Background The calculation of time-integrated activities (TIAs) for tumours and organs is required for dosimetry in molecular radiotherapy. The accuracy of the calculated TIAs is highly dependent on the chosen fit function. Selection of an adequate function is therefore of high importance. However, model (i.e. function) selection works more accurately when more biokinetic data are available than are usually obtained in a single patient. In this retrospective analysis, we therefore developed a method for population-based model selection that can be used for the determination of individual time-integrated activities (TIAs). The method is demonstrated at an example of [177Lu]Lu-PSMA-I&T kidneys biokinetics. It is based on population fitting and is specifically advantageous for cases with a low number of available biokinetic data per patient. Methods Renal biokinetics of [177Lu]Lu-PSMA-I&T from thirteen patients with metastatic castration-resistant prostate cancer acquired by planar imaging were used. Twenty exponential functions were derived from various parameterizations of mono- and bi-exponential functions. The parameters of the functions were fitted (with different combinations of shared and individual parameters) to the biokinetic data of all patients. The goodness of fits were assumed as acceptable based on visual inspection of the fitted curves and coefficients of variation CVs < 50%. The Akaike weight (based on the corrected Akaike Information Criterion) was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. Results The function $$A_{1} { }\beta { }e^{{ - \left( {\lambda_{1} + \lambda_{{{\text{phys}}}} } \right)t}} + A_{1} { }\left( {1 - \beta } \right){ }e^{{ - \left( {\lambda_{{{\text{phys}}}} } \right)t}}$$ A 1 β e - λ 1 + λ phys t + A 1 1 - β e - λ phys t with shared parameter $$\beta$$ β was selected as the function most supported by the data with an Akaike weight of 97%. Parameters $$A_{1}$$ A 1 and $$\lambda_{1}$$ λ 1 were fitted individually for every patient while parameter $$\beta { }$$ β was fitted as a shared parameter in the population yielding a value of 0.9632 ± 0.0037. Conclusions The presented population-based model selection allows for a higher number of parameters of investigated fit functions which leads to better fits. It also reduces the uncertainty of the obtained Akaike weights and the selected best fit function based on them. The use of the population-determined shared parameter for future patients allows the fitting of more appropriate functions also for patients for whom only a low number of individual data are available.
Purpose This project aims to develop and evaluate a method for accurately determining time-integrated activities (TIAs) in single-time-point (STP) dosimetry for molecular radiotherapy. It performs a model selection (MS) within the framework of the nonlinear mixed-effects (NLME) model (MS–NLME). Methods Biokinetic data of [111In]In-DOTATATE activity in kidneys at T1 = (2.9 ± 0.6) h, T2 = (4.6 ± 0.4) h, T3 = (22.8 ± 1.6) h, T4 = (46.7 ± 1.7) h, and T5 = (70.9 ± 1.0) h post injection were obtained from eight patients using planar imaging. Eleven functions were derived from various parameterisations of mono-, bi-, and tri-exponential functions. The functions’ fixed and random effects parameters were fitted simultaneously (in the NLME framework) to the biokinetic data of all patients. The Akaike weights were used to select the fit function most supported by the data. The relative deviations (RD) and the root-mean-square error (RMSE) of the calculated TIAs for the STP dosimetry at T3 = (22.8 ± 1.6) h and T4 = (46.7 ± 1.7) h p.i. were determined for all functions passing the goodness-of-fit test. Results The function $$f_{4d} \left( t \right) = A_{1} /\left\{ {\left( {\frac{1 - \alpha }{{\lambda_{1} + \lambda_{{{\text{phys}}}} }}} \right) - \left( {\frac{\alpha }{{\lambda_{2} + \lambda_{{{\text{phys}}}} }}} \right) - \left( {\frac{1 - 2\alpha }{{\lambda_{bc} + \lambda_{{{\text{phys}}}} }}} \right)} \right\} \cdot e^{{ - \lambda_{{{\text{phys}}}} t}} \cdot \left\{ {\left( {1 - \alpha } \right) \cdot e^{{ - \lambda_{1} t}} - \alpha \cdot e^{{ - \lambda_{2} t}} - \left( {1 - 2\alpha } \right) \cdot e^{{ - \lambda_{bc} t}} } \right\}$$ f 4 d t = A 1 / 1 - α λ 1 + λ phys - α λ 2 + λ phys - 1 - 2 α λ bc + λ phys · e - λ phys t · 1 - α · e - λ 1 t - α · e - λ 2 t - 1 - 2 α · e - λ bc t with four adjustable parameters and $$\lambda_{bc} = \frac{{{\text{ln}}\left( 2 \right)}}{{1\;{\text{ min}}}}$$ λ bc = ln 2 1 min was selected as the function most supported by the data with an Akaike weight of (45 ± 6) %. RD and RMSE values show that the MS–NLME method performs better than functions with three or five adjustable parameters. The RMSEs of TIANLME–PBMS and TIA3-parameters were 7.8% and 10.9% (for STP at T3), and 4.9% and 10.7% (for STP at T4), respectively. Conclusion An MS–NLME method was developed to determine the best fit function for calculating TIAs in STP dosimetry for a given radiopharmaceutical, organ, and patient population. The proof of concept was demonstrated for biokinetic 111In-DOTATATE data, showing that four-parameter functions perform better than three- and five-parameter functions.
