System and method for determining the uncertainty in derived quantities

Abstract

A method and system for determining the value and associated uncertainty of time-cumulative quantities as part of a patient-specific dosimetry in radiopharmaceutical therapy (RPT), is described. The method comprising: obtaining a dataset comprising of one or more dosimetric quantity data values and associated uncertainties at one or more timepoints each representing a quantity of dosimetric interest associated with at least one radiopharmaceutical agent present within a volume of the patient; selecting a dosimetric quantity time representation curve (TRC) model comprised of one or more curves which contiguously span from the time of administration of the radiopharmaceutical; determining one or more parameters associated with at least one of the one or more curves comprising the selected TRC model where each of the one or more curves is directly calculated from the dosimetric quantity data values; determining from the one or more curves a mathematical function which directly relates the time cumulative quantity to the dosimetric quantity data values; calculating the cumulative dosimetric quantity data value using the mathematical function; calculating the uncertainty associated with the cumulative dosimetric quantity data value using the mathematical function by a method of propagation of uncertainty; and returning the cumulative dosimetric quantity data value and associated uncertainty as an output.

Description

[0001] MIR-2024-001WO 26-Sep-2025 Specification_Final System and method for determining the uncertainty in derived quantities Field of the Invention This invention relates to the field of radiopharmaceutical therapy. In particular, the calculation of uncertainty when deriving the cumulative activity or absorbed dose from time-activity curve or dose rate curve modelling when performing radiopharmaceutical therapy dosimetry, for example, based on medical images of a patient undergoing a cycle of molecular radiotherapy. The invention provides means by which the uncertainty in the derived quantities may be determined and statistically characterised to indicate the degree of precision in important quantities when performing clinical dosimetry. Background Radiopharmaceutical therapies (RPTs), including molecular radiotherapy and theranostics, involve the use of one or more radiopharmaceuticals (RPs) as therapeutic or diagnostic agents in the treatment of disease [1]. An RP, once administered, may propagate around the body to a target site, for instance preferentially binding to cancer cells, and delivering therapy by emitting radiation. In other cases, the RP may be administered to the target site directly. The RP may be excreted or remain in the body indefinitely until it has undergone radioactive decay to the point of being effectively stable. Radiation emitted by the RP may be detected by nuclear medicine sensors. At high doses, the radiation may deliver therapeutic levels of ionising energy into nearby tissues. The deposited energy within the patient per unit mass, referred to as absorbed dose, determines the treatment efficacy and any radiation safety considerations for the patient. Estimation of the absorbed dose delivered is known as dosimetry. Multiple sequential administrations, known as cycles, may be given to the patient over time as part of treatment. One or more cycles may involve dosimetric assessment as part of treatment planning or verification. Dosimetric assessment can be used as part of assessments of patient response to treatment. Dosimetric assessments ensure safety margins are not exceeded, and that treatment is both MIR-2024-001WO 26-Sep-2025 Specification_Final effective and worthwhile for the patient. Assessments may lead to adjustment of later cycles or to the cessation of treatment. To be able to make sound clinical decisions dosimetry must be accurate and reliable. One way to improve its accuracy is to make it patient specific. Patient-specific dosimetry favours measurements from the patient being treated over a one-size-fits- all population-based approach. This requires characterisation of the nuclear radioactivity with a quantity known to those skilled in the art as ‘activity’ (number of radioactive decays per unit time). Activity, present in the patient’s body is measured or otherwise determined at one or more sample times (timepoints) following RP administration. This may involve direct measurement of the activity or related quantity such as activity concentration, or a surrogate physical quantity from which activity may be inferred. The measurement approach may depend on the radioactive decay modes involved. The types of activity measurement performed may differ from one cycle to the next, using any combination of imaging or non-imaging detection of activity or an associated surrogate signal. Non-imaging measurements may be performed on a blood, urine or stool samples, or any other matter discharged or sampled from the body via a well counter or any similar device used for measuring activity. External sensors such as radiation dosimeters may be used to estimate the amount of activity in the patient. Imaging measurements may involve nuclear medicine imaging sensors such as those used in positron emission tomography (PET) or scintigraphy via planar or single photon emission computed tomography (SPECT). Such sensors are able to measure the amount of radioactivity in the scanned regions of the body and how it is spatially distributed within the body. Alternatively, or additionally, some RPs may be radiopaque, making them visible in X-ray or computed tomography (CT) imaging. Others may have useful magnetic properties which make their presence visible in magnetic resonance imaging (MRI) sequences. Imaging measurements are useful because they allow spatial localisation of the RP and possibly the associated activity within volumes of the body. Such volumes, among other examples, may be organs, sub-regions of organs, tissue regions, or volumes associated with treatment such as tumours and regions of microscopic disease. Other useful physical quantities, such as radiodensity, may also be MIR-2024-001WO 26-Sep-2025 Specification_Final localised by imaging. The advantage is that dose modelling is able to more accurately calculate how nuclear decays in highly active regions result in ionising energy deposited elsewhere. It also allows special attention to the absorbed dose delivered to regions of dosimetric interest, such as radiosensitive organs-at-risk or the clinically relevant regions being treated. In many clinical RPT workflows RPs are delivered in sufficiently high activities and with long enough half-lives that they remain detectable for days or weeks. Over this time, the distribution of RP may change due to biophysical processes. Multiple images may be acquired at different timepoints in the cycle to measure or otherwise determine how the activity changes with time since any changes in activity would need to be reflected in the dose modelling [1]. Alternatively, each activity measurement timepoint may be used to determine the rate at which energy is deposited to a region per unit mass, known to those skilled in the art as the absorbed dose rate. The absorbed dose rate may be determined at a plurality of timepoints to characterise how it changes with time. The relationship between RP concentration and time is not linear in general. Accurate measurement of the relationship is required for accurate dosimetry. However, due to demands on the clinic, such as imaging resources and patient throughput, and demands on the patient, such as distance travelled and tolerance to repeated long scans, only a small number of measurement images tend to be acquired. As such, imaging timepoints tend to be parsimoniously scheduled to measure this relationship as accurately as possible. For example, initial RP uptake tends to be rapid, requiring an image measurement soon after injection. Eventual radioactive decay and any biological removal of the RP must also be characterised, necessitating a late-acquired image timepoint. Other images may be acquired in-between to improve interpolation between these measurements and thus capture the nonlinear relationship. Further to this, concentration of RP outside of the measured time period must be extrapolated: from injection to the first timepoint, and from the last timepoint until the radionuclide(s) have effectively fully decayed. The post-extrapolation is particularly critical: Any calculations relying on this extrapolation are highly sensitive to the timing and MIR-2024-001WO 26-Sep-2025 Specification_Final accuracy of the final image, requiring a balance between acquiring as late as is practical while avoiding unacceptably low signal-to-noise measurements. Other means of measurement may be used to alleviate demand and supplement information available. For example, lower accuracy but more accessible imaging such as planar scintigraphy may be used. Additional non-imaging measurements may be used. Data from previous cycles or treatments may also be reused. Supplementary information not specific to the patient may also be used such as population-based data. The measurement schedule may vary with the cycle of treatment. For example, when treating metastatic castration-resistant prostate cancer with lutetium-177 prostate-specific membrane antigen (PSMA) the first cycle may consist of 4 SPECT- CT scans to assess how the patient’s body distributes the PSMA over time. Alternatively, a hybrid approach using a combination of 1 SPECT scan and 2 planar scintigraphy images may be used. Then, subsequent cycles may, for instance, acquire only 1 SPECT-CT scan and use it to calibrate and reuse the dosimetry from the first cycle. In another example, yttrium-90 microsphere trans-arterial radioembolisation of liver cancer may only require a single SPECT or PET scan since the spatial distribution of the RP does not generally change after administration. As is seen from these examples, further measurements and imaging combinations and acquisition timings may be used due to considerations such as the rate of RP uptake or washout in a clinically relevant organ for a given RP. In summary, the main factors that affect the ideal treatment and measurement schedule are the clinical indication and the RPT. However, variations may also arise for other reasons, including but not limited to clinical resources and practice, and the patient’s physiology and history. Once the change in RP (or its associated activity or related physical quantities) with time is characterised, dose modelling may be used to calculate the absorbed dose. Dose modelling is the process of calculating how the emitted energy propagates from its origin to be absorbed elsewhere. The cumulative activity due to radioactive decay of the radionuclide(s) associated with the RP is a key quantity for dose modelling. It indicates the total number of radioactive decays and therefore the total energy emitted. Dose modelling may alternatively be used to convert activity MIR-2024-001WO 26-Sep-2025 Specification_Final measurements into dose rate measurements. Dose rates may then be used to calculate the cumulative absorbed dose. The gold standard dose modelling method is Monte Carlo physics simulation. Monte Carlo simulations tend to be costly in terms of time and resources, so more approximate techniques may be used. One such method is the formalism introduced by the Medical Internal Radiation Dose (MIRD) committee, which models propagation of energy between emitting and absorbing regions in the body. Other methods may assume all energy is deposited locally (sometimes referred to as the local deposition method) or use image processing methods such as dose-kernel techniques. Machine learning methods, including deep learning, may also be used. The absorbed dose delivered by each cycle may then also be aggregated to a total cumulated absorbed dose over all cycles of the current treatment or other, prior exposures to ionising radiation. This may involve use of biological effective dose (BED) models, which incorporate information about how ionising radiation was absorbed, at what rate, and how cells may have since recovered. Summarising the resulting absorbed dose estimates to regions of clinical interest are a key endpoint for RPT dosimetry. Such summaries can take many forms, including image maps of absorbed dose (often overlaid on anatomical images), dose-volume histograms, tables of absorbed dose, or electronic information used for further processes such as BED calculations. Clinicians use absorbed dose summaries to make clinical decisions about the patient’s treatment. For example, clinicians may decide to adjust the amount of radiation administered in future cycles, either increasing the administered activity to improve the therapeutic effect or reducing it to stay below radiation safety limits. It is therefore critical to ensure that the uncertainty in the calculations is well characterised. Dosimetry calculations have a degree of inherent uncertainty due to noise on the measurements. The measurement noise propagates to any derived quantities. For example, SPECT scanner data are comprised of the number of photons detected. The number of counts in each detector is characterised by Poisson noise. The SPECT data are reconstructed to create a volumetric image comprised of greyscale voxel intensities. No two repeat scans of the same object will result in identical images: measurement noise propagates through the reconstruction process, MIR-2024-001WO 26-Sep-2025 Specification_Final resulting in different intensity values each time. Similar effects are present in other image and non-image measurements of the activity or surrogate signals from which the activity is inferred. Noise in activity measurements leads to uncertainty in the cumulative activity, directly affecting the dose calculation. Further to this, each activity measurement is only a static observation of a dynamic process and thus each measurement alone may be insufficient to characterise how activity changes over time (due to nuclear decay, RP propagation and interactions within the patient and excretion from the body such as in the urine). It is typical to mathematically model the activity present within a given region over the lifetime of the RP based on the activity measurements. Alternatively, the absorbed dose rate may be modelled over the lifetime of the RP. However, with the small number of measurements in RPT any time-based modelling can remain relatively uncertain. There is therefore a need to be able to characterise the uncertainty in the clinical dose calculation process in RPT workflows with personalised dosimetry, particularly with regards to cumulative activity or absorbed dose estimation based on one or more