“ Log (Viable shell (mm))
5.4 Conclusion
A mouse dosimetry model has been developed to facilitate more accurate absorbed dose calculations during RIT. The self-absorbed dose fraction and cross-dose fraction, for both
and were calculated for 12 major organs. In addition, information based on data
from RLG’s and histological images o f kidney and tumour sections was incorporated into the model.
Each organ, or region within an organ, was modelled as an ellipsoid or cylinder. Each region was subdivided into a 3D array o f elements with each element containing the local activity. The dose distribution to a region surrounding each element was calculated by multiplying the value o f the element by a density matrix created from the MIRD beta dose kernels for
and The accuracy o f this technique depended on the dimensions o f each element
compared to the range o f the emitted electron. Indeed, as the dimensions decreased, the sum o f the elements tended towards the expected values. However, this was accompanied by an increased burden on computation time. Nevertheless, the error was greater for '^’l compared
to due to the shorter range o f the electron.
As expected, the self-absorbed fraction in each organ was greater for ’^’l than ^®Y. As a result, the cross-dose to adjacent organs was smaller. The values for the self-absorbed fractions from ^°Y were within 13 % o f the values from the model by Hui (Hui et al., 1993), for all normal tissues except for cortical bone. In the original model, ^ Y was assumed to remain on bone surfaces whereas here it is assumed to be distributed uniformly throughout and, as shown by Bardies (Bardies et al., 1994) for spherical geometry, this leads to a
significantly larger absorbed fraction. In addition, the value for the absorbed fraction in bone marrow was 5% larger for ^ Y and 18% larger for ’^'l than that calculated by Muthaswamy (Muthaswamy et al., 1998). This was primarily due to a difference in size o f the marrow cavity.
These fractions were generally higher than in the original model, with the largest errors for the smaller organs. This was probably due to a partial volume effect at the surface o f the organ model. In addition, the cross-dose was assumed to distribute uniformly in the target organs. Obviously, areas o f the target organ that are adjacent to the source would absorb
more energy than distant areas. Therefore, a more accurate model would include more information on the structure o f the mouse.
A kidney model was developed and comprised two distinct regions representing the cortex and medulla. The dimensions o f each region were measured and the self-dose was calculated in kidney as a single region, cortex and medulla. In addition, the cross-dose between medulla and cortex and the amount that escapes the kidney was calculated for both regions. The mean dimensions o f the kidney were smaller than previously measured (Hui et al, 93;
Durbin et al, 92) but agree to within experimental error. The absorbed fraction in the kidney,
from agrees w ith the previous model to within 10 %. The error was primarily due to the
smaller dimensions used. Additionally, a significant amount o f the p energy from escapes the medulla, penetrates the cortex and is absorbed in adjacent organs. Likewise, energy from surrounding organs may also be absorbed in the medulla. By contrast, none o f
the energy from that escapes the medulla also escapes the cortex.
The kidney model tended to overestimate the dose delivered to the cortex relative to the medulla. There are three probable sources o f error: The geometry o f the model does not accurately describe the structure o f the kidney; the dimensions o f the cortex may have been overestimated in the original measurements; delineation o f cortex and medulla during validation may have been inaccurate. Nevertheless, the model provides a more accurate measurement o f the actual dose distribution in kidney compared to traditional calculations that assumed uniform distribution.
A tumour model was also developed and consisted o f a spherical necrotic core with a shell representing the viable periphery. The absorbed fractions within uniform isotropic spheres, with various radii, compared well with work by others (O ’Donoghue et al, 95; Bardies & Chatal, 1994). The extent o f viable and necrotic regions was measured from montages o f microscopy images o f histologically stained tumour sections. This was also performed for a range o f tumour sizes. As the tumour size increased, so did the thickness o f the viable shell. This implies that there is concurrent vascularisation with tumour growth. Otherwise, the thickness o f the viable shell would remain constant with the diffusion range o f nutrients.
the cross-dose between regions increased with tumour size for and decreased for However, it is likely that if the tumour size increased further then the cross-dose with would then decrease. Furthermore, the cross-dose from necrosis to viable was greater than that from viable to necrosis. Any electron that escapes the necrosis must pass through the viable region whereas an electron escaping from the viable region does not necessarily pass through the necrosis. Indeed, more electron energy escapes the tumour altogether.
The equations that were used to describe the tumour model were used only to facilitate interpolation between data points. There was no theoretical basis for their form.
Consequently, they cannot be used to extrapolate for tumour sizes that lie outside the range o f sizes presented here.
The tumour model provided a more accurate estimate o f the dose to viable and necrotic areas compared to calculations that assume uniformity o f dose deposition. In addition, the model
for ’^’l described the actual dose values better then the model. Nevertheless, there was an
appreciable difference between model and actual values.
No account was taken o f the spatial heterogeneity o f antibody distribution within viable and necrotic regions. In addition, the morphology o f the tumour was disregarded. Furthermore, cellular radiosensitivity in the tumour was assumed to be a binary function whereas it is probably a continuous function ranging from the most sensitive cells to those that have complete radioprotection. Therefore, a more realistic model would account for the structure o f the tumour and heterogeneity o f dose deposition and response. Indeed, reconstruction o f serial images o f radiolabelled antibody distribution has been used to account for morphology and dose deposition (Roberson et al., 1994; Yorke et al., 1993; Humm et al., 1995).
However, there has been little work on quantitative measures o f the heterogeneity o f response.
The traditional MIRD approach to internal beta dosimetry assumes all the beta energy is absorbed in the source organ. However, this is not a valid assumption when measuring the absorbed dose in the organs o f small animal models. A preliminary model was developed to facilitate more accurate dose estimates for ^®Y labelled antibodies in mice (Hui et al., 1993). In this chapter, this model has been adapted for use with ^^^I labelled antibodies.
Furthermore, information from images o f antibody distribution in tissue sections and tumour morphology has been used to account for dose heterogeneity in kidney and tumour. This new model further improves dose estimates in mice and allows better characterisation o f absorbed dose as well as giving a conceptual basis for considering dosimetry in patients with cancer.