2. Background Information
2.10 Radiation Dosimetry
Dosimetry is the process of approximating the absorbed dose, which is the energy of the ionizing radiation absorbed by the mass of tissue (Stabin, 2008). Dosimetry can be used to verify that treatment doses will be under normal tissue tolerances, hence minimizing radiation toxicity. On the other hand, dosimetry can be used to achieve planned radiation dose and biological effect in the treated tumours. It is also an important in research, like in the case of introducing new radiopharmaceuticals. Dosimetry also provides verification of the planned dose for recording purposes, for radiation protection officials or in case it is needed to make further medical decisions for the patient, like in a case of pregnancy (Sohlberg, 2020).
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Added to that, The Council of the European Union has published a legislation that encourages dosimetry process, as EU Directive 2013/59/EURATOM – Article 56 says:
“For all medical exposure of patients for radio-therapeutic purposes, exposures of target volumes shall be individually planned, and their delivery appropriately verified taking into account that doses to non-target volumes and tissues shall be as low as reasonably achievable and consistent with the intended radio-therapeutic purpose of the exposure.”
The general equation to express absorbed dose in a target mass from a radioactive source is
𝐷 =
𝑘 Ã ∑ 𝑛𝑖 𝐸𝑖 𝑓𝑖m , [35]
where D is the absorbed dose (rad or Gy), Ã is the cumulated activity of the source (µCi × h or MBq × s), ni is the number of particles with energy Ei emitted per nuclear transition, Ei is the energy per particle in (MeV), fi is the fraction of energy absorbed in the target, m is the mass of target (g or kg) and k is the proportionality constant (rad × g
µCi× h × MeV or Gy × kg
MBq× s × MeV) (Stabin, 1999).
The cumulated activity à is the number of disintegrations per unit time that is calculated as the area under the curve from the time-activity curve of the source organ (Stabin, 1999).
Equivalent dose is mathematically derived, and it considers the radiation type in dosimetry process.
Equivalent dose (H) is calculated by multiplying the measured mean absorbed dose (D) with radiation weighting factors (WR) as,
𝐻 = ∑ 𝑊𝑅 𝑅 𝐷𝑅 , [36]
where the equivalent dose unit is J/kg or Sievert (Sv). The radiation weighting factors are defined for different radiation types by characterizing the high linear energy transfer (high-LET) for stochastic effects at low doses (Fisher and Fahey, 2018). The radiation weighting factors for x-rays, gamma rays, beta particles are 1, and it is 20 for alpha particles (Thrall and Widmer, 2016).
Another mathematically derived dose value is the effective dose, where the radiation type and organ radiosensitivity is considered in dosimetry process. Organ weighting factors (WT) are calculated as average for all ages, sizes and for both genders. Effective dose (E) expressed as,
𝐸 = ∑ 𝑊
𝑇 𝑇[
𝐻𝑚𝑎𝑙𝑒+𝐻𝑓𝑒𝑚𝑎𝑙𝑒2
],
[37]where the effective dose unit is J/kg or Sievert (Sv). Organ weighting factors WT are experimentally approximated for different organs, such as 0.08 for gonads, 0.12 for red bone marrow, lung, stomach breasts, 0.04 for bladder, liver, thyroid, 0.01 for skin, brain and 1 for total body (Fisher and Fahey, 2018).
In clinical dosimetry, absorbed dose is used because equivalent dose is applicable to late stochastic effects like cancers but not for immediate effects like radiotoxicity, even though both absorbed dose and equivalent dose are equal in case of x-rays and gamma rays. Effective dose is calculated as reference but
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not for individual patient.Absorbed dose gives a proper clinical indication about the biological effect in tissues (Fisher and Fahey, 2018).
The approximation of absorbed dose can be performed using different methods such as with MIRD formalism, which calculates the mean absorbed dose in the target organ, or by voxel level dosimetry methods, which also consider the inhomogeneity of absorbed dose within the target organ by approximating it for each voxel (Hippeläinen, 2017).
2.10.1 The MIRD Dosimetry
In MIRD formalism, which was developed by the Medical Internal Radiation Dose committee of the Society of Nuclear Medicine (SNM) in 1968, the absorbed dose equation [35] from a single source is simplified to
𝐷 = Ã𝑆, [38]
where à is the cumulative activity and S contains all the other parameters (Hindorf, 2014).