activity measurements of the patient. Any solution to this need must be able to work in the highly varied RPT context, including compatibility with different types of activity measurement and assuming a relatively small number of activity measurement timepoints per treatment cycle. A typical tool for modelling the patient-specific relationship between activity measurements and the cumulative activity is the time-activity curve (TAC), a graphical representation of the relationship between activity and time. Such a curve may be comprised of a single continuous curve, or a plurality of contiguous curves defined in a piecewise fashion. The TAC spans from the time of RP administration(e.g., injection), which defines the origin ^^ = 0, to the point where the activity is fullydecayed. This point is specifically at infinity, though effectively it is after a plurality of radioactive half-lives have occurred. For example, clinical levels of lutetium-177, with a half-life of 6.7 days, may be reasonably described as effectively decayed after 10 half-lives (67 days) by which point it has diminished to one thousandth of its initial activity and is effectively undetectable. This period may be shorter in practice due to biological processes such as excretion from the body. The appropriate curve is MIR-2024-001WO 26-Sep-2025 Specification_Final selected according to the activity measurements. The area under the curve, known to those skilled in the art as the time-integrated activity (TIA), then estimates the cumulative activity. A related tool is the dose-rate curve (DRC), which models the relationship between the absorbed dose rate and the total absorbed dose delivered. The total absorbed dose is the area under the DRC. Recent guidelines [2] emphasised the need for robust uncertainty calculations in patient-specific RPT dosimetry. The guidelines suggest a method for estimating TAC and TIA uncertainty using an asymptotic approximation of the covariance of parameters fitted by weighted least squares [2], which has limited applicability unless using at least 15 activity measurements and ideally more [3]. Similar or equivalent methods based on weighted least squares parameter covariance matrices are common in other key literature addressing uncertainty and TAC modelling in the RPT and molecular radiotherapy field [4, 5]. Reference [5] Describes the current state-of- the-art in RPC dosimetry and is based upon the application of statistical techniques suitable for well posed “best fit” nonlinear curve fitting problems. This is done using approaches such as least squares optimization. The method of this reference relies upon assumptions such as large-N, linearisation, and Gaussian distribution statistical properties. The relationship between the input data points and the resulting curve fit, and the communitive quantity and its associated uncertainty, ends up being an indirect relationship that cannot be expressed in a closed mathematical form. More broadly, uncertainty analysis is often explored in the field of pharmacokinetics in the context of uncertainty across patients at a population level, rather than uncertainty in individual patients as in clinical RPT dosimetry [6]. In an example, a computer implemented method for determining the value and associated uncertainty of time-cumulative quantities as part of a patient-specific dosimetry in radiopharmaceutical therapy (RPT), is provided, the method comprising the steps of: obtaining a dataset comprising of one or more dosimetric quantity data values and associated uncertainties at one or more timepoints each representing a quantity of dosimetric interest associated with at least one radiopharmaceutical agent present within a volume of the patient; selecting a dosimetric quantity time representation curve (TRC) model comprised of one or more curves which contiguously span from the time of administration of the radiopharmaceutical; MIR-2024-001WO 26-Sep-2025 Specification_Final determining one or more parameters associated with at least one of the one or more curves comprising the selected TRC model where each of the one or more curves is directly calculated from the dosimetric quantity data values; determining from the one or more curves a mathematical function which directly relates the time cumulative quantity to the dosimetric quantity data values; calculating the cumulative dosimetric quantity data value using the mathematical function; calculating the uncertainty associated with the cumulative dosimetric quantity data value using the mathematical function by a method of propagation of uncertainty; and returning the cumulative dosimetric quantity data value and associated uncertainty as an output; using the output of the cumulative dosimetric quantity data value and associated uncertainty in at least one of: the planning, adjustment, or assessment of dosimetry data for future radiopharmaceutical therapy, or the planning, adjustment or assessment of future radiotherapy dosages, for one or more patients.. In a preferred embodiment, the one or more patients comprises at least one of: the patient of the patient specific dosimetry RPT, one or more different patients. Preferably, the dosimetric quantity is activity, and the one or more curves comprising the TRC model is a time-activity curve utilised to determine cumulative activity. In an alternative embodiment, the dosimetric quantity is absorbed dose rate and the one or more curves comprising the TRC model is a dose rate curve utilised to determine absorbed dose. Preferably, the dosimetric quantity data value relates to radioactivity present in a patient volume. In an example, the mathematical function is an integrated function, determined analytically or numerically, in order to perform propagation of uncertainty. Preferably, the propagation of uncertainty is by means of a statistical method utilising the dosimetric quantity data values and associated uncertainties and the associated mathematical function. Further preferably the statistical method is a Taylor series expansion which approximates one or more statistical moments of the time cumulative quantity MIR-2024-001WO 26-Sep-2025 Specification_Final In an embodiment of the invention, the TRC model comprises one or more curves. Preferably, the one or more curves comprising the TRC model span from the time of radiopharmaceutical administration to the time at which all radioactivity is taken to be effectively decayed in a contiguous fashion. In an example, at least one of the curves comprised by the TRC are nonlinearly related to the associated dosimetric quantity data values. Preferably. the TRC model is assessed for quality and utilized to adjust inclusion of dosimetric quantity data values or the curves which are comprised by the TRC. In an example, the volume is one or more of: a volume within the patient comprising: parts of the body, organs, sub-regions within organs, tissues, lesions, tumours, sites of microscopic disease; or a volume based on biological material; or the volume represents abstract fractional quantities including metabolic compartments of materials associated with metabolization of the radiopharmaceutical agent. Preferably, at least one dosimetric quantity data value is derived from measurements using at least one of nuclear medicine sensors; medical imaging techniques, well counter sensors and dosimeter sensors. Further preferably, the uncertainty for the dosimetric quantity data value is derived from measurements using at least one of: nuclear medicine sensors, medical imaging techniques, well counter sensors and dosimeter sensors. Preferably, the nuclear medicine sensors comprise one or more of: positron emission tomography (PET), single photon emission computed tomography (SPECT), planar scintigraphy, or dosimeter sensors. In an example, at least one dosimetric quantity data value is derived using surrogate quantities measured using other medical imaging sensors. Preferably, the associated uncertainty for the patient treatment data value is derived from measurements using surrogate quantities measured using other medical MIR-2024-001WO 26-Sep-2025 Specification_Final imaging sensors. In an example. other medical imaging sensors include one or more of: computed tomography (CT) and magnetic resonance imaging (MRI) sensors. Preferably, at least one dosimetric quantity data value is retrieved from the patient’s historical data. Further preferably, the associated uncertainty for the dosimetric quantity data value is derived from at least one of: the patient’s historical data, prior data. In an example, at least one of the dosimetric quantity data values and associated uncertainties are assessed for quality and excluded from further processing to be part of the output when they do not meet a quality threshold. Preferably, the quality assessment involves comparison of the dosimetric quantity data values and / or associated uncertainties to at least one of: biological constraints, physical constraints, the patient’s historical data, patient population data, other TRC model candidates for the volume. In an example, the comparison for the quality assessment of at least one of: the patient treatment data values and the associated uncertainty is performed by an operator or automated process. Preferably, determination of the uncertainty associated with the time cumulative quantities comprises at least one of: physical half-life of any radionuclides, derived quantities which preclude determination of one or more dosimetric quantity values, or other intermediate quantities such as mathematical parameters of any curves which are comprised by the TRC. In an example, there is provided a system for determining the value and uncertainty in patient treatment data as part of a patient-specific dosimetry in radiopharmaceutical therapy (RPT), comprising: a database for storing patient data, a display for displaying information; a processor configured to perform the following steps: obtaining a dataset from the database comprising of one or more dosimetric quantity data values and associated uncertainties at one or more timepoints each representing a quantity of dosimetric interest associated with at least one MIR-2024-001WO 26-Sep-2025 Specification_Final radiopharmaceutical agent present within a volume of the patient; selecting a dosimetric quantity time representation curve (TRC) model comprised of one or more curves which contiguously span from the time of administration of the radiopharmaceutical; determining one or more parameters associated with at least one of the one or more curves comprising the selected TRC model where each of the one or more curves is directly calculated from the dosimetric quantity data values; determining from the one or more curves a mathematical function which directly relates the time cumulative quantity to the dosimetric quantity data values; calculating the cumulative dosimetric quantity data value using the mathematical function; calculating the uncertainty associated with the cumulative dosimetric quantity data value using the mathematical function by a method of propagation of uncertainty; and returning the cumulative dosimetric quantity value and associated uncertainty as an output, to be displayed on the display, wherein the output of the cumulative dosimetric quantity data value and associated uncertainty is used in at least one of: the planning, adjustment, or assessment of dosimetry data for future radiopharmaceutical therapy, or the planning, adjustment or assessment of future radiotherapy dosages, for one or more patients. Brief Description of the Drawings Further details, aspects and embodiments of the invention will be described, by way of example only, with reference to the drawings. In the drawings, like reference numbers are used to identify like or functionally similar elements. Elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. Figure 1A illustrates key principles in biophysical processes Figure 1B illustrates distribution of radioactivity in the body after radiopharmaceutical administration with an example time-activity curve Figure 2 is a flow chart showing the method according to an embodiment of the invention Figure 3 is a flow chart showing the method according to an alternative embodiment of the invention MIR-2024-001WO 26-Sep-2025 Specification_Final Figure 4A indicates how activity data samples may be collected and standardised for use in an embodiment of the invention Figure 4B illustrates how activity values and associated uncertainties may be visualised Figure 5 indicates other data which may be used as prior information when performing embodiments of the invention Figure 6 illustrates a display which may be used by an operator to perform the methods in an embodiment of the invention Figure 7 shows a simplified illustration of how a radiopharmaceutical may propagate through a patient’s body during treatment, indicating how the activity within various regions of the body varies with time Figure 8 illustrates a simplified typical workflow when calculating absorbed dose in personalised radiopharmaceutical therapy dosimetry Figure 9 illustrates a simplified flow chart for the flow of data and derived quantities in a typical dosimetry workflow Figure 10 illustrates how deriving a quantity by nonlinear transformation of a noisy measurement affects the statistical properties of the derived quantity, and how the statistical properties of the derived quantity may be approximated using Taylor’s theorem Figure 11 exemplifies TAC models which may be used in embodiments of the invention described in Figure 1 whereby the TAC is comprised of one or more curves Figure 12 illustrates key concepts in a worked example of how the method may be applied to TAC comprised of a single curve Figure 13 illustrates key concepts in a worked example of how the method may be applied to a TAC comprised of a plurality of curves arranged in a contiguous fashion Figure 14 illustrates a simplified block diagram of an example of a system arranged to perform the methods for determining the value and associated uncertainty of time cumulative quantities as part of patient specific dosimetry MIR-2024-001WO 26-Sep-2025 Specification_Final Detailed Description The present invention is a computer implemented method which calculates the uncertainty in the cumulated activity or cumulative absorbed dose rate which arises due to noise in measurements of activity, or closely related quantities such as activity concentration, and noise or uncertainty in other factors such as surrogate quantities, undertaken for the purpose of clinical patient-specific dosimetry in RPT workflows. This invention has the use of explicit, direct relationships between the input data points and the parameters and commutative quantities to provide a more robust statistical groundwork for calculating the quantities