A theoretical dose-escalation study based on biological effective dose in radioimmunotherapy with ⁹⁰Y-ibritumomab tiuxetan (Zevalin)

Abstract

Aim

To investigate the variation in biological effective dose (BED) produced by the uncertainty in absorbed dose and radiobiological parameters in Zevalin radioimmunotherapy.

Methods

Eight patients scheduled for treatment with standard administration of ⁹⁰Y-ibritumomab tiuxetan (Zevalin) were studied. Patient-specific pretherapy dosimetry was performed by injection of ¹¹¹In-ibritumomab tiuxetan. Absorbed doses and BEDs were calculated for critical organs (COs) and tumours, assuming a 30% dose uncertainty and varying the radiobiological parameters in a reasonable range. In an activity-escalation study, BEDs for the COs were compared with the BED limits of external beam radiotherapy (EBRT) and BEDs for the tumour with the EBRT dose prescriptions.

Results

At standard activities, the absorbed doses per unit activity for the COs were in agreement with those in the literature. Absorbed doses to lesions were rather variable, ranging from 1.47 to 16.7 Gy/GBq. Median tumour absorbed dose to lesions in the range 80–110 g was 9.6 Gy/GBq (range 9.2–16.7 Gy/GBq), yielding a mean BED of about 12 Gy for administration of 15 MBq/kg. For the administration of the myeloablative activity of 45 MBq/kg, risk of liver toxicity in one patient would have been foreseen by the model. Considering also the dose uncertainty, the potential risk of liver toxicity in one more patient, lung toxicity in one patient, and kidney toxicity in one patient would have been suggested. The absorbed dose uncertainty was found to be the main source of uncertainty in the BED. As for radiobiological parameters, at myeloablative activities, the increase in the repair half-time for sublethally damaged tissue (T_μ) from 0.5 h to 5 h induced more consistent increases in mean BED/BED_limit than α/β variation from 2 Gy to 5 Gy: at 53 MBq/kg, 38% for the liver, and 34% for the lungs and kidneys (about threefold higher than that obtained for the increase α/β).

Conclusion

At standard activities, absorbed doses to lesions appear to be effective, even though lower than prescribed by EBRT. At myeloablative dosages, the uncertainty associated with the absorbed doses and radiobiological parameters considerably affect BED evaluation and may account for possible “second-organ” toxicities.

Appendix: Calculation of the Lea-Catcheside factor for different biokinetics in radionuclide targeted therapy

In many cases, the absorbed dose-rate to the tumour, or to the critical organs, increases from an initial value of zero to some maximum value (uptake phase), and then decreases (clearance phase). According to Howell et al. [10], the presence of an uptake phase can be described by the following functional form for the absorbed dose rate:

$$ r(t) = {r_0}\left( {{e^{ - {\lambda_{eff}} \cdot t}} - {e^{ - {\lambda_{in}} \cdot t}}} \right) $$

(A1)

where λ_eff is the effective clearance rate constant and λ_in is the effective uptake rate constant. By defining the effective clearance half-time (T_e) and the effective uptake half-time (T_eu), λ_eff = ln2/T_e and λ_in = ln2/T_eu. Following the procedure of Dale [11], Howell et al. [10] calculated the RE when the equation above is used for describing the biokinetics:

$$ RE = 1 + \frac{{{r_0}}}{{\ln 2}}\left( {\frac{\beta }{\alpha }} \right)\left\{ {\frac{{2T_\mu^4\left( {{T_e} - {T_{eu}}} \right)}}{{\left( {T_\mu^2 - T_e^2} \right)\left( {T_\mu^2 - T_{eu}^2} \right)}} + \frac{{2{T_e}{T_{eu}}{T_\mu }}}{{\left( {T_e^2 - T_{eu}^2} \right)}} \left. { \left( {\frac{{{T_e}}}{{{T_\mu } - {T_e}}} + \frac{{{T_{eu}}}}{{{T_\mu } - {T_{eu}}}}} \right) - \frac{{{T_\mu }}}{{{T_e} - {T_{eu}}}}\left( {\frac{{T_e^2}}{{{T_\mu } - {T_e}}} + \frac{{T_{eu}^2}}{{{T_\mu } - {T_{eu}}}}} \right)} \right\}} \right. $$

(A2)

In the original equations, the initial dose rate r₀ was used, but it was subsequently substituted by the product between the absorbed dose and λ_eff. In this work, Eq. A2 was used for BED calculations when the biokinetics showed an uptake phase.

