Comparison of internal dose estimates obtained using organ-level, voxel S value, and Monte Carlo techniques.

PURPOSE
The authors' objective was to compare internal dose estimates obtained using the Organ Level Dose Assessment with Exponential Modeling (OLINDA/EXM) software, the voxel S value technique, and Monte Carlo simulation. Monte Carlo dose estimates were used as the reference standard to assess the impact of patient-specific anatomy on the final dose estimate.


METHODS
Six patients injected with 99mTc-hydrazinonicotinamide-Tyr3-octreotide were included in this study. A hybrid planar/SPECT imaging protocol was used to estimate 99mTc time-integrated activity coefficients (TIACs) for kidneys, liver, spleen, and tumors. Additionally, TIACs were predicted for 131I, 177Lu, and 90Y assuming the same biological half-lives as the 99mTc labeled tracer. The TIACs were used as input for OLINDA/EXM for organ-level dose calculation and voxel level dosimetry was performed using the voxel S value method and Monte Carlo simulation. Dose estimates for 99mTc, 131I, 177Lu, and 90Y distributions were evaluated by comparing (i) organ-level S values corresponding to each method, (ii) total tumor and organ doses, (iii) differences in right and left kidney doses, and (iv) voxelized dose distributions calculated by Monte Carlo and the voxel S value technique.


RESULTS
The S values for all investigated radionuclides used by OLINDA/EXM and the corresponding patient-specific S values calculated by Monte Carlo agreed within 2.3% on average for self-irradiation, and differed by as much as 105% for cross-organ irradiation. Total organ doses calculated by OLINDA/EXM and the voxel S value technique agreed with Monte Carlo results within approximately ±7%. Differences between right and left kidney doses determined by Monte Carlo were as high as 73%. Comparison of the Monte Carlo and voxel S value dose distributions showed that each method produced similar dose volume histograms with a minimum dose covering 90% of the volume (D90) agreeing within ±3%, on average.


CONCLUSIONS
Several aspects of OLINDA/EXM dose calculation were compared with patient-specific dose estimates obtained using Monte Carlo. Differences in patient anatomy led to large differences in cross-organ doses. However, total organ doses were still in good agreement since most of the deposited dose is due to self-irradiation. Comparison of voxelized doses calculated by Monte Carlo and the voxel S value technique showed that the 3D dose distributions produced by the respective methods are nearly identical.


INTRODUCTION
Absorbed dose calculations for internal radionuclides are used to assess the stochastic risks associated with diagnostic applications of nuclear medicine as well as the deterministic risks to normal tissues associated with therapeutic nuclear medicine; less commonly, such calculations are also used to assess efficacy (i.e., target-tissue dose) for radionuclide therapy. These dose calculations are performed, at least for diagnostic applications, using the methodology developed by the Medical Internal Radiation Dose (MIRD) committee. 1 The general MIRD equation 2 used for calculating the dose to target organs is whereÃ (r S ) is the time-integrated activity (total number of decays integrated over a specified time period) of the source and S(r T ← r S ) is the dose deposited in target r T per unit of cumulated activity in source r S (often referred to as a S value). The time-integrated activityÃ (r S ) is often normalized by the administered activity to form the time-integrated activity coefficient (TIAC). S values are defined using Eq. (2), where m T is the mass of the target, n i and E i are the frequency and energy of each radiation type i, and ϕ i (r T ← r S ) is the absorbed fraction of energy emitted from the source that is deposited in the target for each radiation type emitted by the radionuclide of interest.
The elements of Eqs. (1) and (2) can be categorized into three major components of dose calculation. 1 These components are (i) information about the biodistribution of activity, which is provided by the time-integrated activityÃ (r S ) in all source regions, (ii) physical properties of the radionuclide (n i and E i ), and (iii) a dose estimation method that combines information about the activity distribution and the radionuclide properties to calculate the absorbed dose distribution.
In this work, three dose calculation methods that vary in complexity and in the accuracy of the dose estimates that they produce have been evaluated for four different source radionuclides: 99m Tc, 131 I, 177 Lu, and 90 Y. Doses calculated using the Organ Level Internal Dose Assessment with Exponential Modeling (OLINDA/EXM) software 3 and the voxel S value technique 4 are compared to the results from Monte Carlo simulation, which was considered a reference standard for the purposes of this study. These comparisons were performed in order to investigate the advantages and disadvantages of each method and to study the accuracy of organ-level dose calculations based on reference phantoms.