of interest. This methodology allows the use of theoretical statistical analysis of probability distributions and how they non linearly transformed to determine any statistical measures required to characterise the outputs, including measures of central tendency to obtain the value of a quantity and measures of dispersion to quantify the associated uncertainty. Referring now to Figure 1, which illustrates key principles in biophysical processes following radiopharmaceutical administration and associated radioactivity. On administration to the body, RPs may propagate from the point of origin to elsewhere due to biophysical processes. A number of such processes may occur in sequence or in parallel according to the biophysical properties of the RP and the biology of the patient to which it is administered. A simplified example is shown in Figure 1A whereby a liver 101 is fed by blood vessels 102 along which an RP propagates such that the RP perfuses into the organ via its vessels 103. The arrow 104 indicates the biophysical process direction whereby RP accumulates within the liver, known to those in the art as uptake. Conversely the arrow 105 indicates the biophysical process direction along which the quantity of RP in the liver declines, known to those in the art as washout. In the example, further uptake processes occur, including diffusion of the RP between the organ capillaries and intercellular fluid 106 and, at the cellular level (for instance), binding and unbinding of the RP to receptors on the surfaces of some types of cell 107. Washout processes occur in the equivalent reverse senses of each of 102, 103, 106, and 107, with, in this example, the RP returning to the blood where it may be taken up elsewhere or excreted. MIR-2024-001WO 26-Sep-2025 Specification_Final Uptake and washout processes work against each other and may occur at multiple sites in the body. Each uptake and washout process may occur at a different rate, influencing the concentration and distribution of the RP within organs and tissues over time. In some examples uptake and washout processes may not occur at all, resulting in the RP accumulating permanently within a tissue by irreversibly binding to the cell in 107, or only remaining within the blood vessels 103 but not diffusing into tissues 106. In some cases, the RP may be altered by biological or physical processes. This may result in a plurality of radioactive agents, such as metabolites and free daughter nuclei, being present in the body derived from the original RP. Each type of agent will have its own corresponding pathways of uptake and washout within the body and will differ in general. All of the processes and agents described affect the concentration and spatial distribution of the RP and any derived radioactive agents across the body. All such agents are radioactive such that they emit ionising radiation. The degree of radiation emitted from a volume within the body (either at the cellular, tissue, organ, or systemic level, or otherwise) is a direct consequence of the amount of radioactive material present in the volume. Figure 1B builds on Figure 1A and shows images (i)-(iv), obtained at different time points, as well as a graph (v) of activity vs time since administration of the RP to the patient. The activity decays with time and the area under the curve is the total decay in the patient volume. Shown in image (i) is an example depicting a coronal cross-section of the thorax and abdomen at the first timepoint t1, indicating the body 108, liver 109, spleen 110, left 111 and right 112 kidneys, bladder 113, in addition to a tumour 114 targeted by the RP for treatment. The brightness of each depicted volume indicates the degree of radioactivity as a consequence of the concentration of radioactive material present in the volume, whereby black indicates no radioactivity per unit volume (as exemplified by the region outside the body 115 and empty bladder 113) and white indicates a high degree of radioactivity per unit volume. Since, in this example, the RP is designed to maximally target the tumour 114, it is depicted brightest. Due to the biological properties of the RP, other organs have inadvertently accumulated some MIR-2024-001WO 26-Sep-2025 Specification_Final RP to varying concentrations too, with liver 109 accumulating the most, and the kidneys 111-112 only a little. The concentration of RP and derived agents varies with time due to uptake and washout processes. In this example, a second, third, and fourth cross-section of the same body at later treatment timepoints. The direction of time is indicated by the arrow 116. The timing of each image (i)-(iv) is indicated upon the time arrow 116 at their corresponding timepoints, t1-t4respectively. In the second cross-section (ii) at time t2it can be seen that the amount of radioactivity present in the body 117 in general has dropped. The reduction in radioactivity will be in part due to radioactive decay. Decumulation may also occur due to excretion, for example, as indicated by the now-bright bladder 118. Radioactivity may also diminish in some volumes and not others, due to longer retention in some tissues, or continued uptake of the RP from the body by organs and tissues such as the liver 119 and tumour 120, thereby effectively removing it from the body volume 117. Some volumes, such as the tumour 120, may continue to take up the RP such that the concentration is continues to increase after it has stopped increasing elsewhere. Other volumes may have already started to remove RP faster than taking it up, resulting in a drop in RP concentration in the region. The third (iii) and fourth (iv) cross-sections show the third and fourth later timepoints t3 and t4 respectively at which the total degree of radiation has dropped even further in the body 121, including excretion from the bladder 122 (and thereby the body entirely). All healthy tissues have continued to remove radioactive material from their tissues, resulting in lower concentrations. The tumour 123 too, in this example, has started to exhibit a lower degree of radioactivity. However, since it has retained a higher RP concentration than elsewhere it is now relatively much brighter than the surrounding body. The tissues of the body may continue to process the radioactive materials in this way such that the concentration of radioactive agents continues to decrease. Furthermore, radioactive decay of the radioactive material guarantees the reduction in radioactivity overall with time, until eventually all ionising energy has been emitted. The graph (v) shows the total degree of radioactivity present in the right kidney over the time period covered by this example. The axes 124 indicate the time since MIR-2024-001WO 26-Sep-2025 Specification_Final administration as the independent variable and the activity as the dependent variable. The curve 125 indicates the change in activity over time and the markers 126 indicate the images (i)-(iv) at their corresponding timepoints. The curve starts at 0 at the point of RP administration t0, increasing in the right kidney as it uptakes radioactive material. Washout, excretion, and radioactive decay processes then lead to a reduction in activity with time, such that the curve would eventually decay to 0 (not shown). Since activity is a rate, i.e., decays per unit time, the area under the curve indicates the total number of decays that occur between the administration time t0 and the point at which the curve would decay to 0, as indicated by the annotation arrow 127. While the processes described take place, energy in the form of ionising radiation is emitted from the decaying nuclei and absorbed into the surroundings. The ionising effect of the radiation has an adverse biological effect on cells, causing harm to healthy tissues such as the liver 109 and possibly therapeutic effects to malignant tissues such as the tumour 114. The energy delivered per unit mass is known to those in the art as absorbed dose, a physical quantity related to the resulting harm on cells and tissues. Another key aspect of the ionising radiation is that it travels a distance, depending upon the physical properties of the emitting nuclide, the type(s) of radiation, and the surrounding materials. Consequentially radioactivity in one volume of the body may lead to absorption of ionising energy within that volume, but also other volumes within the patient or elsewhere. Therefore, to identify the absorbed dose delivered to a volume of interest, such as the tumour 114 when assessing chance of treatment success or the liver 109 when assessing the chance of treatment harm and associated complication, the radioactivity present in all other volumes of the body must be considered, since the radiation emitted there may contribute. Clinical workflows such as dosimetry involve measurement of radioactivity (either directly or by indirectly using properties of the associated RP) and thereby the resulting absorbed dose. Some workflows may measure the rate of radioactive decay (activity) to determine the total number of decays (cumulative activity) in each radioactive (source) volume and thereby the total energy emitted. Such workflows then may use absorbed dose models to calculate the resulting absorbed dose delivered to each target volume. Volumes of the body may be source or target MIR-2024-001WO 26-Sep-2025 Specification_Final volumes, or both. Other workflows may instead measure the activity in source volumes and use absorbed dose models to calculate the rate of absorbed dose delivery to target volumes. Since activity changes with time at different rates in each source volume in general, the absorbed dose rates will also vary with time. Such workflows may then determine the absorbed dose delivered to each target volume by cumulation of the volume’s associated absorbed dose rate. Referring now to Figure 2, which shows an illustrated simplified block diagram of an example method for determining the value and uncertainty of the cumulative activity for a patient undergoing a cycle of RPT in an embodiment of this invention. In an example, a computer implemented method for determining the value and associated uncertainty of time-cumulative quantities as part of a patient-specific dosimetry in radiopharmaceutical therapy (RPT), is described comprising one or more steps as outlined below. A set comprised of one or more activity values and associated uncertainties at one or more timepoints (hereby activity data samples) 201 are retrieved from a database 202 or other electronic transmission. Preferably, a dataset comprising of one or more dosimetric quantity data values and associated uncertainties at one or more timepoints each representing a quantity of dosimetric interest associated with at least one radiopharmaceutical agent present within a volume of the patient is obtained. In an example, at least one dosimetric quantity data value is derived from measurements using at least one of nuclear medicine sensors; medical imaging techniques, well counter sensors and dosimeter sensors. Further preferably, the uncertainty for the dosimetric quantity data value is derived from measurements using at least one of: nuclear medicine sensors, medical imaging techniques, well counter sensors and dosimeter sensors. In an example, the nuclear medicine sensors comprise one or more of: positron emission tomography (PET), single photon emission computed tomography (SPECT), planar scintigraphy, or dosimeter sensors. Preferably, at least one dosimetric quantity data value is derived using surrogate quantities measured using other medical imaging sensors. Further preferably, the associated uncertainty for the patient treatment data value is derived from measurements using surrogate quantities measured using other medical imaging MIR-2024-001WO 26-Sep-2025 Specification_Final sensors. In an example, other medical imaging sensors include one or more of: computed tomography (CT) and magnetic resonance imaging (MRI) sensors. Each value of the dataset may represent, for example, the activity present in a volume of interest (VOI) within the patient's body. Such VOIs may represent the whole body, groups of organs, single organs, sub-regions within organs, tissues or groups of tissues, or other such anatomically- or functionally defined volumes, areas, surfaces, or points in or on the body, including clinically relevant regions such as lesions, tumours, or sites of microscopic disease. Preferably, the volume is one or more of: a volume within the patient comprising: parts of the body, organs, sub- regions within organs, tissues, lesions, tumours, sites of microscopic disease; or a volume based on biological material; or the volume represents abstract fractional quantities including metabolic compartments of materials associated with metabolization of the radiopharmaceutical agent. The VOI may instead represent or be associated with a more abstract volume, such as the blood within the body, a specific material, tissue, or cell type, or metabolic compartments of materials related to underlying biological processes. These examples are not exhaustive; any other such representations associated with activity data may also be used. Each activity value, and optionally its associated uncertainty, may be determined using one or more associated 2D or 3D activity maps, which may be derived from medical images. In some embodiments 1D activity measurements may be used, such as from a whole-body dosimeter. Activity data may also be derived from previous treatment cycles for the patient or population averages. Further examples are provided in Figure 4. In some embodiments the activity data samples undergo quality assurance 203 to assess whether any outliers are present. Preferably, at least one of the dosimetric quantity data values and associated uncertainties are assessed for quality and excluded from further processing to be part of the output when they do not meet a quality threshold. In an example, the quality assessment involves comparison of the dosimetric quantity data values and / or associated uncertainties to at least one of: biological constraints, physical constraints, the patient’s historical data, patient population data, other TRC model candidates for the volume. Further preferably, the MIR-2024-001WO 26-Sep-2025 Specification_Final comparison for the quality assessment of at least one of: the patient treatment data values and the associated uncertainty is performed by an operator or automated process. Outliers may be identified as clearly implausible or unphysical values such as negative activity measurements. They may instead be identified according to the historical data or prior data based on knowledge of the RP, or other such constraints. Such outliers may be determined by an operator or by some automated process. In step 204 a TAC model