ORIGINAL ARTICLE 
Annals of Nuclear Medicine Vol. 12, No. 1, 1-5, 1998 
Calculating internal dose by convolution from SPECT/MR fusion images 
Juha S. LAMPINEN,* Hanna K. POHJONEN** and Sauli E. SAVOLAINEN *** 
*Department of Physics. University of Helsinki **Medical Engineering Centre, Helsinki University Central Hospital ***Department of Radiology, Helsinki University Central Hospital, Finland 
A new computer program was developed to calculate the absorbed dose. The program is based on the use of the convolution method and abdominal SPECT/MR fusion images. The applicability of the method was demonstrated by using data from 111In-labeled thrombocyte and 99mTc-labeled colloid studies of three healthy volunteers. Dose distributions in the volunteers and the average absorbed doses in liver and spleen were calculated. The average doses for 99mTc-labeled colloid study were 0.07 +- 0.02 (liver) and 0.046 +- 0.005 mGy/MBq (spleen). The results are in good agreement with a Monte Carlo (MC) based method (0.074 for liver and 0.077 mGy/MBq for spleen) used by the International Commission on Radiological Protection (ICRP). For 111In-labeled thrombocyte study the doses were 0.33 +- 0.05 (liver) and 8.9 +- 1.2 mGy/MBq (spleen) versus O.730 and 7.50, respectively. The differences in dose estimates in the 111In-labeled thrombocyte study are mainly due to the approximation used in activity quantitation. Convolution of the activity distribution with a point dose kernel is an effective method for calculating absorbed dose distribution in a homogeneous media. Activity distribution must be aligned to anatomical data in order to utilize the calculated dose distribution. The program developed is applicable to and practical for clinical use provided that the input data needed are available. 
Key words: internal dose, point dose kernels, convolution, SPECT/MRI fusion 

INTRODUCTION 
METHODS for patient-specific dosimetry are needed both in radionuclide therapy and in diagnostics. In systemic radionuclide therapy , for example in radioimmunotherapy (RIT), the knowledge of the absorbed dose distribution in the tumor as well as in the neighboring healthy tissues is needed in order to optimize the treatment. In nuclear medical laboratories, where new isotope-antibody combinations for diagnostic use are studied, a practical method for dose distribution determination is needed. The traditional method used for internal dose calculations is that developed by the Medical Internal Radiation Dose (MIRD) committee.1 In the MIRD formalism a mathematical standard phantom with Monte Carlo (MC) 
Received July 7, 1997, revision accepted September 15, 1997. For reprint contact: Juha S. Lampinen. Department of Physics, P.O. Box 9, FIN-00014 University of Helsinki, FINLAND. E-mail : Juha.Lampinen@Helsinki.fi 
simulation methods is used to calculate the mean absorbed dose to each organ. The quantities used are S-values, where S(Target-source) [mGy/MBq¥s] is the absorbed dose to the target organ from unit cumulative activity in a given source organ. The MIRD formalism assumes a uniformly distributed activity. There is a computer program, MIRDOSE3, for calculating the S-values for a large number of radioisotopes.2 In RIT the homogeneity of the activity distribution is determined by the kinetics of the isotope-antibody combination in that particular patient. The activity distribution is, therefore, always patient-specific. In RIT it is important to estimate heterogeneous distribution of the absorbed dose rather than to calculate the mean dose absorbed by the organ.3 The dose calculation procedure should take both these facts into consideration. With these requirements, the MIRD formalism is not suitable for patient-specific dose assessment in RIT. Patient-specific dose assessment methods developed to be used in RIT are based on point dose kernels4 used either as lookup tables5 or convoluted with activity distribution maps.3,6,7 A patient-specific direct MC approach has also been suggested.8 The convolution procedure is usually done by using a Fast Fourier transform (FFT) in 3 dimensions. The result of the convolution is the dose rate distribution. The point dose kernels are produced by MC simulations in homogeneous medium. The FFT procedure also assumes a homogeneous medium. The patient-specific MC simulation is able to deal with body heterogenities such as bones and lung tissue, so that accuracy is better than with the convolution method, but clinical applicability is restricted by the long computation time. A few additional problems limit the applicability of both methods, direct MC simulation and the convolution method. Aligning the calculated dose rate distribution with patient specific anatomical data is difficult. Another problem is how to quantitate the activity in the patient in absolute units, which are needed in order to calculate the dose in absolute units. Single photon emission computed tomography (SPECT) imaging provides only a count distribution and is affected by various sources of error. These errors have recently been discussed in detail by Sipila et al.9 In this work we present a computer program which uses registered SPECT/MR images10,11 to align patient specific anatomical data with the dose distribution calculated from the activity distribution by the convolution method. The capabilities of our program are demonstrated in 111In-labeled thrombocyte and 99mTc-labeled colloid studies of healthy volunteers. The results provided by our program are compared with those of established methods. Comparison with a computer program based on the MIRD formalism, MIRDOSE3,2 is made by using S-values. Another comparison is made with the results given in a report12 from the International Commission on Radiological Protection (ICRP) in which a biokinetical model for each radio-pharmaceutical has been used with the MIRD formalism. 

