: assessing the feasibility of regional MLEM reconstruction as a quantification tool. IEEE Nucl Sci Symp Conf Rec 2012 (poster). [18] Gianoli C, Bauer J, Kurz C, Riboldi M, Parodi K, Baroni G. A clinical study on 4D PET optimization and quantification in off-line treatment verification. In: 52nd Annual Conference of the Particle Therapy Co-Operative Group. 2013. [19] Jan S, Santin G, Strul D, Staelens S, Assie K, Autret D, et al. GATE: a simulation toolkit for PET and SPECT. Phys Med Biol 2004;49(19):4543. [20] Gonias P, Bertsekas N, Karakatsanis N, Saatsakis G, Gaitanis A, Nikolopoulos D, et al. Validation of a GATE model for the simulation of the Siemens biographTM 6 PET scanner. Nucl Instrum Methods Phys Res A 2007;571(1/2):263–6. ˜ S, Herraiz JL, Vicente E, Vaquero JJ, Desco M, Udías JM, et al. PeneloPET, [21] Espana a Monte Carlo PET simulation tool based on PENELOPE: features and validation. Phys Med Biol 2009;54(6):1723. 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[23] Defrise M, Kinahan PE, Townsend DW, Michel C, Sibomana M, Newport DF. Exact and approximate rebinning algorithms for 3-D PET data. IEEE Trans Med Imag 1997;16(2):145–58. [24] Panin VY, Defrise M, Casey ME. Restoration of fine azimuthal sampling of measured TOF projection data. IEEE Nucl Sci Symp Conf Rec 2010:3079–84. [25] Jakoby BW, Bercier Y, Conti M, Casey ME, Bendriem B, Townsend DW. Physical and clinical performance of the mCT time-of-flight PET/CT scanner. Phys Med Biol 2011;56(8):2375. [26] De Bernardi E, Mazzoli M, Zito F, Baselli G. Evaluation of frequency-distance relation validity for FORE optimization in 3-D PET. IEEE Trans Nucl Sci 2007;54(5):1670–8. [27] Prekeges J. Nuclear medicine instrumentation. Canada: Jones & Bartlett Publishers; 2012. p. 53–71. [28] Conti M, Bendriem B, Casey M, Chen M, Kehren F, Michel C, et al. First experimental results of time-of-flight reconstruction on an LSO PET scanner. Phys Med Biol 2005;50(19):4507–26. [29] Conti M. Why is TOF PET reconstruction a more robust method in the presence of inconsistent data? Phys Med Biol 2011;56(1):155–68. [30] Defrise M, Casey ME, Michel C, Conti M. Fourier rebinning of time-of-flight PET data. Phys Med Biol 2005;50(12):2749–63. Chiara Gianoli was born in Sondalo, Italy in 1984. She has obtained her M.Sc in Biomedical Engineering in 2009 and a PhD in Bioengineering in 2013 from Politecnico di Milano, Italy. Her interests cover methods and technologies for 4D CT and 4D PET imaging with application in conventional photon radiotherapy and ion beam therapy, with particular reference to PET-based treatment verification in ion beam therapy. She is actively participating to two European Projects, ENVISION (European NoVel Imaging Systems for ION therapy) and ULICE (Union of Light Ions Centres in Europe). In the framework of ENVISION collaborations, she is currently a postdoctoral research fellow at Heidelberg Ion Beam Therapy Center and Department of Radiation Oncology, Heidelberg University Hospital. Marco Riboldi was born in Monza, Italy, in 1977. He received his M.Sc in Biomedical Engineering in 2002, and a PhD in Bioengineering in 2006 from Politecnico di Milano (Italy). He worked as post-doctoral fellow at the Nuclear Science and Engineering Department at the Massachusetts Institute of Technology (Cambridge, USA) and served as research fellow at Massachusetts General Hospital – Harvard Medical School (Boston, USA). He is currently Assistant Professor at Politecnico di Milano and staff of the Bioengineering Unit at the Italian National Center for Particle Therapy (CNAO). His research interst mainly comprise Image Guided Radiation Therapy (IGRT) and advanced particle therapy. He is currently participating to European projects in the 7th Framework Programme with top level research institutions on particle therapy related topics: the ULICE (Union of Light Ion Centers in Europe) and ENVISION (European NoVel Imaging Systems for in vivo monitoring and quality control in ION beam therapy) projects. He is also acting as principal investigator for the research project entitled “Validation of real time tumor tracking models with four-dimensional magnetic resonance imaging”, funded by AIRC (Italian Association for Cancer Research). Christopher Kurz was born in Neuwied, Germany in 1986. He received his Diploma in physics from the University of Heidelberg in 2011, working on a first experimental-based characterization of Oxygen ion beams at the Heidelberg Ion-Beam Therapy Center (HIT). At present, he is writing his doctoral thesis on timeresolved (4D) offline PET-based treatment verification at the same institution. His main research interests are motion management in radiotherapy, post-irradiation PET verification and PET imaging at very low counting statistics. Elisabetta De Bernardi received a Master Degree in Biomedical Engineering in 2002 and a PhD in Bioengineering in 2007 from Politecnico di Milano. She is currently Assistant Professor at the Department of Health Science, University of Milano-Bicocca, Italy. Her main research interests are in the field of PET image reconstruction, processing and quantification. Julia Bauer was born in Sinsheim, Germany, in 1981. She received her diploma in physics in 2007 from the University Karlsruhe (Germany) working in the field of