is selected. The TAC serves as an estimation of the relationship between activity and time from the time of RP administration (hereby the origin) to a time by which all activity is assumed to have effectively decayed to zero (hereby infinity), which may be comprised of a single continuous curve such as a decaying monoexponential or biexponential, or a plurality of curves arranged in a contiguous piecewise fashion, such as a combination of lines and monoexponentials. In an embodiment, a dosimetric quantity time representation curve (TRC) model comprised of one or more curves which contiguously span from the time of administration of the radiopharmaceutical is selected. Selection of each curve 204 may involve the activity data samples from step 201 or, of quality assurance has taken place, step 203. Selection may involve use of historical data. In other embodiments, curve selection may be based on default settings, which may be dependent upon the RP, time placement of the activity data samples, VOI being modelled, and other such considerations. The selection may be performed by an operator according to the above or based on visual feedback. The selection may instead be performed by some automated process. In step 205, the shape and placement of the curve or curves which constitute the TAC are determined. The shape and placement of each curve is controlled according to its parameters, which are directly and explicitly calculated from the activity values. That is, there is a direct relationship between the activity and the curve parameters, and this is used to calculate the curve. This direct relationship may be applied analytically. Preferably, one or more parameters associated with at least one of the one or more curves comprising the selected TRC model are determined, where each of the one or more curves is directly calculated from the dosimetric quantity data values. Preferably, the TRC model comprises one or more curves. Further preferably, the one or more curves comprising the TRC model span MIR-2024-001WO 26-Sep-2025 Specification_Final from the time of radiopharmaceutical administration to the time at which all radioactivity is taken to be effectively decayed in a contiguous fashion. Preferably, at least one of the curves comprised by the TRC are nonlinearly related to the associated dosimetric quantity data values. In an embodiment, the TRC model is assessed for quality and utilized to adjust inclusion of dosimetric quantity data values or the curves which are comprised by the TRC. In some embodiments, the TAC determined in step 205 is assessed for quality 206. This may involve visual inspection, comparison to the patient’s historical data, prior data from a patient population (e.g., retrieved from the database 202), goodness-of- fit criteria or other measures such as uncertainty in the determined curve parameters, biophysical constraints, or some other means of assessing whether the TAC is appropriate for the intended use, such as calculating the cumulative activity or absorbed dose within the VOI, or some other use-case. In an example, the quality assessment involves comparison of the dosimetric quantity data values and / or associated uncertainties to at least one of: biological constraints, physical constraints, the patient’s historical data, patient population data, other TRC model candidates for the volume. Further preferably, the comparison for the quality assessment of at least one of: the patient treatment data values and the associated uncertainty is performed by an operator or automated process. A decision is made according to the quality assurance 207. If the TAC is considered unacceptable 208 then previous steps may be repeated. For example, an operator may decide that including or excluding other activity data samples may yield a better result, and so return to step 203. Alternatively, or additionally, any of the curve(s) used to construct the TAC model may be altered, adjusted, redefined, or replaced by returning to step 204. For example, extrapolating the tail of the TAC with a monoexponential fitted to the final two activity values may yield growing exponential, a non-physical result. This may then be addressed by instead using a monoexponential which decays according to the physical half-life of the radionuclide, guaranteed to give a calculable result. Steps 203-207 are then repeated as needed, possibly comparing to previous results to assist with decision making, until an acceptable TAC is obtained 209. In step 210 the determined and, optionally, quality assured TAC is used to estimate the cumulative activity emitted within the associated VOI. Preferably, a mathematical function which directly relates the time cumulative quantity to the dosimetric quantity MIR-2024-001WO 26-Sep-2025 Specification_Final data values is determined from the one or more curves. Further preferably, the cumulative dosimetric quantity data value is calculated using the mathematical function. In an embodiment, the uncertainty associated with the cumulative dosimetric quantity data value is calculated using the mathematical function by a method of propagation of uncertainty The cumulative activity emitted within the associated VOI is calculated by assessing the area under the TAC. If the TAC is piecewise, then the area under each curve is calculated and summed to yield the total cumulative activity. Preferably, the mathematical function is an integrated function, determined analytically or numerically, in order to perform propagation of uncertainty. Since each curve can be directly calculated from the activity data then one example method to calculate the total cumulative activity is to determine an integrated function to directly relate the total cumulative activity to the activity data. Preferably, the mathematical function is an integrated function, determined analytically or numerically, in order to perform propagation of uncertainty. Further preferably, the propagation of uncertainty is by means of a statistical method utilising the dosimetric quantity data values and associated uncertainties and the associated mathematical function. In a preferred embodiment, the statistical method is a Taylor series expansion which approximates one or more statistical moments of the time cumulative quantity. The uncertainty associated with the cumulative activity value is also calculated. This is based on the uncertainties associated with the activity values used to determine the curve(s) and, in an example, the mathematical function which directly relates the total cumulative activity to the activity data, using an uncertainty propagation method. Uncertainty in other quantities (e.g., physical constants such as the half-life of the radionuclide), or intermediate derived quantities (e.g., the curve parameters) may also be used. If the TAC is piecewise the uncertainty of each curve may be calculated and combined using statistical techniques, for example, by considering covariance between the curves. Preferably, determination of the uncertainty associated with the time cumulative quantities comprises at least one of: physical half-life of any radionuclides, derived quantities which preclude determination of one or more dosimetric quantity values, or other intermediate quantities such as mathematical parameters of any curves which are comprised by the TRC. MIR-2024-001WO 26-Sep-2025 Specification_Final In an embodiment, the cumulative dosimetric quantity data value and associated uncertainty as an output. The cumulative activity value and associated uncertainty are returned as an output of the system 211. A further step comprises using the output of the cumulative dosimetric quantity data value and associated uncertainty in at least one of: the planning, adjustment, or assessment of dosimetry data for future radiopharmaceutical therapy, or the planning, adjustment or assessment of future radiotherapy dosages, for one or more patients. Examples of how the output of the cumulative dosimetric quantity data value and associated uncertainty may be used are as follows: A calculated dose for a sensitive organ, such as the kidney, may be higher than desired. For future cycles of treatment the cumulative dosimetric quantity data value and associated uncertainty as determined above could be used to lower the administered activity in order to bring the total dose to the kidney within acceptable limits. In this case, the data is used for future treatment of the same patient, but it may also be used for the treatment of ther patients. In a multi-modality treatment regime the radiopharmaceutical therapy could be followed by some external beam radiotherapy. In that case the cumulative dosimetric quantity data value and associated uncertainty as determined above to the tumour lesions and the healthy organs could be used to plan the external beam radiotherapy so that the total combined dose to tumour or healthy organs meets requirements (sufficiently high for lesions or sufficiently low for healthy organs). Typically, this regime will be for the original patient, but in some cases, it may be used to adjust treatment for other patients. In a clinical trial for a radiopharmaceutical treatment. Cumulative dosimetric quantity data value and associated uncertainty as determined above can be calculated for a range of organs and lesions for a cohort of patients. This can be used to determine the relationship between dose and various outcomes. For example dose to the parotid gland might correlate with patients experiencing xerostomia (dry mouth due to lack of saliva production). This information can be used to inform future doses and ensure patients receive correct information about side effects to treatment. In this case, the patients in the clinical trial may or may not include the original patient who provided the initial dosimetry data. MIR-2024-001WO 26-Sep-2025 Specification_Final In some embodiments other outputs may also be included associated with the process, such as goodness-of-fit measures used to perform quality assurance on the determined TAC. In some embodiments the process described by steps 201-211 may be applied to activity data samples for a plurality of VOIs sequentially or in parallel. Alternatively, or in addition, some embodiments may also apply the process described by steps 201-211 to a plurality of RPT cycles used to treat the patient. The process may involve comparisons and relationships between the VOIs and cycles to assist with quality assurance steps 203 & 206, model selection 204, TAC determination 205, and cumulative activity uncertainty calculation 210. Each step may be applied differently for each VOI or cycle. Processing within each VOI or cycle may influence other VOIs or cycles. In other embodiments, or in addition, steps 201-211 may be repeated to obtain a plurality of TAC models and associated outputs for comparison, in which case selection of the best model is performed at the end of the process (not shown), whereby such selection may be determined by the operator, an algorithm, or some other automated process. Once all such combinations of comparisons have been completed, the process ends. The resulting cumulative activity values and associated uncertainties are then stored locally or remotely or transmitted for further processing such as absorbed dose calculations. In a preferred embodiment, the dosimetric quantity is activity, and the one or more curves comprising the TRC model is a time-activity curve utilised to determine cumulative activity. Referring now to Figure 3, which shows an illustrated simplified block diagram of an example method for determining the value and uncertainty of the absorbed dose for a patient undergoing a cycle of RPT in an embodiment of this invention. In an example, a computer implemented method for determining the value and associated uncertainty of time-cumulative quantities as part of a patient-specific dosimetry in radiopharmaceutical therapy (RPT), is described comprising one or more steps as outlined below. In this embodiment, the dosimetric quantity is absorbed dose rate and the one or more curves comprising the TRC model is a dose rate curve utilised to determine absorbed dose MIR-2024-001WO 26-Sep-2025 Specification_Final A set comprised of one or more dose rate values and associated uncertainties at one or more timepoints (hereby dose rate data samples) 301 are retrieved from a database 302 or other electronic transmission. Preferably, a dataset comprising of one or more dosimetric quantity data values and associated uncertainties at one or more timepoints each representing a quantity of dosimetric interest associated with at least one radiopharmaceutical agent present within a volume of the patient is obtained. Preferably, a dataset comprising of one or more dosimetric quantity data values and associated uncertainties at one or more timepoints each representing a quantity of dosimetric interest associated with at least one radiopharmaceutical agent present within a volume of the patient is obtained. In an example, at least one dosimetric quantity data value is derived from measurements using at least one of nuclear medicine sensors; medical imaging techniques, well counter sensors and dosimeter sensors. Further preferably, the uncertainty for the dosimetric quantity data value is derived from measurements using at least one of: nuclear medicine sensors, medical imaging techniques, well counter sensors and dosimeter sensors. In an example, the nuclear medicine sensors comprise one or more of: positron emission tomography (PET), single photon emission computed tomography (SPECT), planar scintigraphy, or dosimeter sensors. Preferably, at least one dosimetric quantity data value is derived using surrogate quantities measured using other medical imaging sensors. Further preferably, the associated uncertainty for the patient treatment data value is derived from measurements using surrogate quantities measured using other medical imaging sensors. In an example, other medical imaging sensors include one or more of: computed tomography (CT) and magnetic resonance imaging (MRI) sensors. Each value in the dataset may represent, for example, the absorbed dose rate delivered to a volume of interest (VOI) within the patient's body, as described in Figure 2. Preferably, the volume is one or more of: a volume within the patient comprising: parts of the body, organs, sub-regions within organs, tissues, lesions, tumours, sites of microscopic disease; or a volume based on biological material; or the volume represents abstract fractional quantities including metabolic MIR-2024-001WO 26-Sep-2025 Specification_Final compartments of materials associated with metabolization of the radiopharmaceutical agent. Each dose rate value, and optionally its associated uncertainty, may be determined using one or more associated 2D or 3D