1.A. Organ-level dose calculation with OLINDA/EXM
OLINDA/EXM is one of the most widely used programs for organ-level dose calculations. Using OLINDA/EXM, the user inputs organ TIACs and the program calculates the resulting mean absorbed dose for each organ. These doses are estimated using organ-level S values S(organ T ← organ S ) precalculated by Monte Carlo simulation in standard phantoms representing the average male or female. In these simulations, activity is assumed to be uniformly distributed in source organs and the dose is assumed to be uniformly deposited throughout each target organ.
Clearly, the S values based on standard phantoms are not patient-specific. OLINDA/EXM can make first-order adjustments for patient-specific organ masses if these are known, but not for the shapes and relative positions of organs, which can, of course, also vary from patient to patient. To correct for patient-specific organ masses for alpha and beta emissions, the dose scales linearly with the mass. For photon emissions, the absorbed fraction scales with the cube root of the mass for self-irradiation and directly with the mass for crossirradiation. 3 Tumor doses are approximated by OLINDA/EXM using precalculated absorbed fractions to spheres of different sizes filled with uniform activity. These spheres are treated as isolated objects, so cross-dose to or from other tumors or organs is not accounted for.

1.B. Voxel S values
The voxel S value approach considers activity distributions at the voxel level and calculates the corresponding voxelized dose distribution. 4,5 This method uses lookup tables of absorbed dose fractions in an array of target voxels due to radiation emitted from a single source voxel. These voxel S value S(voxel T ← voxel S ) lookup tables are precalculated by Monte Carlo simulation and are radionuclide-, voxel size-, and tissue-specific. 6 Free databases of voxel S values for selected radionuclides and voxel sizes have also recently become available. 7 Dose calculation with voxel S values is performed by convolving the precalculated table of voxel doses per unit of cumulated activity in a source voxel with the patient-specific cumulated activity distribution. In a volume of N source voxels, the dose to each target voxel is calculated using The drawback of the voxel S value technique is that the lookup tables are calculated for a source material of uniform density and tissue inhomogeneities are not accounted for. However, the advantage of using the voxel S value approach is that it makes 3D dose calculations simple and fast. Furthermore, the assumption of uniform tissue density when voxelized dose distributions are calculated within organs or tumors is a reasonable approximation for many areas in the body.

1.C. Monte Carlo simulation
Monte Carlo techniques use the known physics of photon and particle interactions with matter to simulate radiation transport. Reconstructed SPECT images provide quantitative information about the activity distribution and radioactive emissions can be simulated and propagated through a computerized patient model to determine the resulting 3D dose distribution. The computerized model can be constructed based on a CT image set of the patient, and the method is thus able to take into account patient-specific source and target organ geometries and tissue inhomogeneities.
Monte Carlo simulation is the most robust method for dose estimation, but its use may be quite complicated and it requires very long computation times. Example Monte Carlo codes commonly used for radiotherapy and nuclear medicine applications include the electron gamma shower (EGS) code, 8 MCNP, 9,10 PENELOPE, 11 and the GEANT code. 12,13 The EGS code is considered to be a reference standard for clinical radiation dosimetry applications. 14 The latest EGS version, EGSnrc, is accompanied by the user code, DOSXYZnrc, which facilitates calculation of dose distributions in a rectilinear voxel phantom. [15][16][17]

2.A. Patient studies
A total of 6 patients (3 males and 3 females) injected with 800-1000 MBq of 99m Tc-hydrazinonicotinamide-Tyr 3octreotide were included in this study. For each patient, a series of 3-4 whole body planar scans were acquired over a period of 24 h following injection. In addition, a single SPECT/CT scan was acquired approximately 3 h after injection. Further details regarding these patient studies have previously been described. 18