In MIRD method constant factor k from equation [35] calculated to be 2.13, which is the absorbed dose in rad from activity in µCi, mass in g and energy in MeV. Constant factor k can be calculated to give the absorbed dose in Gy from activity in Bq and energy in MeV (Stabin et al., 1999).
Since the radionuclides are concentrated in more than one organ, the absorbed dose needs to be calculated for each target-source combination separately. The MIRD equation [38] is modified to calculate the total absorbed dose in the target organ (𝑟𝑡) as a sum of doses from source organs (𝑟𝑠) as
𝐷𝑟𝑡 = ∑ Ã 𝑆 (𝑟𝑡 ← 𝑟𝑠). [39]
More modifications can be applied if the cumulated activity à is normalized to the activity administered A0, which is a definition of the residence time (𝜏𝑠)
𝜏𝑠 = Ã𝑠
𝐴0 . [40]
By substituting equation [40] in [39], the absorbed dose becomes 𝐷𝑟𝑠 = 𝐴0∑ 𝜏𝑠 𝑆 (𝑟𝑡 ← 𝑟𝑠) [41]
The S values for different organ pairs are determined for phantoms representing different ages and genders. By providing dosimetry software system with cumulative activity Ã𝑠 or with administered activity A0 and residence time 𝜏𝑠, the absorbed dose can be calculated for given target organ using equations [39]
or [41] (Stabin et al., 1999).
MIRD formalism has been used widely in clinical practice due to its straightforward nature after the S values are known. However, the use of S values assumes that the distribution of radioactivity in organs is homogeneous, and organ masses are constants (Snyder et al., 1975), which are evidently limitations for
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this method. More advanced voxel level dosimetry techniques that are implement for each patient separately try to answer this problem.
2.10.2 Voxel Level Dosimetry
The main difference from MIRD formalism is that in voxel level dosimetry, the dose estimations are performed for each voxel and result in a patient-specific dose map (Sohlberg, 2020).
The voxel level dosimetry can be performed using multiple methods, the first method is conversion method or local deposition, which assumes that all radiation is absorbed locally. So, the total number of decays (TIAC) in a voxel is directly converted into absorbed dose by a multiplication with the dose conversion factor (DCF). It is fast and simple method, but obviously does not consider the cross irradiation between voxels (Hippeläinen, 2017).
Second method relies on dose point kernels (DPK), where the absorbed dose is calculated by convolving the uptake image with the DPK to get the dose distribution. It is also fast method, but needs a specifically implemented software to compute the convolution. Added to that it does not consider the tissue inhomogeneity, as the DPK is specific to one material, and it produces artefacts between boundaries due to difference in tissue densities (Hippeläinen, 2017).
Third method is Monte Carlo (MC) simulation, which is a statistical investigation to estimate all possible random pathways of photon interactions in three dimensions (Kost et al., 2015). Monte Carlo simulation is a solution to a macroscopic system by simulating its microscopic interactions, including scattering and absorbing events, specific medium characteristics. The accuracy of MC simulations depends on the initial number of simulated particles (Seco and Verhaegen, 2013; Juste et al, 2020).
Application of MC simulation starts with defining the input events, followed by generating uncorrelated, uniformly distributed random numbers in [0,1] interval. Then, the deterministic computation is applied on the input to form the result. The applied deterministic computations are numerical integrations for intervals [a,b] for defined function, where MC integration is applied after scaling the [a,b] interval to [0,1]
interval (Seco and Verhaegen, 2013). MC techniques improve the accuracy of absorbed dose detection and allow the consideration of tissue inhomogeneity and patient specificity in the dosimetry process, but it takes longer time than the other methods (Seco and Verhaegen, 2013; Hippeläinen, 2017).
In this study, the voxel level doses are measured using HERMES software (HERMES Medical Solutions, Stockholm, Sweden). Dosimetry process utilizes a semi-Monte Carlo simulation. The photons are simulated by a full Monte Carlo because they will be used for reconstruction and dose calculation. But electrons are simulated with local deposition as their accurate MC simulations are slow and it does not improve accuracy substantially (Sohlberg, 2020).