dose rate maps, which may be derived from activity maps (as described in Figure 4). In some embodiments 1D dose rate measurements may be used, such as from a whole-body dosimeter. Dose rate data may also be derived from previous treatment cycles for the patient or population averages. In some embodiments the dose rate data samples undergo quality assurance 303 to assess whether any outliers are present. Preferably, at least one of the dosimetric quantity data values and associated uncertainties are assessed for quality and excluded from further processing to be part of the output when they do not meet a quality threshold. In an example, the quality assessment involves comparison of the dosimetric quantity data values and / or associated uncertainties to at least one of: biological constraints, physical constraints, the patient’s historical data, patient population data, other TRC model candidates for the volume. Further preferably, the comparison for the quality assessment of at least one of: the patient treatment data values and the associated uncertainty is performed by an operator or automated process. Outliers may be identified as clearly implausible or unphysical values such as negative dose rate measurements. They may instead be identified according to the historical data or prior data based on knowledge of the RP, or other such constraints. Such outliers may be determined by an operator or by some automated process. In step 304 a DRC model is selected. The DRC serves as an estimation of the relationship between dose rate and time from the time of RP administration (hereby the origin) to a time by which all activity is assumed to have effectively decayed to zero (hereby infinity), which may be comprised of a single continuous curve such as a decaying monoexponential or biexponential, or a plurality of curves arranged in a contiguous piecewise fashion, such as a combination of lines and monoexponentials. In an embodiment, a dosimetric quantity time representation curve (TRC) model comprised of one or more curves which contiguously span from the time of administration of the radiopharmaceutical is selected. MIR-2024-001WO 26-Sep-2025 Specification_Final Selection of each curve 304 may involve the dose rate data samples from step 301 or, of quality assurance has taken place, step 303. Selection may involve use of historical data. In other embodiments, curve selection may be based on default settings, which may be dependent upon the RP, time placement of the dose rate data samples, VOI being modelled, and other such considerations. The selection may be performed by an operator according to the above or based on visual feedback. The selection may instead be performed by some automated process. In step 305, the shape and placement of the curve or curves which constitute the DRC are determined. The shape and placement of each curve is controlled according to its parameters, which are directly calculated from the dose rate values. Preferably, one or more parameters associated with at least one of the one or more curves comprising the selected TRC model are determined, where each of the one or more curves is directly calculated from the dosimetric quantity data values. Preferably, the TRC model comprises one or more curves. Further preferably, the one or more curves comprising the TRC model span from the time of radiopharmaceutical administration to the time at which all radioactivity is taken to be effectively decayed in a contiguous fashion. Preferably, at least one of the curves comprised by the TRC are nonlinearly related to the associated dosimetric quantity data values. In an embodiment, the TRC model is assessed for quality and utilized to adjust inclusion of dosimetric quantity data values or the curves which are comprised by the TRC. Preferably, one or more parameters associated with at least one of the one or more curves comprising the selected TRC model are determined, where each of the one or more curves is directly calculated from the dosimetric quantity data values. In some embodiments, the DRC determined in step 305 is assessed for quality 306. In an example, the quality assessment involves comparison of the dosimetric quantity data values and / or associated uncertainties to at least one of: biological constraints, physical constraints, the patient’s historical data, patient population data, other TRC model candidates for the volume. Further preferably, the comparison for the quality assessment of at least one of: the patient treatment data values and the MIR-2024-001WO 26-Sep-2025 Specification_Final associated uncertainty is performed by an operator or automated process. This may involve visual inspection, comparison to the patient’s historical data, prior data from a patient population (e.g., retrieved from the database 302), goodness-of-fit criteria or other measures such as uncertainty in the determined curve parameters, biophysical constraints, or some other means of assessing whether the DRC is appropriate for the intended use. A decision is made according to the quality assurance 307. If the DRC is considered unacceptable 308 then previous steps may be repeated. For example, an operator may decide that including or excluding other dose rate data samples may yield a better result, and so return to step 303. Alternatively, or additionally, any of the curve(s) used to construct the DRC model may be altered, adjusted, redefined, or replaced by returning to step 304. For example, extrapolating the tail of the DRC with a monoexponential fitted to the final two dose rate values may yield growing exponential, a non-physical result. This may then be addressed by instead using a monoexponential which decays according to the physical half-life of the radionuclide, guaranteed to give a calculable result. Steps 303-307 are then repeated as needed, possibly comparing to previous results to assist with decision making, until an acceptable DRC is obtained 309. In step 310 the determined and, optionally, quality assured DRC is used to estimate the absorbed dose delivered to the associated VOI. Preferably, a mathematical function which directly relates the time cumulative quantity to the dosimetric quantity data values is determined from the one or more curves. Further preferably, the cumulative dosimetric quantity data value is calculated using the mathematical function. In an embodiment, the uncertainty associated with the cumulative dosimetric quantity data value is calculated using the mathematical function by a method of propagation of uncertainty. The absorbed dose delivered to the associated VOI calculated by assessing the area under the DRC. If the DRC is piecewise, then the area under each curve is calculated and summed to yield the total absorbed dose. Preferably, the mathematical function is an integrated function, determined analytically or numerically, in order to perform propagation of uncertainty. Further preferably, the propagation of uncertainty is by means of a statistical method utilising the dosimetric quantity data values and associated uncertainties and the associated mathematical function. In a preferred embodiment, the statistical method is a Taylor series expansion which approximates one or more statistical moments of MIR-2024-001WO 26-Sep-2025 Specification_Final the time cumulative quantity. Since each curve can be directly calculated from the dose rate data then one example method to calculate the total absorbed dose is to determine an integrated function to directly relate the absorbed dose to the dose rate data. In some cases, other mathematical functions may be used to determine the absorbed dose. The uncertainty associated with the absorbed dose value is also calculated. This is based on the uncertainties associated with the dose rate values used to determine the curve(s) and, in an example, the integrated function which directly relates the absorbed dose to the dose rate data, using an uncertainty propagation method. Uncertainty in other quantities (e.g., physical constants related to absorbed dose modelling), or intermediate derived quantities (e.g., the curve parameters) may also be used. If the DRC is piecewise the uncertainty of each curve may be calculated and combined using statistical techniques, for example, by considering covariance between the curves. In an embodiment, the cumulative dosimetric quantity data value and associated uncertainty as an output. The absorbed dose value and associated uncertainty are returned as an output of the system 311. In some embodiments other outputs may also be included associated with the process, such as goodness-of-fit measures used to perform quality assurance on the determined DRC. In some embodiments the process described by steps 301-311 may be applied to dose rate data samples for a plurality of VOIs sequentially or in parallel. Alternatively, or in addition, some embodiments may also apply the process described by steps 301-311 to a plurality of RPT cycles used to treat the patient. The process may involve comparisons and relationships between the VOIs and cycles to assist with quality assurance steps 303 & 306, model selection 304, DRC determination 305, and absorbed dose uncertainty calculation 310. Each step may be applied differently for each VOI or cycle. Processing within each VOI or cycle may influence other VOIs or cycles. In other embodiments, or in addition, steps 301-311 may be repeated to obtain a plurality of DRC models and associated outputs for comparison, in which case selection of the best model is performed at the end of the process (not shown), whereby such selection may be determined by the operator, an algorithm, or some other automated process. Once all such combinations of comparisons have been completed, the process ends. The resulting absorbed dose values and associated MIR-2024-001WO 26-Sep-2025 Specification_Final uncertainties are then stored locally or remotely or transmitted for further processing such as biologically effective dose (BED) calculations. In either of the methods of figure 2 or figure 3, the dosimetric quantity data value preferably relates to radioactivity present in a patient volume. Preferably a system is provided to execute the methods of figures 2 and 3, where the system is a system for determining the value and uncertainty in patient treatment data as part of a patient-specific dosimetry in radiopharmaceutical therapy (RPT), and comprises a database for storing patient data, a display for displaying information: a processor configured to perform one or more of the steps outlined above, and to output the cumulative dosimetric quantity value and associated uncertainty as an output, to be displayed on the display. Figure 4A indicates some example means by which activity data samples may be obtained as part of a clinical RPT workflow with personalised dosimetry for a patient undergoing a cycle of RPT treatment or a simulation of a cycle of treatment. Activity data may be obtained directly from the patient 401. Activity data may be obtained in the form of a 3D spatial map using medical imaging techniques 402, which may involve measurements of the 3D spatial distribution of a RP using radioactivity, a surrogate signal, or both, indicating the amount of associated activity. Examples include PET detection of annihilation events 403 or SPECT detection of gamma ray emission events within one or more photon energy windows 404. Surrogate methods include use of CT measurements of radiodensity 405 or MRI measurements of magnetisation signals 406 to observe RPs which may be detectable on the respective modality, and from which the associated activity can be determined 407. Activity data may also be obtained in the form of a 2D spatial map 408 by use of one or more gamma cameras to detect gamma ray emission events within one or more photon energy windows 409. These may be combined into a single image to reduce measurement noise. Activity data may also be obtained in the form of 1D (point) measurements 410. For example, a well counter 411 may be used to measure the amount of activity within the RP vial before and after administration to determine the injected activity 412. MIR-2024-001WO 26-Sep-2025 Specification_Final Samples may be taken from the patient, such as blood samples 413, and the activity present measured using the well counter 411. Another example of point measurement is the use of a dosimeter 414, such as a wall- or arm-mounted dosimeter to measure the activity emitted by the whole body overall 415, or a hand- held dosimeter to measure activity in parts of the body. Other, related activity data 416 may also be obtained from a database or other storage medium 417 which stores historical data. Activity data, as described above but from previous treatment, may be retrieved 418. Other useful patient non-specific data may also be retrieved, such as sensor calibration measurements 419 or other data required for processing raw measurements to obtain activity data or correct said data for artefacts such as those in imaging. Historical data associated with uncertainty in activity data may also be retrieved. Other sources of prior data may be used 421 and are described further in Figure 5. One or more sets of activity data may be obtained at one or more times after the RP administration for the treatment or simulation of treatment. These may be obtained from any combination of the types described above, or other such measurements. Activity data are used as a measurement or representation of the activity within a VOI in the patient. Such VOIs may represent the whole body, groups of organs, single organs, sub-regions within organs, tissues or groups of tissues, or other such anatomically- or functionally defined volumes, areas, surfaces, or points in or on the body, including clinically relevant regions such as lesions, tumours, or sites of microscopic disease. The VOI may instead represent or be associated with a more abstract volume, such as the blood within the body, a specific material, tissue, or cell type, or metabolic compartments of materials related to underlying biological processes. These examples are not exhaustive; any other such representations associated with activity data may also be used. In some embodiments, one or more regions may be defined in the 2D or 3D activity map(s) associated with the VOI for the purpose of obtaining one or more 1D activity values. The regions may be single pixels or voxels or an aggregation of a group of pixels or voxels. Such groups may be determined using masks or delineated using shapes or contours, or other such means of selecting a plurality of pixels or voxels. MIR-2024-001WO 26-Sep-2025 Specification_Final Multiple such regions may be defined and grouped in a way relevant to the anatomy or underlying biological processes. In some embodiments the activity data may not be