2.B. SPECT reconstruction
The SPECT images were reconstructed with our quantitative qSPECT method using the iterative ordered-subsets expectation maximization algorithm. 19 These reconstructions included resolution recovery, CT-based attenuation, and analytic scatter corrections. Six iterations and ten subsets were used. A calibration experiment was performed in order to determine the sensitivity factor (in units of counts/minute/kBq) to be used to convert the reconstructed count rate to activity. This calibration experiment was performed using a planar acquisition of a point source of known activity (determined by a dose calibrator), placed in air about 20 cm from the surface of each of the two detectors. In previous work, we have shown that accurate activity estimates with errors less than 5% can be achieved using this in air planar calibration method along with our reconstruction technique. 19

2.C. Calculation of TIACs
All data were processed and analyzed with the MATLABbased internal dosimetry package, JADA. 20 A hybrid planar/SPECT approach was employed to plot and integrate time-activity curves for all tumors and each organ with a perceptibly greater activity concentration than that in the surrounding background tissue, which were the kidneys, liver, and spleen. To use the hybrid planar/SPECT approach, counts obtained from the planar scans for each investigated region were plotted versus time. Next, each image-derived tumor or organ time-activity curve was fit to a monoexponential function. Each such curve was then scaled to pass through the corresponding activity determined from the SPECT image (A SPECT ) at the time of the SPECT acquisition (t SPECT ). The fitted exponential curves were integrated to find the cumulated activity (Ã) of the 99m Tc in each source regioñ where λ eff is the effective elimination constant obtained from the exponential fit. The 99m Tc TIACs needed for organ-level dose calculation were determined by dividing the cumulated activities by the injected activity (Ã/A inj ). Additionally, predicted TIACs were calculated for 131 I, 177 Lu, and 90 Y assuming a pharmaceutical labeled with these radionuclides would follow the same time-dependent biodistribution as the 99m Tc labeled tracer. A summary of the half-lives and emissions for each of the radionuclides investigated in this study is included in Table I.

2.D.1. Organ-level dosimetry
Mean organ doses to each segmented organ from the 99m Tc injection and the predicted organ doses from 131 I, 177 Lu, and 90 Y injection were calculated using OLINDA/EXM. The mean dose calculated for each organ included contributions from the self-dose as well as the cross-dose from other segmented regions. The OLINDA/EXM sphere model was used to calculate the dose to tumors.

2.D.2. Voxel level dosimetry
The voxel S value method and Monte Carlo simulation were used to calculate 3D dose rate distributions as well as mean and total doses for tumors and organs. For voxel S value dose calculation, the voxel S values were precalculated using the EGSnrc user-code DOSXYZnrc Monte Carlo program. The relevant parameter settings for creation of the voxel S values were 10 9 histories originating from a single source voxel with dimensions of 4.42 mm on edge at the center of a 215 × 215 × 215 voxel grid inside a soft tissue equivalent medium. The size of this voxel array was large enough so that cross-dose could be calculated between all ROIs using the voxel S value method. The large number of histories used for this Monte Carlo simulation allowed us to achieve low statistical error for the voxel S value lookup table.
For Monte Carlo dose calculation, the total number of histories simulated per source voxel was 100 000 photons and 100 000 electrons sampled from each radionuclide's emission spectrum. Patient-specific SPECT and CT images were used as input for these Monte Carlo simulations. 20 The total number of voxels simulated from the liver, kidneys, and spleen of each patient was on the order of 10 4 voxels, so that an approximate total of 10 9 histories were simulated for each patient. The EGSnrc input parameter, ECUT, which is the electron cutoff energy (sum of rest mass and kinetic energy) for which a history is terminated and energy is deposited in the current voxel, was set at 0.561 MeV for the 99m Tc simulation, 0.591 MeV for the 177 Lu simulation, 0.611 MeV for the 131 I simulation, and 0.711 MeV for the 90 Y simulation. These ECUT values were selected after extensive investigation into what ECUT values could be used to reduce the simulation time without a substantial loss of accuracy in the resulting dose distribution (larger ECUT requires less simulation time).
The 3D dose rate distributions calculated by Monte Carlo simulation and the voxel S value technique were multiplied by the factor exp(λ eff · t SPECT )/λ eff in order to convert them to 3D dose distributions. Similar to the organ level calculations, these dose distributions included self-dose as well as the cross-doses from all organs with considerable uptake. Only patients with entire organs (kidneys, liver, and spleen) visible in a single SPECT field of view were included in this analysis. For each source organ, a separate dose distribution in the volume enclosing all target regions was calculated so that a set of S values could be determined. These S values were found by dividing the mean dose to each target region r T by the cumulated activity in source region r S , For example, the cross-organ S value for activity in the spleen irradiating the liver, S(liver ← spleen), was calculated as the mean dose to the liver, calculated by Monte Carlo (or voxel S values) using the spleen as a source organ, divided by the cumulated activity in the spleen.
The total dose to each target was also determined by summing the dose distributions calculated for each source organ. After the Monte Carlo and voxel S value calculations were performed for the 99m Tc activity distribution, these calculations were repeated using sources of 131 I, 177 Lu, and 90 Y.