MATERIALS AND METHODS 
Structure of the program The new program, later referred as intdose, is given three equally sized (N*N*N) input matrices: point dose kernel, activity distribution and organ matrices. The first of these is generated once for each radionuclide from a known point dose kernel, K(r) [cGy/Bq¥s] where r is the distance from the source. The two latter represent the data obtained from registered SPECT/MR images and they are presented in the same co-ordinate system. The use of Fourier transform limits the size of these matrices so that N must be a power of 2.13 The point dose kernel, K(r) describes how the absorbed dose distribution behaves per one decay of specific radionuclide in water. In the convolution procedure the point dose kernel is considered as a response function. The origin of the response function must be positioned in the origin of the co-ordinate system. Since the origin of a matrix is in the corner and the response function is assumed to be periodic, the negative dimensions are mirrored on the other side of the matrix,13 The dose contribution from the b-decays is assumed to be local in the scale of the size of the matrix voxel. The total b-energy per one decay14 is therefore added in the origin of the point dose kernel matrix. The activity distribution matrix A(r) represents the absolute activity [Bq] in each voxel of the phantom describing the patient. The absorbed dose rate distribution b(r) is calculated by the convolution of the point dose kernel K(r) with the activity distribution A(r)7 
The convolution is executed by 3 dimensional Fast Fourier transformations (FFT)7 
In order to calculate the dose distribution or the average dose in an organ or in another region of interest (ROI) the boundaries of that region are needed. The ROIs are segmented from MR images which are presented in the same co-ordinate system as the activity distribution. The result of the segmentation procedure is a ROI matrix filled with zeros (outside ROIs) or with ROI specific numbers (inside ROIs). 
Demonstrations 
Abdominal SPECT/MR fusion images from three healthy volunteers were used. The volunteers are later referred to as 1, 2 and 3. Two different uptake studies were performed for each volunteer. For volunteer 3, however, data were available for only one study. The volunteers were first administered 111In-oxine-labeled thrombocytes and two days later 99mTc-labeled tin colloids.11 The study was approved by the local ethical committee and informed consent was obtained from all volunteers. In the reconstruction of the transversal SPECT images only attenuation correction was performed. The imaging protocols and the registration technique were recently described in detail by Pohjonen et al.11 The program was given as an input registered SPECT and MR image sets, each of which consisted of 128*128*128 images. Each dimension of a voxel was 2.88 mm. The point dose kernel was also calculated for a similar matrix. The photon point dose kernels used in the demonstrations, for 99mTc and 111In isotopes, were taken from Furhang et al.4 in which a mathematical fit is given for several isotopes. The general expression given for the fit is4 
The total (with both b- and gamma-contribution) point dose kernels used in this work are presented in Figure 1. Each set of registered MR images was manually segmented to identify liver and spleen. Two kinds of calculations were performed with intdose. First, patient-specific dose distributions were calculated for each study performed. From these distributions mean absorbed doses to liver and spleen were calculated. Here we assumed that the relative activity distribution does not change and the activities in each voxel decay as predicted by the physical half-life T1/2 for that nuclide. The activity distributions A(r) were calculated from the SPECT images by assuming that all of the activity is present in the volume given by these images. The activity (A) vs. counts (c) ratio [Bq/counts] was calculated as where Atot is the total activity administered and Ctot is the number of total counts in the SPECT images. The activity distribution matrix A(r) was then calculated by multiplying the counts (from SPECT image) by the activity vs. the counts ratio. The mean doses to liver and spleen calculated this way were compared to doses given by ICRP.12 Other kinds of calculations were used to compare the S-values from MIRDOSE3 with the corresponding values from intdose. The S-values S(liver-spleen), S(liver-liver). S(spleen-liver) and S(spleen-spleen) were calculated by considering only the activity in one source organ (liver or spleen) at a time. In the program each voxel occupies 2 bytes, so the memory taken by each matrix is about 8 megabytes. During the FFT procedure, both the activity distribution and the point dose kernel must be in the computer's memory. Intdose was programed with C-language under the Linux operating system. 