directly comparable. The data may be processed or combined in some way to standardise them, enabling like-for- like comparisons. Further to this, a plurality of measurements may be combined or aggregated, for example, as the mean or median value, or some other statistic associated with central tendency. Alternatively, they may be identified or characterised as such a value through physical modelling arguments. The activity values may then be compared or otherwise grouped with other activity data described above, thereby comprising a set of consistent and comparable activity values at one or more timepoints in the cycle. Activity data processing 422 may also involve quantification uncertainty in the activity values. Such uncertainties arise from noise in measurements, such as uncertainty in the sensors, calibration, data processes such as image reconstruction or standardisation technique, or method of localisation. Uncertainties may also arise when deriving activity values from surrogate physical quantities or other indirect measurements. These uncertainties may be characterised using a statistical measure of dispersion such as standard deviation, variance, standard uncertainty, or interquartile range. In some embodiments, values may have a more complex or descriptive statistical characterisation such as an associated ‘probability density function’ (hereby the probability distribution) which indicates the frequency of occurrence of each given value. The probability distribution, which may be determined empirically or from theoretical arguments. These characterisations may be based on present measurements, previous measurements, prior information, or estimated from simulations (computational or phantom-based), or some other method of determination. The activity values and associated uncertainties may be quantified in an absolute (i.e., in units of Becquerels, Becquerels-per-millilitre, milli-Curies, or equivalent) or relative fashion. Relative quantification may involve leaving the standardised activity data in arbitrary units or some uncalibrated units such as counts per second or defining the quantity relative to some other absolute quantity such as the administered activity or activity data from previous cycles. In some embodiments, MIR-2024-001WO 26-Sep-2025 Specification_Final standardisation may involve more complex methods such as TAC analysis and rescaling. For example, a TAC may be determined using a plurality of activity values in arbitrary (but consistent) units. An absolutely quantified activity value sampled at a different time may then be used to rescale the whole TAC to convert it to absolute quantification. The result of the above processes is a set of one or more activity data samples at one or more timepoints 423, each sample comprised of value and associated uncertainty relevant to determining the cumulative activity for one or more associated VOIs and, optionally, dosimetry calculations. The activity values and associated uncertainties may then be stored locally or remotely or otherwise transmitted to other processes for purposes such as visualisation or analysis. Figure 4B illustrates an example of how activity data samples in step 423 may be visualised. The visualisation is comprised of a set of axes 424 indicating (for example) activity against time. The dependent variable may be another related quantity as described in step 422 such as activity concentration or activity as a percentage of the administered quantity. The independent variable is in units of time (or equivalent), typically set relative to the time of RP administration, such that it defines the origin. Each activity data sample is placed sequentially in time (sometimes referred to as a timepoint) to indicate how the activity within the associated VOI varies with time. Samples may be demarcated by markers 425 which indicate the activity value and error bars 426 which indicate the associated uncertainty on the value. Other equivalent visualisations are possible, including bar charts, histograms, box plots, and violin plots. Figure 5 indicates other data which may be used as prior information when performing embodiments of the invention. In an embodiment, at least one dosimetric quantity data value is retrieved from the patient’s historical data. Preferably, the associated uncertainty for the dosimetric quantity data value is derived from at least one of: the patient’s historical data, prior data The invention is primarily concerned with assessing uncertainty in derived quantities in RPT dosimetry. However, when deriving these quantities or determining associated uncertainties other information may be used to improve the uncertainty MIR-2024-001WO 26-Sep-2025 Specification_Final calculation, perform quality assurance in the method, or set default configurations for the system. In some embodiments historical patient data 501 may be used. The patient may have had previous therapies involving ionising radiation exposure to relevant parts of the body. Such information may be used to, for example, adjust safety targets to organs-at-risk in the current cycle or identify key regions where precision is critical, and therefore a need for accurately quantifying uncertainty. Furthermore, it is common for a patient to receive multiple cycles of treatment with a given RP. Activity or dose rate data samples (possibly including associated uncertainties) or any associated analysis from a previous cycle may be used to supplement the current cycle, including reuse as data samples. In another embodiment the use of priors relating to physical process or biological process 502 may be used. For example, a simple physical prior is that the activity must decay with time. Therefore, any model that would result in calculation of an infinite cumulative activity is clearly non-physical. For embodiments involving dose rate uncertainties physical priors may involve information about the dose modelling used to derive the dose rate values. More advanced priors, based on simulations, analysis of patient populations, knowledge of biokinetics of tissues with the administered RP, or physiology may also be included and used. Some types of prior data may be specific to determination of uncertainty 503 in activity or dose rate samples and may be used in lieu of direct measurement of the associated data samples. For example, it may be known that the activity data acquired with a specific imaging sensor results in activity measurements with a specific probability distribution (and thereby associated measures of statistical dispersion). In another example, the uncertainty in the data samples may have been simulated, derived, or modelled based on physical arguments. Such means of uncertainty characterisation in the data may be preferable to direct measurement depending on the embodiment of the invention and the type(s) of data used. Some embodiments of the invention may involve use of default configurations 504. For example, certain TAC models and TAC parameters may be initially preferable for a given tissue perfused with a given RP when measured at specified sample times. Other clinically relevant information about the patient (e.g., the disease, smoking MIR-2024-001WO 26-Sep-2025 Specification_Final status, sex, or use of neoadjuvant therapies) may also determine a default configuration. Such default configurations assist in automation of the method for an operator. Other configurations may be used, either as a result of analysis related to the default configuration or otherwise. Other such data associated with automation may also be used. Other data used in this way may be determined ahead of time and stored on a storage system in a way suitable for such data, such as a database. Where relevant, the storage may consist of data specific to the current patient, or other non-specific data associated with other patient(s) including populations of patients, research subjects, or hypothetical subjects such as a physical or computational phantom. The storage is then accessed by processes as required by any such embodiment of the invention. Figure 6 illustrates an example display featuring a graphical user interface (GUI) used by an operator to visualise, assess, or otherwise interact with methods and processes in an embodiment of the invention for the purposes of RPT dosimetry. This will be used with a computer processor that can execute one or more of the steps of the methods described above, to output the results of the analysis. The GUI 601 is comprised of a one or more associated visualisation components. These components may be shown together, or may be accessible sequentially, such as by use of tabs or pop-up windows. The GUI may have an image rendering engine component 602 which processes and presents to the user medical image(s) associated with the current patient and any informational overlays. For example, the engine may display anatomical images 603 and associated delineation(s) of one or more VOIs 604 in addition to depictions of the spatial distribution of relevant quantities 605. Here the anatomical image relates to a set of 2D image slices from a 3D medical image. This may be one used as part of the derivation of the activity data samples indicated in Figure 4. The relevant quantities may be presented as a voxelized heatmap which indicates the cumulative activity values, absorbed dose values, or associated uncertainties. The image rendering engine may additionally have input controls 606 to allow the user to navigate or adjust what is shown in the image display. In some embodiments the MIR-2024-001WO 26-Sep-2025 Specification_Final input controls 606 may allow the user to edit the displayed information, for example by using manual or (semi-)automatic tools to create, edit, or delete VOI delineations. The GUI may have a curve modelling component which presents information about any TAC (or DRC) modelling and associated uncertainties 607. In an embodiment of the invention, this may consist of a pair of axes 608 showing activity against time since RP administration for a given VOI. Each activity data sample comprised of value and associated uncertainty may be shown as a marker with error bars 609. The curve model, such as the examples in Figure 11, may be displayed 610 optionally with uncertainty in the shape parameters indicated 611 such as confidence intervals on the curve. One or more curves may be displayed at once to convey pertinent information relating to comparison of different models for the same set of activity data samples, different VOIs, or to historical data, such as the curve for the same VOI at a previous cycle. The modelling component may have associated input controls 612 to allow the user to adjust the display. In some embodiments the input controls 612 may allow the user to interact with the curve and uncertainty models. This may be in response to what is shown in the GUI 601. For example, the user may be able to remove outliers. In some embodiments, the user may be able to manually, semi-automatically, or automatically select curve model(s) as part of an initial analysis of the patient case or otherwise select more appropriate curves based on that analysis. Automatic and semi-automatic selection may be determined using default settings for a given protocol or RP. In another embodiment, the automatic selection may be based on other information available such as population data about the patient (e.g., the disease, smoking status, sex, or use of neoadjuvant therapies). Other examples of such information are indicated in Figure 5. The GUI may display quantities derived from the curve and uncertainty modelling in graphical format 613. For example, a pair of axes 614 indicating the total cumulative activity emitted within each VOI may be shown, whereby a bar 615 indicates the total cumulative activity value determined each VOI with the associated uncertainty indicated by error bars 616. Other derived quantities may be indicated graphically, such as absorbed dose values and associated uncertainties, comparisons to MIR-2024-001WO 26-Sep-2025 Specification_Final historical data for the VOI, or quantities related to the curve and uncertainty modelling. The GUI may display other derived quantities in a non-graphical format such as a table 617. One or more derived quantities may be displayed alongside each other. For example, the total cumulative activity value and associated uncertainty may be shown for each VOI. Other pertinent statistical or technical data which may aid the user perform or optimise, e.g., the dosimetry. For example, quality assurance measures related to the curve modelling may be shown, such as goodness-of-fit metrics or useful statistical quantities. Any of the described components may additionally show quality assurance or quality control information. For example, a red-amber-green traffic light motif may be displayed to indicate to the user if any clinically relevant risks may be present, such as exceedance of absorbed dose safety limits for a given VOI, or activity data samples which seem to be outliers, or curves which may result in unlikely or unphysical quantities. Finally, visual information displayed by the GUI may be saved to disk or transmitted for further offline processing 618. For example, screen captures may be taken to keep record of the analysis performed to a patient as part of a clinical workflow. In some embodiments, the spatial distribution of cumulative activity values and associated uncertainties may be used as input for RPT dose modelling software. In other embodiments, the GUI may display the full dosimetry calculation performed as part of the embodiment, undertaken as part of a treatment plan which has not yet taken place but has been modelled using simulated treatment based on a theranostic RP pair. Figure 7 is a simplified depiction of how an RP propagates around the patient’s body with true TACs indicated for various organs and sub-regions. Typically, one or more RPs are injected, inhaled, implanted, or otherwise administered 701 to the patient’s body 702. The RP may propagate around the body 703. The exact nature of how the propagation occurs depends on factors such as the properties of the RP, pharmacokinetics, and the physiological state of the patient. In some cases, the RP may remain at the site of administration. MIR-2024-001WO 26-Sep-2025 Specification_Final As the RP propagates it may flow through blood vessels 704 and be taken up into tissues, such as the liver parenchyma, by biological processes 705. A process known to those skilled in the art as ‘wash out’ may remove RP from the tissue, where it may be taken up by another tissue or pool within the organ or return to the blood 706. The RP may then be taken up elsewhere 707. The RP may eventually be excreted 708, removing it permanently from the patient’s body. Through these processes