2.E. Evaluation of dose estimation methods
The 99m Tc, 131 I, 177 Lu, and 90 Y dose estimates obtained using each of the three methods were evaluated by In each assessment, the Monte Carlo dose distributions were assumed to be the reference standard that the two other methods were compared to.

2.E.1. Comparison of reference and patient-specific S values at the organ-level
The values of S(r T ← r S ) based on the reference phantoms used by OLINDA/EXM, S(r T ← r S ) OLINDA , were compared to the S values calculated by Monte Carlo simulation, S(r T ← r S ) MC , using patient-specific CT images. This assessment was done by finding the percentage difference between the two S values for each source and target region pair. The OLINDA/EXM S values were mass corrected using patient-specific organ masses. The percentage difference S OLINDA (r T ← r S ) for each S value array element was calculated as follows: Since three regions were investigated (kidneys, liver, and spleen), this comparison yielded a 3 × 3 array of percentage differences for each patient, which were then used to find the average, standard deviation, minimum and maximum percentage difference for each array element over the entire patient population.
Similarly, the organ-level S values calculated from the voxel S value method, S(r T ← r S ) VSV , were compared to the Monte Carlo determined S values to find

2.E.2. Total dose assessment
The mean organ and tumor doses calculated using Monte Carlo were compared to the organ and tumor doses calculated using OLINDA/EXM and voxel S values by finding the percentage difference between doses estimated by each of these methods. To compare normal organ doses, the evaluated doses included contributions from self-and cross-organ irradiation. Tumor doses calculated by OLINDA/EXM using the sphere model, which considers self-dose only, were compared to both Monte Carlo self-dose calculations and to Monte Carlo total dose (self-plus cross-dose) calculations.
The Monte Carlo results were analyzed further to determine the percentage of total dose that was due to cross-organ irradiation. In addition, the assumption by OLINDA/EXM that electrons are fully absorbed by source organs was tested by assessing the percentage of the total dose that was due to cross-organ irradiation from electron emissions.

2.E.3. Paired organ analysis
The Monte Carlo dose calculation was used to assess the dose to the right and left kidney separately in order to investigate potential limitations of the assumption made by OLINDA/EXM that paired organs each receive equal dose. The percentage difference between right and left kidney doses K was found using:

2.E.4. Monte Carlo and voxel S value voxel-by-voxel comparison
The 3D dose distributions calculated by Monte Carlo simulation and the voxel S value method were compared visually by plotting cumulative dose volume histograms (DVHs). In addition, a voxel-by-voxel analysis was carried out to determine the average (±standard deviation) percentage difference between corresponding voxels in the two 3D dose distributions calculated for each patient.

RESULTS
The cumulated 99m Tc activity concentrations for each of the investigated source organs and tumors are summarized in Table II. The highest cumulated organ activity concentration was most commonly found in the spleen, followed by the kidneys and then the liver. The largest variation in source region concentration was found in tumors, where the cumulated tumor activity concentration in patient 4 was four times greater than in patient 2. There were tumors in three of the patients included in this study. In patient 2, there was a 23 ml paraganglioma located paravertebral at the Th10-11 level; in patient 3, there was a 95 ml neuroendocrine tumor in the pancreas; and in patient 4, there was a 76 ml neuroendocrine tumor in the small bowel.

