Updated anatomical data and mathematical models for embryo/fetus dosimetry

PURPOSE OF THE STUDY: It is proposed to fill in the gaps in the existing data matrix of mass/volume of uterus, its contents as well as mass of fetal organs by mathematical techniques down to 6 week gestation and relate this dynamic target mass during in-utero growth to recently revised Medical Internal Radiation Dose (MIRD) 21 schema. MATERIALS AND METHODS: The existing data is subjected to numerical interpolations using a standard 4 degree polynomial for certain set of variables. Interpolations of mass, volume, etc., of various components of the uterus (placenta, embryo/fetus, brain, uterine wall, etc.) at weekly/biweekly intervals have been carried out. Subsequently, the step wise regression starting with three predictors - placental mass (W(p)), total fetal mass (W(f)) and greatest length (H) for the augmented data set led to identification of “H” and “W(f)” as the most significant predictors for 10 fetal organ masses W(i) using standard software “MS Excel”. RESULTS AND DISCUSSION: Further analysis utilizing allometric equations reveal that there is strong evidence in favor of W(f) compared to H for predicting (P < 0.001) the individual organ mass “W(i)”. The prediction of W(i) -liver, heart, thymus, pancreas, and thyroid fall under the linear case of prediction (predictor is ln [W(f)]); whereas the brain, lung, kidney, spleen, crown-heel length, etc., fall under linear-quadratic case (where ln (W(f)) plus [ln (W(f))](2)) are the predictors) respectively. The estimates indicate a rapid decline of “brain mass/total mass” ratio from 80% to 39% during 7-9 weeks. Information on specific absorbed fraction Φ (=φ/m(T)) is required to arrive at the dose estimates (φ being the absorbed fraction). The very small target mass m(T)-few milligrams (for 90% of organs) to a maximum 11 g for brain during early pregnancy; the fetal thyroid, with its mass variation of about 300% during 10-13 weeks can impact Φ. Reported standardized doses are presented and variation of Φ with source-target distance for individual specific scaling of Φ is discussed. CONCLUSION: Time dependent mass m (t) of the target and consequently Φ(t) [=φ(t)/m(T) (t)] of the revised MIRD dose expression can be of relevance in fetal dosimetry when source-target distances are in reasonable limits.