the amount of RP within regions of the body may increase and decrease over time in a complex manner. Since the RP is radioactive an increased concentration within a tissue corresponds to an increase in radioactive decay rate (activity) occurring in that tissue. Due to the nature of radioactivity, activity naturally drops with time, such that the RP may eventually be considered to be no longer radioactive. To illustrate the complex nature of RP (and associated activity) propagation in the body, 3 graphical examples are show, indicated as 3 VOIs: the liver 709, the aorta blood pool 710, and the left kidney cortex 711. As illustrated for the liver, each VOI has a pair of axes 712 which indicates the relationship between the amount of RP present in the VOI and time since administration of the RP. Analogous relationships such as activity, dose rate, or some other associated quantity may also be shown. The time axis generally starts at the time of administration ^^^714 such that it defines the origin, but any start time may be used. In the liver example the relationship is indicated by a curve 715 which rises swiftly and then decays with time. This is in contrast to the equivalent curve 716 for the aorta, which rises faster and decays faster. The kidney cortex is different too, its curve 717 illustrating a slow rise to the peak with a gentler decay. Generally, all such curves will have an initial rise due to time taken for the RP to reach the VOI and then accumulate there. They may then have a decreasing phase due to processes which remove the RP (or associated metabolite) from the VOI to elsewhere in the body. In the clinical RPT context continuous measurement of the RP, either by its activity or some other means, is not generally possible. Instead, samples are taken in a discontinuous manner at specific timepoints 715-7 which may be selected according to the expected nature of the true curve. For example, an initial timepoint ^^^718 could be obtained to measure the initial uptake peak. A second timepoint ^^ଶ719 MIR-2024-001WO 26-Sep-2025 Specification_Final could be obtained to determine the downward slope. A final third timepoint ^^ଷ720 could be obtained to characterise the tail of the curve. The true time dependence of the RP and associated activity as represented by the continuous curves 715-717 is unknown in general and must be inferred using the samples at the specified times 718-720. This is described further in Figure 11. Figure 8 illustrates simplified typical workflow with two variations when calculating absorbed dose in personalised RPT dosimetry. Activity imaging data and, optionally, additional anatomical imaging data are acquired 801. These are reconstructed into images. Such data may be acquired and reconstructed a plurality of times during treatment. Each activity image obtained constitutes a single time sample (hereby a timepoint) of the activity distribution in the patient. Spatial correspondences between a plurality of images may be calculated using image registration techniques 802. Volumes of interest (VOIs) are identified within the patient 803. Such VOIs represent the whole body, groups of organs, single organs, sub regions within organs, or clinically relevant regions such as lesions, tumours, or sites of microscopic disease. The VOI instead represent a more abstract volume, such as the blood within the body, a specific tissue or cell type, or metabolic compartments of materials related to underlying biological processes. Other such representations of the VOIs relevant to the dosimetry calculation may also be used. The pixels or voxels associated with the VOI are determined. This may optionally include delineation with contours, selection with masks or segmentation maps, or other such means of selection. Further examples of are given in Figure 4. In some embodiments, an activity value is sampled from the associated VOI at each timepoint. These activity values are then used to fit a curve 804 known to those in the art as a time-activity curve (TAC). Such a curve characterises activity at times not sampled. The area under the curve is taken as an estimate of the cumulative activity in the associated VOI 805. The cumulative activity can then be used as-is or in combination with cumulative activities of other VOIs to calculate absorbed dose values 806. MIR-2024-001WO 26-Sep-2025 Specification_Final In other embodiments, the activity images may first be converted into dose rate images using absorbed dose modelling calculations 807. Analogously to step 805, a dose rate value is sampled from each VOI at each timepoint. These dose rate values are then used to fit a curve 808, known to those in the art as a dose rate curve (DRC). Such a curve characterises dose rate at times not sampled directly. The area under the curve is then taken as the absorbed dose to the VOI 809. Once performed for all VOIs, the absorbed dose delivered to each VOI is returned 810. Figure 9 illustrates the how uncertainty arising from measurements propagates through a plurality of calculations to derived quantities in an example dosimetry calculation. Physical principles teach that the absorbed dose delivered to a VOI being assessed 901 (hereby the target VOI) depends directly upon the ionising energy absorbed by tissues in the target VOI 902 and the physical mass of the absorbing tissue 903. The energy absorbed in step 902 may be estimated by Monte Carlo simulation, dose- voxel kernels, local deposition, or some other absorbed dose calculation method. Such absorbed dose calculations estimate how the ionising energy emitted by one or more radioactive VOIs of the body 904 (hereby source VOIs) contributes to the target VOI. The energy emitted by each source VOI is proportional to the total number of decays (cumulative activity) within it 905, which can be determined using the area under the source VOI’s TAC 906. The TAC selected to characterise the time-distribution of activity in the source VOI depends strongly upon its associated activity value(s) 907. Activity values may be derived from one or more data sources as described in Figure 4. Values may be from non-imaging sources such as well counter measurements of bodily fluids 908. They may also be from one or more voxels or pixels in one or more activity images 909 reconstructed from activity imaging data 910. Activity imaging data 910 or the associated reconstructed activity images 909 typically require calibration 911 and other corrections to reduce uncertainties in the data acquisition such as recovery coefficients. MIR-2024-001WO 26-Sep-2025 Specification_Final Image-based activity values and VOI masses depend on localisation of VOIs in the body 912. These may be voxels, groups of voxels, delineated volumes, or other such depictions. The VOIs are localised using spatial information in activity images 912 and, optionally, anatomical images such as computed tomography images 913 reconstructed from associated imaging data 914. Anatomical images 913 may also be used to determine tissue densities 915, which may be used to calculate the mass of a target VOI 903. The example chain of causality depicted indicates how noise and uncertainty (in various forms) in any of these inputs propagates to the next step in the process. Inherent statistical uncertainties in measurements will ultimately impact the degree of confidence in the resulting absorbed dose calculation. Since absorbed dose values are used to make clinical decisions, it is critical to characterise the associated precision, uncertainty, or degree of trust in any calculated values. Figure 10 illustrates how deriving a quantity by nonlinear transformation of a noisy measurement affects the statistical properties of the derived quantity, and how the statistical properties of the derived quantity may be approximated using Taylor’s theorem. A measured quantity, ^^, varies around its true value as illustrated by an axis of measured values 1001 with a given frequency of occurrences 1002, mathematically referred to by ‘probability density function’ Pr^^^^ (the probability distribution). Such statistical variation of the measurements can accurately be modelled when all randomness, due to noise for example, of the measurement process is well known. It can also be inferred empirically from numerical or phantom simulations or from historical data. The probability distribution of the measured quantity offers a complete characterisation of the uncertainty on the measured quantity. Deriving anew quantity, ^^, from the measured quantity using nonlinear algebraic functions, ^^ =^^^^^^, such as an exponential function 1003 also transforms the probabilitydistribution of the measured quantity to a different shape 1004. Analytical calculation of this transformed probability distribution is often not straightforward, impairing the ability to statistically characterise the derived quantity and thus accurately assess its uncertainty. In this example, the direct relationship between the curve and the dosimetry data is determined statistically. Any suitable method to determine the MIR-2024-001WO 26-Sep-2025 Specification_Final measure of central tendency (mean, median etc..) can be applied using these principles to obtain the curve parameters based on the direct relationship. However, it is possible to use Taylor’s theorem to approximate the statistical effect of the nonlinear algebraic function. In general mathematics, Taylor’s theorem may be used to approximate a function in the neighbourhood of a specified value using a unique polynomial of specified order. In the context of statistics, the value may be a statistic of central tendency associated with either the measured or derived quantity’s true value, such as a mean, median, or mode. Application of the theorem then allows estimation of statistical moments around this central value, such as the variance, without requiring explicit characterisation of the derived quantity’s probability distribution 1004. For example, using a third order Taylor polynomial 1005 would implicitly give rise to probability distribution 1006. As an approximation, differences may remain between this and the true distribution. In this illustrative example, values near the mean 1007 of the initial distribution are preserved by the transformation, whereas a less central measurement may be poorly approximated 1008. Accuracy of the approximation may be improved using higher order terms in the Taylor polynomial. A worked example is given in Figure 12. Figure 11 shows some key concepts when modelling TACs, as shown on graph axes indicating activity versus time. Example embodiments of the invention are indicated in boxes A-F. The same concepts also apply to DRCs. In each of these examples, the curve model must explicitly describe the direct relationship between the curve and the datapoints used to determine the curve, however, the datapoints do not need to sit on the curve. In each embodiment of the invention one or more activity data samples may be used, each comprised of a value 1101 and associated uncertainty 1102 as determined at time since RP administration ^^^1103. Uncertainty in the activity value may be indicated by error bars 1102. Error bars may or may not be symmetric depending on the measure used to represent the uncertainty. The activity data may or may not be corrected for physical decay effects to a defined time, such as the time of RP administration ^^^1104. In some embodiments, a plurality of contiguous curve segments is used to construct a piecewise time-activity curve (box A) 1105-1106. Such piecewise models may be MIR-2024-001WO 26-Sep-2025 Specification_Final linear 1105 or nonlinear (e.g., exponential) 1106 curves fitted to a subset of activity values. Other types of curve may be used. Each curve comprising the piecewise TAC is applied separately and considered as an estimation of the true activity between its specified time limits. Each such curve and associated time interval is hereby referred to as a segment. The interval associated with each segment may be defined according to the sample times (timepoints) associated with the activity data, or to other salient times relevant to the TAC model, such as the time of administration ^^^1104 or the time at which all nuclear decays have occurred ^^^1107(i.e., at ^^ = ∞). The curve of a given segment may be determined using activity datasamples outside the interval within which the segment is applied, e.g., 1108. The shape and position of each segment curve is controlled by its parameters. The curve parameters are determined by some analytical fitting criteria such that the curve passes near to or through the associated activity values. For example, an initial segment may extrapolate beyond the time before the first sample (i.e., ^^^to ^^^, hereby the ‘pre-sample’ interval), estimating the true activity within the interval using a straight line 1109 from ^0,0^ to ^^^^,^^^^ where ^^^is the activity value at ^^^1101.Then, further linear segments may be used to interpolate between activity values at^^^, ^^ଶ, and ^^ଷ 1110. Then, a final segment may be defined to extrapolate beyond thefinal timepoint 1111 (i.e., from ^^ଷto ^^^, hereby the ‘post-sample’ or ‘tail’ interval). In some embodiments, a monoexponential curve may be used 1106, where the rate constant of the curve is intended to represent the reduction in activity due to both physical and biological (hereby biophysical) decay effects. The monoexponential curve may be determined from an analytical relationship to the final two timepoints ^^ଶand ^^ଷ1108, and then subsequently only applied for the tail 1111. Since each activity value has an associated uncertainty within which the true activity value may be found, the activity data samples used to determine each curve give rise to uncertainty in its shape and position, such that other candidate curves within, e.g., the shaded region 1112 may be plausible. Such a shaded regions may be indicated for each curve in the figure but are omitted where possible for visual clarity. In another embodiment, a different piecewise TAC may be constructed using the same activity data samples but using differently defined segments (box B). In this case the pre-sample extrapolation segment uses a flat line under the assumption MIR-2024-001WO 26-Sep-2025 Specification_Final that activity was constant before measurement 1113. A linear segment is applied for the first interpolating segment 1114. A monoexponential tail segment may be once again calculated using the final timepoints ^^ଶand ^^ଷ1115 but instead applied across a segment 1116 which both interpolates across ^^ଶto ^^ଷ, and extrapolates the tail beyond ^^ଷ. One use of TACs is to estimate the cumulative activity within the VOI it represents. When the TAC is piecewise the total cumulative activity may be calculated by evaluating the area under each segment 1117-1119 