3.A. Comparison of organ-level S values
When the S values used by OLINDA/EXM for each source and target region pair and the corresponding S values calculated using Monte Carlo simulation were compared using Eq. (3), there was generally a good agreement in S values for self-irradiation, but a very poor agreement in S values for cross-irradiation (Tables III-VI for 99m Tc, 131 I, 177 Lu, and 90 Y, respectively). The S values for self-irradiation all agreed within 2.3%, on average, regardless of the radionuclide used. Comparison of the Monte Carlo generated crossorgan S values with those used by OLINDA/EXM gave percentage differences S OLINDA (r T ← r S ) that ranged between −83% for S(Liver ← Kidneys) in patient 3 (with 177 Lu) and 105% for S(Kidneys ← Spleen) in patient 4 (with 99m Tc). The S OLINDA (r T ← r S ) values for cross-organ irradiation were similar for all radionuclides except for the average S(Kidneys ← Liver) values, which were found to be −23% for 99m Tc and −40% for 177 Lu. The cross-organ S values for 90 Y were not included in this comparison since the 90 Y cross-dose was negligible. In the comparison of S values calculated by the voxel S value method and Monte Carlo simulation, there was again good agreement in the S values for self-irradiation (Tables III-VI). Unlike the Monte Carlo comparison to OLINDA/EXM S values, there was reasonable agreement with S values calculated using the voxel S value method for cross-irradiation between the kidneys and liver and between the kidneys and spleen, where the average S VSV (r T ← r S ) was found to be 11% or less. There was not good agreement between the liver and spleen where the average values of S VSV (Spleen ← Liver) and S VSV (Liver ← Spleen) ranged from 14% with 131 I to 31% with 99m Tc. Differences in patient specific-anatomy leading to the large discrepancies between OLINDA/EXM and Monte Carlo generated S values can be explained by visualizing the anatomy of two example patients displayed in Fig. 1. The corresponding S value comparisons for these two patients are listed in Tables VII-IX for 99m Tc, 131 I and, 177 Lu, respectively.

3.B. Total organ and tumor dose assessment
There was good agreement between the total organ doses calculated by OLINDA/EXM and the mean doses calculated by Monte Carlo simulation (Fig. 2), regardless of the radionuclide used. The worst agreement was found in the spleen of patient 1 (using 177 Lu), where the percentage difference between OLINDA/EXM and Monte Carlo doses was −6.2%. Similarly, total doses calculated using the voxel S value method were in good agreement with the Monte Carlo results. In this case, the worst agreement was found in the liver of patient 6 (using 99m Tc), where the percentage difference between the voxel S value and Monte Carlo doses was 7.4%. In the comparison of tumor self-doses calculated by Monte Carlo with the tumor doses calculated using the sphere model     in OLINDA/EXM, the average percentage differences between these doses were −0.9% ± 5.1%, −3.5% ± 4.7%, −3.5% ± 5.1%, and −0.8% ± 3.9% for 99m Tc, 131 I, 177 Lu, and 90 Y, respectively. When total doses, including self-plus cross-dose contributions calculated by Monte Carlo were considered, these differences became −8.8% ± 11.1%, −6.0% ± 5.4%, −3.8% ± 5.2%, and −0.8% ± 3.9% for 99m Tc, 131 I, 177 Lu, and 90 Y, respectively. The average percentage differences between the Monte Carlo and voxel S value derived tumor doses were 1.1% ± 1.9%, −1.1% ± 4.0%, −1.5% ± 4.6%, and −0.4% ± 3.1% for 99m Tc, 131 I, 177 Lu, and 90 Y, respectively. Analysis of the cross-organ irradiation data from Monte Carlo simulation revealed that cross-organ doses made the greatest contribution to total dose calculated for 99m Tc distributions and the least contribution for 90 Y distributions (Fig. 3). For example, cross-organ irradiation with 99m Tc contributed as much as 20% to the total organ dose (in the left kidney of patient 6), whereas the largest contribution to total organ dose from 90 Y cross-organ irradiation was 1.3% (also in the left kidney of patient 6). Electron emissions were found to contribute less than 0.05% to cross-organ doses in most cases. In situations where two organs were in close contact (e.g., the left kidney and the spleen or the right kidney and the liver), the beta cross-dose contribution was around 0.5% for 131 I and around 1% for 90 Y.  For tumors, cross-organ irradiation contributed as little as 0% (with 90 Y in patients 3 and 4) and as much as 16.2% (with 99m Tc in patient 2) to the total tumor dose.