Seleksi model merupakan aspek penting dari analisis data farmakokinetik. Seleksi model dilakukan untuk memperoleh fungsi terbaik yang selanjutnya digunakan dalam perhitungan nilai TIACs pada dosimetri individu. Data yang digunakan pada penelitian ini berupa data biodistribusi radiofarmaka 177 Lu-DOTATATE pada organ ginjal dari 8 pasien PRRT. Setiap data pasien difitting dengan menggunakan beberapa fungsi. Pada setiap fungsi yang diterapkan, dilakukan analisa goodness of fit. Pada setiap fungsi yang memenuhi kriteria goodness of fit dilakukan perhitungan nilai AICc dan nilai pembobotan AICc. Fungsi dengan nilai pembobotan AICc terbesar dipilih menjadi fungsi terbaik. Berdasarkan proses seleksi model yang dilakukan, fungsi 𝑓 2𝑎,1𝑒𝑥 (𝑡) = 𝐴 1 𝑒 −(𝜆 1 +𝜆 𝑝ℎ𝑦𝑠 )𝑡 diperoleh sebagai fungsi terbaik untuk pasien 1,3,4,5,6, dan 7. Sementara itu, fugsi 𝑓 2𝑏,2𝑒𝑥 (𝑡) = 𝐴 1 𝑒 −(𝜆 1 +𝜆 𝑝ℎ𝑦𝑠 )𝑡 + (100 − 𝐴 1 ) 𝑒 −(𝜆 𝑝ℎ𝑦𝑠 )𝑡 menjadi model terbaik untuk pasien 2 dan fungsi 𝑓 1𝑎,1𝑒𝑥 (𝑡) = 𝐴 1 𝑒 −(𝜆 𝑝ℎ𝑦𝑠 )𝑡 untuk pasien 8.
This study aims to identify the most important parameters in the Physiologically-Based Pharmacokinetic (PBPK) model of Peptide Receptor Radionuclide Therapy (PRRT). By knowing the size of the contribution of physiological parameters to the PBPK model, it can reduce the variability of the absorbed dose (AD) in organs at risk, such as the kidney and tumor between individuals. The small variability has the potential to increase the accuracy of planning individual radionuclide therapy treatments. This study uses the extended Fourier Amplitude Sensitivity Test (eFAST) Global Sensitivity Analysis method, the best variance-based global method in analyzing the PBPK model. A whole-body PBPK model that has been developed for treatment planning in PRRT therapy for meningioma patients (n = 7). The parameters of interest analyzed were organ receptor densities Rdens, organ flows f, organ release rates, and peptide binding rate. AD as the desired output from the eFAST algorithm by calculating Si and STi from each AD Kidney and AD Tumor. All parameters of interest are converted into the lognormal distribution. The sampling strategy based on eFAST sampling, the interference factor is equal to 4. To see the convergence of the convergence value of Si and STi , a simulation was performed with a total evaluation of 129, 257, 513, 1025, 2049, 4097, and 8193. The results of the simulation, inter-individual variability of tumor AD (coefficient of variation CV up to CV = 73%) was higher than that organ at risk (e.g. kidneys CV around 22%). Based on GSA analysis, the most important parameter determined the AD of tumors, tumors receptor density (Si = 0.8, S Ti = 0.93), kidneys AD was kidneys receptor density (Si = 0.66, STi = 0.71). After validating Si by fixing every parameter considered important, the results can reduce the CV of the kidney AD from 22% to 1%, with a decrease in CV presentation of around 95%. CV AD tumor 1 was reduced by 68% from CV 44% to 14%, and CV in tumor AD 2 from 72% to 17% with a reduced CV presentation of about 77%. It was concluded that receptor measurement is important because it can improve the accuracy of radionuclide therapy treatment.
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