Baechler et al. [14] provided a general model for the calculation of the G factor, whatever the number of exponential clearance components or source organs:

$$ {G_{s,n}} = \frac{{2 \cdot \sum\limits_{m,h}^s {\sum\limits_{k,i}^n {\frac{{{f_m} \cdot {f_h} \cdot {S_m} \cdot {S_h} \cdot {a_{k,m}} \cdot {a_{i,h}}}}{{\left( {{\lambda_{k,m}} + {\lambda_{i,h}}} \right)\left( {\mu + {\lambda_{k,m}}} \right)}}} } }}{{{{\left( {\sum\limits_h^s {\sum\limits_i^n {\frac{{{a_{i,h}}{f_h}{S_h}}}{{{\lambda_{i,h}}}}} } } \right)}^2}}} $$

(A3)

where s is the number of source organs, n is the number of clearance exponential components, S_h (or S_m) is the S value from the source organ h (or m), f_h (or f_m) is the “initial activity fraction” for the source organ h (or m) obtained by extrapolating to zero time a multiexponential expression fitted to the time–activity curve, and a_k,m (or a_i,h) is the activity fraction coefficient of the k-th (or i-th) exponential clearance component in the multiexponential expression fitted to the time–activity curve. For a unique source with monoexponential clearance (i.e. s = n = 1), G_1,1 = λ/(λ+μ), and the resulting RE is identical to that of the Dale formula [38].

For a unique biexponential decaying source, the G factor is derived as follows:

$$ {G_{1,2}} = \frac{{\frac{{a_1^2}}{{{\lambda_1}\left( {\mu + {\lambda_1}} \right)}} + \frac{{2 \cdot {a_1} \cdot {a_2}}}{{\left( {{\lambda_1} + {\lambda_2}} \right)\left( {\mu + {\lambda_1}} \right)}} + \frac{{2 \cdot {a_2} \cdot {a_1}}}{{\left( {{\lambda_2} + {\lambda_1}} \right)\left( {\mu + {\lambda_2}} \right)}} + \frac{{a_2^2}}{{{\lambda_2}\left( {\mu + {\lambda_2}} \right)}}}}{{{{\left( {\frac{{{a_1}}}{{{\lambda_1}}} + \frac{{{a_2}}}{{{\lambda_2}}}} \right)}^2}}} $$

(A4)

Equation A4 was used here for BED calculations when the biokinetics indicated only clearance phases (e.g. for the lungs). When activity is located in two source organs, considering monoexponential clearance for each one (i.e. s = 2 and n = 1) the factor G_2,1 is expressed as follows:

$$ {G_{2,1}} = \frac{{\left\{ {\frac{{f_1^2S_1^2}}{{{\lambda_1}\left( {{\lambda_1} + \mu } \right)}} + \frac{{2{f_1}{f_2}{S_1}{S_2}}}{{\left( {{\lambda_1} + {\lambda_2}} \right)\left( {{\lambda_1} + \mu } \right)}} + \frac{{2{f_1}{f_2}{S_1}{S_2}}}{{\left( {{\lambda_2} + {\lambda_1}} \right)\left( {{\lambda_2} + \mu } \right)}} + \frac{{f_2^2S_2^2}}{{{\lambda_2}\left( {{\lambda_2} + \mu } \right)}}} \right\}}}{{{{\left( {\frac{{{f_1} \cdot {S_1}}}{{{\lambda_1}}} + \frac{{{f_2} \cdot {S_2}}}{{{\lambda_2}}}} \right)}^2}}} $$

(A5)

The above equation was used in this work when the contributions from two source organ were taken into account in calculating the BED, i.e. for the red marrow (red marrow and remainder of the body) and the heart wall (heart wall and heart content).