3.C. Right and left kidney doses
Results from the comparison of right and left kidney doses, calculated by Monte Carlo simulation, are reported in Table X. For 99m Tc, the doses deposited in the right and left kidneys agreed within 7.3% in four out of six patients. Two extreme cases where there was a relatively large difference between individual kidney doses were observed for patients 1 and 6 (Fig. 4).
There was generally a poor agreement between kidney doses calculated with 131 I, 177 Lu, and 90 Y activities. This was due to a combination of the long physical half-lives of these radionuclides and differences in the washout rates between the two kidneys (demonstrated by the differences in biological half-lives listed in Table X for the right and left kidneys).

3.D. Monte Carlo and voxel S value comparison
The dose distributions calculated with the voxel S value method closely matched the dose distributions obtained with Monte Carlo simulation. To illustrate the similarity between the calculated dose distributions, an example comparison of the cumulative DVHs determined by the two methods is   177 Lu, and 90 Y, respectively. When the dose distributions were analyzed voxel-by-voxel, the largest percentage difference between corresponding voxels averaged over all voxels in the target organs of a single patient was 6.1% ± 6.6% in patient 6 with 99m Tc.

DISCUSSION
In general, good agreement was found between total organ doses calculated using OLINDA/EXM, Voxel S-values, and Monte Carlo for all analyzed isotopes. However, more detailed analysis of these results clearly indicates that patient anatomy had a large impact on cross-organ S values. For example, the value of S OLINDA (Kidneys ← Spleen) was −38% for patient 2 and 105% for patient 4 when using 99m Tc ( Table VII). As illustrated in Fig. 1, the spleen is found closer to the left kidney in patient 2 then it is in patient 4 leading to the relative differences observed in this S value comparison. Similar results were reported by Divoli et al., who compared 131 I S values used by OLINDA/EXM to patient-specific values calculated by the MCNPX2.5.0 Monte Carlo code. 21 They reported percentage differences between OLINDA/EXM and patient-specific S values ranging from −51% to 84%.
The cross-organ S values calculated using voxel S values and Monte Carlo simulation were in good agreement between the liver and kidneys and between the spleen and kidneys since the volume enclosing each of these pairs of regions is a relatively uniform tissue medium. However, there was poor agreement in the cross-organ S values between the liver and spleen, where the voxel S value technique overestimated the Monte Carlo calculation by about 30% on average for 99m Tc and 177 Lu, and by about 15% on average for 131 I. This overestimation was caused by radiation attenuated in the spine lying partly between the spleen and liver, which was properly handled by Monte Carlo simulation, but was not accounted for by the voxel S value calculation where a uniform soft tissue medium was assumed. The overestimation was not as severe for 131 I due to the higher energy gammas (364 keV) it emits compared to the other two radionuclides.
Despite the disagreements in cross-organ S values, the total mean organ doses calculated by each technique remained in reasonable agreement (Fig. 2). This was due to the fact that the self-organ S values were in good agreement (Tables III-VI) and the self-dose accounted for the majority of the dose to each organ containing activity (Fig. 3). The errors in organ cross-dose calculated by OLINDA/EXM may become more relevant in organs with no specific uptake of the radiopharmaceutical; however, this was not investigated as a part of this study.