RESULTS 
Figure 2 shows registered SPECT and MR images and calculated dose distributions for both 99mTc-colloid and 111In-thrombocyte studies of one volunteer. The calculated average absorbed doses to each patient's liver and spleen as well as the results from ICRP12 are summarized in Table 1. The calculated S-values and values from MIRDOSE32 are presented in Table 2. 

DISCUSSION 
A new computer program was developed to calculate the absorbed dose in any isotope study. The program is based on a combination of the convolution of activity distribution and point dose kernel and SPECT/MR fusion imaging. The convolution theorem takes the duration of the response to be the same as the period of the data.13 This means that if the dose distribution from a source voxel would in fact exit the calculation matrix, the convolution procedure folds the dose distribution to the other side of it. Calculational error in dose distribution caused by this phenomenon is determined by the distance between source voxels and the matrix border and by the gradient of the response function (point dose kernel). In practice, the error caused by the folding phenomenon in the convolution procedure is insignificant since the point dose kernels for the isotopes used have large gradients, as can be seen in Figure 1. The use of convolution for calculating the dose rate distribution from the activity distribution with the point dose kernel has been validated by Giap et al.7 According to them the calculated absorbed dose agreed well inside the phantom but outside of it the calculation overestimates the dose because the convolution method assumes homogeneous media, water in this case.7 The calculation time for one dose distribution was about 105 s when a Pentium 200 MHz computer with the Linux operating system was used. The calculation time is short considering that the matrix size used in the demonstrations was 128*128*128. The doses calculated by the program agreed reasonably well with those given in the ICRP publication,12 Table 1. The results in the ICRP report are based on a standard biokinetic model, which ignores any patient-specific fluctuations in relative organ uptakes. On the other hand, in the demonstrations of this work, activity changes in time were ignored. We also assumed that all the activity administered is present in the volume covered by SPECT images. The activity per count calculated this way is the maximum possible. According to the biokinetic model used by ICRP,12 fractions of 0.30 and 0.10 of 111In-labeled thrombocytes are immediately deposited in spleen and liver. The remaining fraction (0.60) is cleared from the blood (0.25 to red bone marrow, 0.2 to liver and 0.05 to spleen) with a half-time of 4 d. For 99mTc-labeled colloids, fractions of 0.70 and 0.10 are deposited in liver and spleen and no redistribution or excretion occurs. 12 In our program the activity is assumed to decay as predicted by its physical half-life T1/2. This is valid in the case of 99mTc-labeled colloids. In the case of 111In-labeled thrombocytes, the half-life assumption is justified since spleen/liver activity ratios in 111In-labeled thrombocyte studies did not change remarkably after 1 hour, as can be seen in Figure 3 in Pohjonen et al.,11 even though the major fraction of the 111In activity is still circulating with the blood. The quantity of activity obtained by one SPECT imaging, especially in liver, is however underestimated in the case of 111In-labeled thrombocytes because activity is cleared from the blood to liver and spleen. Doses calculated for liver in Table 1 are smaller than those given by ICRP12 as expected. Because of these facts, doses calculated for 99mTc studies are to be considered more accurate. This is emphasized by the superior imaging characteristics of 99mTc compared to 111In,11 Because the self dose to each organ is the main contributor, the effect of patient size (in terms of organ distances) on the average doses to organs with the isotopes used is not significant. The size of the source organ is here the most important factor. Since the total activity is constant, a large organ has a lower activity concentration [Bq/ml] than a small organ. As can be seen in Table 2, the S-values for cases where the target equals the source calculated by the intdose agree with MIRDOSE3. The differences between S-values calculated by the intdose and MIRDOSE3 can be explained by comparing the organ volumes. According to Pohjonen et al.,11 the liver sizes as estimated from MRI were 1.70, 2.63 and 1.43 liters for volunteers 1, 2 and 3. The volume of the liver in the MIRD phantom is 1.83 liters.15 Correspondingly, the spleen sizes of the volunteers were 196 ml, 302 ml and 106 ml11 while the volume of the spleen in the MIRD phantom is 176 ml.15 As can be seen, the ratio of organ volumes of two individual male adults may be as high as 2.8 (spleen volume ratio of volunteers 2 and 3). Our results are in good agreement with previous data. The program developed is applicable and practical for clinical use providing that registered absolute activity distribution and segmentation data are available. 