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experimental top-quark physics. For her diploma thesis, she worked out an analysis of high-energy physics data acquired at the CDF collider experiment at FERMILAB (USA). In 2010, she received a PhD in physics from the Karlsruhe Institute of Technology (KIT, Germany) for her work on the search for top-quarks produced via the electroweak interaction in proton-proton collisions at the Large Hadron Collider at CERN. During her PhD period, she spent 10 month at the research center CERN, participating in the commissioning of the CMS silicon tracker and the early acquisition of cosmic-myon data. In 2010 she started as a post-doctoral fellow at the Heidelberg Ion-Beam Therapy Center, where she was involved in the implementation of post-therapeutic PET-based treatment verification. Having completed the clinical implementation, she currently focuses on several improvements of the method concerning the prediction of irradiation-induced tissue activation and advanced analysis strategies evaluating the measurements in terms of clinical significance. Giulia Fontana was born in Melzo, Italy, in 1986. She received her M.Sc. in Biomedical Engineering in 2011 from Politecnico di Milano in Milan, Italy. Her Master degree thesis focuses on the management of organ motion induced by respiration in radioand hadron therapy treatment planning and verification. In this contest she developed tools for 4D CT/3D CT tumor contours evaluation and 4D PET optimization for dosimetry verification through 4D PET sinograms processing. In 2011 after graduation she worked in the Radiology Department at the Istituto Europeo di Oncologia (IEO) in Milan, Italy. At IEO she was involved in research activities on Magnetic Resonance Imaging (MRI), particularly on MR diffusion and MR perfusion image post processing. From 2012 she has been working in the Clinical Bioengineering Unit of the Centro Nazionale di Adroterapia Oncologica (CNAO) in Pavia, Italy. She is actually involved in clinical activity since CNAO is equipped with high accuracy patient positioning systems, implementing Image Guided Hadron Therapy (IGHT). Mario Ciocca born in 1961 in Italy, married, two children, medical physics expert. He got his Master in Physics in 1987 and diploma of Specialization in Medical Physics in 1995, both at the University of Milano, Italy. His main fields of interest are represented by radiation dosimetry and protection, intra-operative radiation therapy, scanned particle beam radiotherapy (hadrontherapy), Quality Assurance and patient safety in modern radiotherapy, safety in MR. Head of the Medical Physics Unit at the CNAO Foundation (hadrontherapy facility) in Pavia. Teacher at the University of Milano, School of Specialization in Medical Physics and author/coauthor of more than 50 peer-reviewed published papers. Katia Parodi received in 2004 her Ph.D. in Physics from the University of Dresden, Germany, for her work done at the Research Center of Dresden-Rossendorf. From 2004 to 2006 she held a postdoctoral fellowship at Massachusetts General Hospital and Harvard Medical School in Boston, USA. From 2006 until 2012 she worked as a senior scientist and group leader at the Heidelberg Ion Therapy Center, Germany. After her Habilitation in Physics at the University of Heidelberg in 2009, she received in May 2011 the call to a full professorship at the Ludwig Maximilian University in Munich, Germany, where she is the chair of Experimental Physics – Medical Physics since August 2012. Her main research interests are to promote high precision radiation therapy with special focus on ion beams. Guido Baroni was born in Milano, Italy, in 1968. He received a Master degree in Mechanical Engineering from Politecnico di Milano (1993) and a PhD degree in Bioengineering in 1999 from the same institution on movement biomechanics in microgravity. He is currently Associate Professor at the Department of Bioengineering of Politecnico di Milano. He teaches Technologies for Computer Assisted Surgery to Biomedical Engineering master and Ph.D. students. His interests cover technologies and methods for 3D/4D optical human motion analysis and tracking with application in surgical navigation and image guidance in radiotherapy and particle radiation therapy. His research activity is documented by more than 60 peer-reviewed international papers on stereo-photogrammetry, human movement biomechanics and integrated technologies for patient set-up and target localization in high precision radiotherapy. He is responsible of the Computer Assisted Radiotherapy Laboratory of the Department of Bioengineering of the Politecnico di Milano and of the Clinical Bioengineering Unit of the Centro Nazionale di Adroterapia Oncologica (CNAO).


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