Cross-organ contributions were greater with 131 I than with 177 Lu. This can be attributed to the higher intensity (82%) of the 364 keV gamma rays emitted by 131 I compared to the 113 and 208 keV gamma rays emitted by 177 Lu with 6.4% and 11% intensities, respectively. Another factor affecting crossorgan contribution is the gamma ray energy. Lower energy photons will deposit more energy close to the source, while higher energy photons will be attenuated less and will have a greater probability of depositing energy in targets farther from the source. As expected, results of this study demonstrated that bremsstrahlung contributions to cross-organ doses are negligible. The tumor self-doses calculated by Monte Carlo and the tumor doses calculated with the sphere model in OLINDA/EXM agreed within an average of 3.5% for all radionuclides, demonstrating that tumor shape did not have a large impact on the accuracy of the sphere model approach. Including the cross-dose contribution in the Monte Carlo tumor dose calculation led to greater percentage differences with the sphere model doses. These differences were greatest with 99m Tc, followed by 131 I, 177 Lu, and then 90 Y. The greatest difference occurred using 99m Tc in patient 2, where the tumor dose calculated with the sphere model underestimated the total tumor dose calculated with Monte Carlo by 22%. In the same patient, the tumor dose calculated with the sphere model underestimated the total tumor dose by 12%, 10%, and 5% using 131 I, 177 Lu, and 90 Y, respectively. These differences between sphere model and total tumor dose are less than those previously reported by Johnson and Colby 22 and by Howard et al. 23 In the study by Johnson et al., 35 tumors ranging in radius from 1.0 to 2.0 cm were simulated and neglecting crossdose contributions was found to underestimate tumor doses by 10%-25%. 22 In the study by Howard et al., 57 tumors in a wide range of sizes from 2 to 423 ml were evaluated and use of the sphere model was found to underestimate total tumor dose by up to 31%. 23 Conversely, Divoli et al. investigated tumors only 7 g in size and found the differences between the sphere model and Monte Carlo total tumor dose calculations to be less than 5%. 21 The present study only included three tumors, which ranged in volume from 23 to 95 ml. These tumors were larger than the tumors studied by Divoli et al. and by Johnson et al. and they fell inside the range of tumor volumes studied by Howard et al. The likely reasons that crossdose contributions played a relatively small factor in the total tumor doses of the present study are that these tumors were isolated from other areas with high activity concentration and two of the three tumors (patients 3 and 4) had high cumulated activity concentrations compared to the other source organs (Table II).
In the paired organ analysis, it is interesting to note the influence of the different physical half-lives of the investigated radionuclides. For the shorter lived radionuclide, 99m Tc, differences in right and left kidney doses were caused by differences in the total activity uptake [ Fig. 4(a)] and proximity to highly radioactive organs [ Fig. 4(b)], whereas for the longer lived radionuclides, 131 I, 177 Lu, and 90 Y differences in left and right kidney doses were also heavily influenced by differences in the rates of washout from these organs. For example, in patient 2, the right and left kidney doses agreed within 2.3% for 99m Tc, but a difference of 4.7 h in the biological half-lives of each kidney raised the percent difference to 10% for 131 I and 177 Lu.
Finally, 3D dose distributions calculated by the voxel S value method in approximately 1 h were found to produce very similar dose distributions to those calculated by Monte Carlo simulation, which took 30 h or more. The use of the fast Hartley transform could be used to substantially decrease the computation time of the voxel S value calculation. 24

CONCLUSIONS
Several aspects of OLINDA/EXM dose calculations (which are based on reference phantoms representing the average patient) were tested by comparing them with patientspecific Monte Carlo dose estimates. Although anatomy can differ considerably between patients, organ doses calculated by OLINDA/EXM were found to be in good agreement with Monte Carlo mean dose estimates. Furthermore, the sphere model used by OLINDA/EXM agreed reasonably well with Monte Carlo dose estimates with therapeutic agents ( 131 I, 177 Lu, and 90 Y) even with cross organ irradiation. The treatment of paired organs by OLINDA/EXM was found to be inaccurate in several cases where the dose to the right and left kidneys differed by up to 73%. Furthermore, the lack of voxelized dose information is a major limitation of organlevel calculations since nonuniform dose distributions may have important clinical implications. Although Monte Carlo simulation may not currently be feasible for routine patient dose calculations, voxel S values have been shown to produce nearly equivalent 3D dose distributions.