ACKNOWLEDGMENTS 
The authors thank Mr. Eero Salli M. Sc. (Eng.) for assisting with the image manipulation. 

REFERENCES 
1. Loevinger R. Budinger TF, Watson EE. MIRD primer for absorbed dose calculation. New York, Society of Nuclear Medicine, 1988. 
2. Stabin MG. MIRDOSE: Personal Computer Software for Internal Dose Assessment in Nuclear Medicine. J Nucl Med 37: 538-546, 1996. 
3. Erdi AK, Erdi YE, Yorke ED, Wessels BW. Treatment planning for radio-immunotherapy. Phys Med Biol 41 : 2009-2026, 1996. 
4. Furhang EE. Sgouros G, Chui C-S. Radionuclide photon dose kernels for internal dosimetry. Med Phys 23: 759-764, 1996. 
5. Sgouros G, Barest G, Thekkumthala J, Chui C. Mohan R, Bigler RE, et al. Treatment planning for internal radionuclide therapy: three-dimensional dosimetry for nonuniformly distributed radionuclides. J Nucl Med 31 : 1881-1891 , 1990. 
6. Uchida I, Yamada Y, Oyamada H. Nomura E. Calculation algorithm of three-dimensional absorbed dose distribution due to in vivo administration of nuclides for radiotherapy. KAKUIGAKU (Jpn J Nucl Med) 29: 1299-1306, 1992. (in Japanese) 
7. Giap HB. Macey DJ. Podoloff DA. Development of a SPECT-based three-dimensional treatment planning system for radioimmunotherapy. J Nucl Med 36: 1885-1894, 1995. 
8. Furhang EE, Chui C-S. Sgouros G. A Monte Carlo approach to patient-specific dosimetry. Med Phys 23: 1523-1529, 1996. 
9. Sipila O, Nikkinen P. Pohjonen H, Poutanen V-P. Visa A, Savolainen S, et al. Accuracy of a Registration Procedure for Brain SPECT and MRI: Phantom and Simulation Studies. Nucl Med Commun 18: 517-526, 1997. 
10. Pohjonen H, Nikkinen P. Sipila O. Launes J. Salli E, Salonen O, et al. Registration and display of brain SPECT and MRI using external markers. Neuroradiology 38: 108-114, 1996. 
11. Pohjonen HK, Savolainen SE. Nikkinen PH. Poutanen V-PO. Korppi-Tommola ET, Liewendahl BK. Abdominal SPECT/MRI fusion applied to the study of splenic and hepatic uptake of radiolabeled thrombocytes and colloids. Ann Nucl Med 10: 400-417, 1996. 
12. International Commission on Radiological Protection. Radiation Dose to Patients from Radiopharmaceuticals, Publication 53. Oxford, Pergamon Press, 1987 
13. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed., Cambridge, Cambridge Press, pp. 496-536, 1992. 
14. Browne E, Firestone RB. Shirley VS. Table of Radioactive Isotopes. New York, John Wiley and Sons, Inc., 1986. 
15. Snyder WS, Ford MR, Warner GG, Fisher HL. Estimates of absorbed fractions for monoenergetic photon sources uniformly distributed in various organs of a heterogeneous phantom. J Nucl Med: suppl. N3: 7-52, 1969.