The two types of correction of absorbed dose estimates for internal emitters

Authors

  • Lawrence E. Williams Ph.D.,

    Corresponding author
    1. Division of Radiology, City of Hope National Medical Center, Duarte, CaliforniaDivision of Radiation Oncology, City of Hope National Medical Center, Duarte, California
    • Division of Radiology, City of Hope National Medical Center, Duarte CA 91010===

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    • Fax: (626) 930-5451

  • An Liu Ph.D.,

    1. Division of Radiology, City of Hope National Medical Center, Duarte, CaliforniaDivision of Radiation Oncology, City of Hope National Medical Center, Duarte, California
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  • Dave M. Yamauchi M.D.,

    1. Division of Radiology, City of Hope National Medical Center, Duarte, CaliforniaDivision of Radiation Oncology, City of Hope National Medical Center, Duarte, California
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  • George Lopatin B.S.,

    1. Division of Radiology, City of Hope National Medical Center, Duarte, CaliforniaDivision of Radiation Oncology, City of Hope National Medical Center, Duarte, California
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  • Andrew A. Raubitschek M.D.,

    1. Division of Radiology, City of Hope National Medical Center, Duarte, CaliforniaDivision of Radiation Oncology, City of Hope National Medical Center, Duarte, California
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  • Jeffrey Y. C. Wong M.D.

    1. Division of Radiology, City of Hope National Medical Center, Duarte, CaliforniaDivision of Radiation Oncology, City of Hope National Medical Center, Duarte, California
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Abstract

BACKGROUND

Two types of correction for absorbed dose (D̄) estimates are described for clinical applications of internal emitters. The first is appropriate for legal and scientific reasons involving phantom-based estimates; the second is patient-specific and primarily intended for radioimmunotherapy (RIT).

METHODS

The Medical Internal Radiation Dose (MIRD) relationship (D̄) = S à is used, where S is a geometric matrix factor and à is the integral of source organ activities. Internal consistency of the data and the size of organ systems in the humanoid phantom must be assured in both types of estimation.

RESULTS

The first dose estimate correction (I) is one whereby computations refer to one or another standard (e.g., MIRD-type) phantom. In this case the S value remains as given, but the measured patient à data must be standardized. The correction factor is the phantom's ratio of organ mass to whole-body mass divided by the same ratio for the volunteer or patient. The second dose estimate correction (II) is patient-specific. While the à value is unchanged for this application, a correction term is provided for the phantom-derived S matrix. The dominant (nonpenetrating radiation) component of this correction factor can be obtained via the ratio of the patient to phantom organ masses. In both corrections, we recommend that true organ sizes, necessary in each method of estimation, be determined in a separate sequence of anatomic images.

CONCLUSIONS

In both dose estimation corrections, true sizes of the patient's or volunteer's internal organs must be obtained. Correction due to organ mass size can be severalfold and is probably the dominant uncertainty in the internal emitter absorbed dose calculation process. Cancer 2002;94:1231–4. © 2002 American Cancer Society.

DOI 10.1002/cncr.10290

Because of the usual impossibility of direct measurement, absorbed dose is necessarily an estimated parameter. Two possible types of dose estimate corrections are suggested in current clinical practice. These will be referred to as phantom-specific (I) and patient-specific (II) computations. Both can be based on the same mathematic formulation. It is not clear, however, if dose estimators are aware of the different methodologic aspects of these two applications.

The general Medical Internal Radiation Dose MIRD method1 is used in this analysis to estimate internal emitter whole organ absorbed doses. Correction factors must be applied to patient-derived data so that standard S matrix results1 are applicable for both phantom and patient dose estimates. These corrections will be dependent upon the specific organ (and tumor) sizes of the phantom and patient involved in the estimation process.

Materials and Methods

Following the MIRD framework, it is appropriate to assume that the average target organ dose (D̄t) is given by:

equation image(1)

where Sts is a matrix element giving the dose (cGy or rads) to target organ t per unit decay in the source organ s. The Ãs variable is the integral of the activity (in MBq-sec or μCi-h) in the source organ s. Generally, this integral is carried out to infinite time, although finite values are acceptable if the convergence is pronounced. In MIRD Pamphlet 11, values of S for an assumed phantom geometry and radionuclide were determined for a number of radionuclides using a Monte Carlo program.2 One should note that the geometry is relatively simple in such computations (e.g., the brain is an ellipsoid and each kidney is an ellipsoid cut by a plane). Up to now, some six such phantoms have been studied and corresponding S values produced. Standard sizes (in grams) for various pseudo-organs are also defined for the six phantoms. These results are tabulated and available, for example, in the MIRDOSE program.3