As an output, time activity curves (TAC) are generated for each voxel. For more accurate fitting, TAC is divided to three times segments, shown in Figure [20]. First segment spans from the time of
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radiopharmaceutical administration to the beginning of the time of scan (t1), where instant uptake is assumed (Sohlberg, 2020).
Figure [20]: Time activity curve (Figure adapted from Hermes Medical Solutions, 2019, p.13).
Second segment from time of scan (t1) to time point selected by user uses trapezoidal integration (Sohlberg, 2020). Trapezoidal integration approximates that area under the curve is trapezoid and the calculation takes form (Kaw and Kalu, 2008)
∫ 𝑓(𝑥)𝑑𝑥𝑎𝑏 = (𝑏 − 𝑎).𝑓(𝑎)+𝑓(𝑏)
2 . [42]
Third segment from t1 to the last measured data point, where an exponential decay with physical half-life assumed and integrated analytically (HERMES Medical Solutions, 2019). As an output, this generates the dose-map, which is the map of the absorbed dose for each voxel.
Finally, the doses can be plotted as dose volume histograms, which give accurate volumetric distribution of the absorbed dose.
2.11
177Lu-PSMA Therapies
Prostate cancer is the commonly diagnosed cancer and loses in deadliness only to lung cancer in men. It is treated in the common ways of treating cancer such as, surgery, chemotherapy, radiotherapy, brachytherapy, but that are not sufficient in the case of metastatic castration-resistant prostate cancer (mCRPC) (Özkan et al., 2020).
Targeted radionuclide therapy (TRT) is used for treatment of mCRP cases, where prostate specific membrane antigen (PSMA) inhibitor labelled with radionuclide is used as a target (Rahbar et al., 2018).
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PSMA is present in the cell membrane of normal prostate epithelial cells and is upregulated in case of prostate cancer. Besides that, PSMA is also present in lower concentrations in other tissues such as, salivary glands, duodenum mucosa, renal tubular cells, central nervous system and in any other neoplastic tissues (Rahbar et al., 2018; Özkan et al., 2020).
For PSMA targeted therapy, Yttrium-90 (90𝑌) and Lutetium-177 (177𝐿𝑢) were used as radiolabels. In first clinical trials, they caused grade 4 hepatotoxicity as a result of used large size monoclonal antibodies (mAb), which have slow clearance from the systemic circulation in tissues of interest. This side effect was solved by synthesis of smaller molecule inhibitors of PSMA. Another radionuclide tested was 131𝐼-labelled PSMA ligand, which shows mild haematological toxicity and good treatment response. From radiation safety side, 131𝐼 has high energy, long half-life of 8.02 days with maximum 𝛽- particle range of 2.4 mm in soft tissue compared to 177𝐿𝑢, which has shorter half-life of 6.7 days with maximum 𝛽- particle range of 2.1 mm in soft tissue. That give the advantage to 177𝐿𝑢 to be used beside that 131𝐼 can accumulate in the thyroid (Rahbar et al., 2018).
The efficacy of 177Lu-PSMA treatment is determined by evaluating the prostate specific antigen (PSA) levels, which should be lowered to baseline levels by week 8 after first cycle if the treatment works. Added to that, the amount of tumour spread should be reduced. Usual patient reported outcomes are improvement in pain relief, quality of life and health performance (Fendler et al., 2017).
The toxicity and side effects reported post 177Lu-PSMA therapy are usually considered as low grade such as, dry mouth, fatigue, nausea. Renal toxicity is not reported yet but can be a long-term complication that occurs. The most serious reported side effect is usually haematological toxicity for patient with skeletal metastases and haemoglobin or platelets reduction (Emmett et al., 2017).
In this study, 7.4 GBq of 177Lu-PSMA was administered to mCRPC patients. Treatment was given in 6 week intervals for a total of 4 to 6 cycles, depending on patient’s response and determined risks. SPECT/CT imaging was done after 4 and 24 hours to track the radiopharmaceutical distribution. Patients left the clinic after the treatment as the measured effective dose rates were low. Similar to values reported previously, such as 23 ± 6 µSv/h after 4 hours and 7 ± 2 µSv/h after 24 hours (Kratochwil et al., 2019).