Results

Corrections for Phantom-Specific Absorbed Dose Estimates (Type I Calculations)

The primary application of Equation 1 has been in the estimation of absorbed doses for clinical radiopharmaceutical trials. Generally, data were obtained from animal studies or, preferably, from human patients or volunteers for this type of calculation. What has not been clear in these historical efforts, however, is the method of correction for organ mass differences between the necessarily limited human population studied and the MIRD phantom. Since the patient or volunteer (pt) may have a different organ or whole body mass (or both) than the gender- and age-adjusted phantom, a lowest-order correction to the cumulated activity data is:

equation image(2)

Here, M stands for whole body mass. The correction term on the right side of Equation 2 essentially takes into account perfusion differences between the patient or volunteer and the standard geometry of the phantom. For example, consider a patient having the same whole-body mass as the MIRD phantom but a liver one-half the size of the phantom's liver. In that case, the measured liver activity at any given time should be increased by a factor of 2 before substitution into Equation 1 and before the use of standard MIRD S values.

The organ mass normalization of Equation 2 has historically been applied in cases of animal biodistributions in which organ mass (ms) and whole-body mass (M) were each quite different from their respective phantom values. This normalization, however, should also be included in estimates made with human uptake results. We would urge that future calculations made with such human data be standardized, via Equation 2, to the MIRD phantom mass and be clearly labeled as MIRD phantom dose estimates. One use of this type of analysis is the Investigational New Drug application to the Food and Drug Administration.

Phantom-standardized dose estimates may also be used to compare two or more radiopharmaceuticals (e.g., all colon cancer antibodies) that have the same intended patient population. It is only when all estimates are performed in the MIRD or other standard phantom context that the various agents may be compared as to possible benefit and risk. Notice that absorbed dose may be both a benefit (in tumors) and a risk (in normal organs). This application of Equation 2 could eventually become its most important usage.

Correction for Patient-Specific Absorbed Dose Estimates (Type II Calculations)

In the case of radioimmunotherapy (RIT) or other forms of internal emitter therapy, the treatment planning team will need a second type of correction for absorbed dose estimates. Here, one will use the individual's integrated imaging data (Ã) directly but will have to change the tabulated phantom S values to suit the patient. This is because the MIRD S value is premised on a standard MIRD phantom geometry2,3 that may not be appropriate for the individual being considered for treatment. The most obvious such correction is applied to the nonpenetrating (np) radiation emitted by the source organ:

equation image(3)

In this case, we have used the finding that Snp is inversely proportional to the target organ mass.1 This correction is clearly not complete. Photon contributions, if present, may also be included by interpolation methods4 or by direct Monte Carlo estimation.5 Such penetrating contributions (Sp) are intentionally only small fractions of the particulate absorbed dose estimates and may justifiably be considered second-order effects. We would propose that absorbed dose estimations made with these corrections for the target organ mass be considered patient-specific values and be labeled as such.

It was shown in a recent study that the mass correction factor given in Equation 3 can be on the order of two- or threefold for colon cancer candidates for RIT.6 While pathology was not involved with those patients, it is possible that disease considerations may also cause increased mass, such as in the spleen of a lymphoma patient. A summary of the two corrections of absorbed dose estimation and specific methods of adjusting à and S factors is given in Table 1.

Table 1. Types of Correction for Internal Emitter Absorbed Dose Estimates
Correction TypeType IType II
  1. MIRD: Medical Internal Radiation Dose; Snp: MIRD S value for nonpenetrating radiation.

GeometryMIRD or other phantomPatient anatomy
à CorrectionOrgan-to-body mass ratioNone required
S CorrectionNone requiredOrgan mass ratio for Snp

One should discuss the optimal method for determining anatomic organ mass for the above analyses. It is recommended that organ sizes be determined with imaging modalities such as computed tomography (CT) or magnetic resonance imaging. Several reasons may be given. For example, anatomic volumes are used by clinicians when referring to the extent of patient illness. In the case of treating the cancer patient, the radiation oncologist also follows disease progression via serial anatomic evaluation. Use of organ volumes obtained from nuclear imaging is generally problematic. The primary limitation of that method is the difficulty of finding the true edge, and hence the size, of any radioactive volume. If single photon emission computed tomography (SPECT) images are not available, there is the additional problem of determining the true sizes of several organs that are superimposed in planar projections. An example of this problem is determination of right kidney and liver size.

In the case of manifestly nonuniform uptake in an organ or lesion, however, the nuclear image should be taken into account. By fusing it onto the anatomic image, the dose estimator can segment the calculation of absorbed dose into geometric regions within the tissue. Even in this case, it is probably best that the anatomic volume be used for the segmental and overall size measurements. Note that resultant absorbed dose estimates will now have a spatial variation within a given organ system. This is a generalization of Equation 1, where D̄t would now have spatial dependence.

In order to estimate the magnitude of the two corrections involved, we measured the size of each pair of kidneys in a sequence of patients about to receive a combination of RIT and 5-fluorouracil chemotherapy for metastatic colorectal cancer.7 Five patients were female and 10 were male; their total body masses were obtained by weighing. Because of incidental hydronephrosis, one of the female patients was excluded from the analysis. Table 2 contains a summary of the results for both Type I and Type II corrections. It was found that the mean correction was indeed close to unity, but that a wide variety of individual correction factors was observed. In the case of the male population, for example, Type I and Type II corrections varied over the ranges 0.67–1.49 and 0.58–1.45, respectively. We have previously seen Type II correction factors of twofold and higher in our earlier studies involving patient hepatic and splenic absorbed dose estimates in RIT.6 The magnitude of these CT results points out the reason why the corrections are important and why they must be made on a patient-by-patient basis.

Table 2. Magnitudes of Type I and Type II Renal Correction for Patients Receiving RIT and 5-FU Therapy
 Type I renal correctionType II renal correction
MeanRangeMeanRange
  1. RIT: radioimmunotherapy; 5-FU: 5-fluorouracil.

Women (n = 4)1.21 ± 0.160.98–1.341.01 ± 0.220.69–1.20
Men (n = 10)0.91 ± 0.250.67–1.490.84 ± 0.260.58–1.45

Discussion

Two types of corrections for human absorbed dose estimates for internal emitters have been outlined. These have been termed phantom-specific (Type I) and patient-specific (Type II) formulations. Each has its place in clinical practice; indeed, the RIT practitioner will need both types of computation in setting up and subsequently performing clinical trials of cancer therapy. Each type, however, requires correction, based on organ size, of either the à value or the S matrix.

Type I normalization, as seen in Equation 2, is a general requirement if one uses standard S matrices for dose estimation. If a point-source8 or voxel-source kernel convolution strategy6,9 were employed, the à as taken would also have to be corrected as input into the dose integration process. This follows from the fact that the patient or volunteer has a different organ mass distribution than that assumed in the standard (e.g., MIRD) phantom.

It should not be anticipated that contemporary MIRD phantoms3 would have indefinite application in Type I estimation. Recently, Johnson et al.5 demonstrated the ability to make Monte Carlo computations of absorbed dose for a set of transaxial CT slices obtained from a particular patient. After obtaining averages from such clinical anatomic information, one could decide upon a standard human shape and organ size for both genders at a variety of ages. Such novel S matrix results may differ considerably from those obtained with any of the more simplistic MIRD phantoms.2, 3 Even in this case, however, the à correction cited above would still be necessary when factoring patient or volunteer data into the new standard phantom computation of estimated absorbed dose.

Target organ mass correction, as given in Equation 3, is suggested for patient-specific, whole-organ dose estimates using the MIRD standard phantom Snp values. While such calculations will be done in the immediate future, one cannot be certain that smaller-scale computations will not supersede them. In the case of external beam treatment planning, dose estimations are now being compared using dose-volume histograms. Such distributions could also become an objective in RIT and other internal emitter therapies. In that case, one would use a point-source8 or voxel kernel6,9 approach that obviates organ mass corrections. This is one of the attractions of convolution approaches to Type II corrections, which may eventually make the mass corrections of Equation 3 unnecessary.

In conclusion, two types of correction have been proposed for absorbed dose estimates involving internal emitters. Both result from the difference between patient or volunteer organ sizes and those assumed in a standard phantom. Type I corrections involve à rescaling so as to partially account for organ perfusion differences. Type II changes result from differences between patient and phantom target organ sizes and involve S manipulation. Using renal CT images from our RIT patients, we have found that the corrections can approach a factor of 2 if one assumes a MIRD adult phantom. These corrections are probably the dominant uncertainty in the estimation of internal emitter absorbed dose.

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