separately and summing. Since uncertainties in the activity values contribute to uncertainty in the associated segment curve (e.g., 1112), uncertainty also arises in any derived quantities such as the cumulative activity. As such, each area value 1117-1119 will also have an associated uncertainty. The uncertainty associated with the cumulative activity value for each segment then contributes to the uncertainty associated with the total cumulative activity calculated for the TAC overall. A worked example of this is given in Figure 13. Another embodiment of the invention is shown in box C. This example uses 3 linear segments to interpolate between ^^^and ^^ସ1120. However, a user or program may decide that the pre-sample segment is better modelled by a decaying monoexponential whose rate constant is determined by the physical half-life of the associated radionuclide 1121. Further, it may be decided that a monoexponential curve 1122 fitted to the activity value at ^^ସmay also only have a rate constant as determined by the physical half-life for the tail segment. Another embodiment shown in box D instead may model a biophysical monoexponential curve in the pre-sample segment 1123. Another example embodiment is shown in box E, where a single continuous curve 1124 is used to span from ^^^to ^^^. In this embodiment involving 3 activity data samples 1125-1127, the central sample 1125 has been identified as an outlier and omitted from the fitting of the biophysical monoexponential 1124 passing through the first 1126 and third 1127 activity values. Determination of the outlier 1125, or other means of identifying the best activity values to use to determine the curve, may involve information related to the values and associated uncertainties in any of (but not limited to): the activity samples 1125-1127, the parameters which determine the MIR-2024-001WO 26-Sep-2025 Specification_Final shape and position of the curve 1128, or the resulting cumulative activity. Outlier determination may also involve other information, such as data related to the patient’s previous treatment cycles, population data, biophysical constraints such as unreasonably high activity values, or physical constraints such as activity values which are zero or otherwise negative. A final example embodiment is shown in box F. Figure 11F discusses use of priors as part of the curve model, illustrated with a datapoint which has a known fractional contribution 1132 from the slow exponential decay component 1131. Other priors explicitly relating any or all datapoints to the line could conceivably be employed which could result in a scenario where no points lie upon the line. In this example, the TAC model is selected to be a single continuous biexponential function 1129 which spans from ^^^to ^^^. The biexponential curve 1129 is the sum of two monoexponential terms, one which decays rapidly 1130 and one which decays slowly 1131. Three activity data samples at ^^^, ^^ଶ, and ^^ଷrespectively may be used to analytically determine each monoexponential (and therefore the biexponential), but, as is known to those in the art, this is insufficient to uniquely characterise the parameters which control the shape of the curve. As such, additional data or constraints may be included to determine a unique biexponential. One such example is prior knowledge of a likely fractional contribution of each underlying monoexponential to the activity value at ^^ଶ1132. Such prior data may be determined through a number of methods, such as empirical determination from historical data with more than 3 activity data samples where unique solutions exist, by simulations, or by other means of indicating the likely TAC. Prior data may be dependent upon the type of RP, the tissue(s) within the VOI, and patient physiology. Prior data values may also have associated uncertainty which may be taken into account when calculating the cumulative activity. Other such examples involving use of prior data are also possible. Selection of which curves are appropriate and over which time intervals is part of a design process undertaken by a human or machine, which may be based on experience, prior data, heuristics, optimisation, and so on. There is no standard way to model any given TAC in clinical practice since it may vary with the RP, the patient, and the type of measurements. Any system which calculates the uncertainty in the area under the piecewise parametric curves in examples A-D or otherwise must also MIR-2024-001WO 26-Sep-2025 Specification_Final be able to handle any such combination of segment models. In all of the examples in FIG 11, and others there is a difference between selection of a curve and determination of a curve. To select a curve is to identify which family of curves will describe the time-behaviour of the measured quantity, to determine the curve is to identify which specific curve from this family of curves represents the datapoints at hand. Human or machine may perform the former; the direct relationships between input data and the parameters may be used to perform the latter as described previously. Figure 12 illustrates key concepts in a worked example of how an embodiment may be applied to calculate uncertainty in cumulative activity when representing the whole TAC with a single monoexponential determined from two activity data samples. In this worked example, consider a pair of axes 1201 displaying activity values against time since RP administration with two activity data samples within a singlecycle of RPT, 1202 and ^^ଶ = ^^^ଶ,^^ଶ^ 1203 where the activity ^^ଶ < ^^^.These points are depicted upon the graph as a mean value with error bars indicating the uncertainty. The activity values may be determined, for example, by a SPECT image of the patient at each timepoint, where the mean activity within an organ-at- risk is measured in each image. The associated time ^^ is the time since administration of the RP, thereby determining the origin of the plot. According to measurement theory, ^^^has statistical properties illustrated by the probability distribution 1204 shown on axes 1205 of possible values of ^^^against the probability of such values occurring Pr^^^^^. Such properties include a value which represents the central tendency of the distribution ^ത^^1206. There may also be an associated measure of dispersion or uncertainty ^^^in the value 1207. The same is true of ^^ଶas depicted on axes 1208, though the distribution of possible values of ^^ଶ1209 may be different in general, along with the measures of central tendency ^ത^ଶ1210 and uncertainty ^^ଶ1211. These statistical properties may be measured empirically, known prior to measurement, assumed, simulated, or otherwise determined. In this example the mean values ^ത^^and ^ത^ଶare used but other measures of central tendency, such as the median or mode, may be preferable according to the statistical distributions of ^^^and ^^ଶ. Similarly, this example uses the standard MIR-2024-001WO 26-Sep-2025 Specification_Final deviations ^^^and ^^ଶto indicate the uncertainty in ^^^and ^^ଶrespectively, but othermeasures of dispersion may be preferable such as the interquartile range. Further,^^^ and ^^ଶ may be statistically dependent, having a non-trivial joint probabilitydistribution with combined properties such as covariance. However, in this example^^^ and ^^ଶ are assumed independent.Next, suppose that the cumulative activity is to be determined from these measurements. One such approach is to represent the activity present in the VOI using a TAC 1212 mathematically described by function ^^ spanning from the time ofinjection ^^ = 0 to the point at which all radioactive decays have occurred, ^^ = ∞.One such choice of ^^ 1212 is that of the decaying monoexponential function. The curve may describe physical-only decay. Alternatively, it may describe mixed biological and physical (hereby biophysical) decay effects arising from the physical decay and washout of RP from the associated VOI. In another embodiment, the activity values may be pre-corrected for physical decay and only the biological effect is modelled by the curve. In this example, the model is biophysical. The area under the TAC, indicted by the shaded region 1213 and attributed the mathematical symbol ^^, estimates the cumulative activity. The shaded region ^^ is calculated by integrating the ^^ 1212 over the specified time interval 1214. In this case, the integral can be expressed as an analytical function and ^^ଶ, where Δ^^ = ^^^ − ^^ଶ. This expression was calculated by using a single continuousfunction to extrapolate and interpolate the full range from ^^ = 0 to ^^ = ∞. Otherchoices are possible. For example, the interval for which ^^ is calculated may be limited to the tail segment. This may also be part of a piecewise TAC comprised of a plurality of functions each representing the activity over a corresponding segment contiguously over the full timespan. In such a case, a plurality of analytical expressions of the partial cumulative activity of the full TAC will be defined over their respective time intervals. As described above, ^^^and ^^ଶhave statistical properties as illustrated in 1205 and 1208. Since ^^ is derived from ^^^and ^^ଶ, it too will have statistical properties, as MIR-2024-001WO 26-Sep-2025 Specification_Final illustrated on axes 1215. The exact nature of the statistical properties of ^^ depends on the input variables and their relationship with output variable. As such, ^^ will have statistical properties according to some probability distribution 1216 which may be unknown or difficult to compute analytically. As above, this distribution may be characterised by a measure of central tendency ^̅^ 1217 and associated measure of dispersion or uncertainty, ^^^, 1218 which is partly dependent upon ^^^and ^^ଶ. In an embodiment of the invention, Taylor’s theorem may be used to approximate or otherwise determine the uncertainty in ^^ arising due to properties of ^^^and ^^ଶand its relationship to them, such as is shown by the 2D surface 1219 on 3D axes 1220. For example, the variance in ^^, ^^^ଶ, may be calculated as an indication of its uncertainty. According to Taylor’s theorem, the variance in ^^ may be approximated using a series expansion consisting of covariances of central moments of the two input variables up to order ^^ according to Cov^^^^ ^ି^^^ ^ଶ , ^^^^ ^^ℓି^ଶ ൧ To evaluate this series expansion the ^^^୦order partial derivatives of the expression for cumulative activity with respect to ^^^and ^^ଶis required. These are evaluated at the mean values ^ത^^and ^ത^ଶ1221. The covariances between the products ofdeviations of the input variables ^^^ = ^^^ − ^ത^^ are also required, as determined by theirstatistical properties. The partial derivatives may be determined using any numerical or analytical techniques known to those in the art. Further, in this example it can be seen that ^^ is a nonlinear function of the inputs. Such nonlinear functions require many such partial derivatives to be evaluated in general. However, if the expression for ^^ is linear, such as when using line functions to interpolate between activity values, only the first derivatives are nonzero. This simplifies the calculation considerably since all termsvanish except those for ^^^, ℓ^ = ^1,1^ and the approximation becomes exact.The covariances in the series expansion may be determined experimentally, empirically, using tabulated data, using theoretical or assumed distributions, or based on some other knowledge of the statistical properties of ^^^and ^^ଶ. For MIR-2024-001WO 26-Sep-2025 Specification_Final example, by assuming independence of ^^^and ^^ଶthe covariance coefficientbecomes where ^^ denotes the expectation operator. Each expectation term in this expression denotes the central moments of the probability distributions of ^^^and ^^ଶseparately, allowing straightforward calculation if the distribution is known and has a tractable moment generating function. For example, if ^^^and ^^ଶare known to be normally distributed with means ^ത^^and ^ത^ଶand standard deviations and ^^ଶrespectively, then the ^^^୦central moment of each variable may be calculated according to ^^ = 0^^ odd ^^ evenwhere ‼ denotes the double factorial. Alternatively, the log-normal, Poisson, gamma, exponential, uniform or any other named or unnamed distribution may be used. The moments may be calculated using the distribution’s moment generating function (if it exists) or any other such method. Equivalent strategies may be taken when applying the Taylor method to statistical quantities such as the median and interquartile range, or to more complex relationships between the input variables arising from their non-independence, and when applying the method to more than 2 input variables. Bringing this all together by considering the contribution of each order indices ^^ and ℓto the full series expansion to order ^^ = 2, the zeroeth order contribution ^^^ is^^^ = 0The first order contribution is^^^ = ^^ଶ ଶ ଶ^^ σ^ + ^^ ଶ^^ σଶThe second order contribution is And, finally, third order contribution MIR-2024-001WO 26-Sep-2025 Specification_Final Here the shorthand has been used Finally, evaluating each and summing ^^^ up to ^^ = 3 gives the 3rd order Taylorapproximation to the variance of ^^ assuming 2 independent, normally distributed activity values. If the TAC is a piecewise continuous curve comprised of a plurality of segments over defined intervals, each segment’s contribution to the total TAC’s cumulative activity will have its own uncertainty represented as, e.g., the variance, calculated as shown in the example. The uncertainty of the full cumulative activity must then further consider covariances between each two adjacent segments. This is illustrated in Figure 13. Figure 13 indicates key concepts and ideas in a worked example illustrating how an embodiment may calculate uncertainty in cumulative activity when representing the TAC as a piecewise continuous curve comprised of a set of functions and corresponding time intervals (segments). In this worked example, the TAC displayed on the axes 1301 is represented by 4 segments comprised of functional representations of each curve, ^^^, 1302 and corresponding time intervals indicated by the dots on the dashed line 1303 which continues to infinity as indicated by the arrowhead 1304. The shape and position of each curve is determined analytically using 4 activity values at specified activity datasamples ^^^ = ^^^^ ,^^^^ 1305, each of which has an associated uncertainty indicated byerror bars. Other configurations are also possible, in terms of how the segments are arranged and which functions are selected to represent them. The segments are defined as follows: ^^^is a line function for the pre-samplesegment 1306 under the assumption that ^^^^,^^^^ = ^0,0^. Therefore 1306 is onlystatistically dependent upon ^^^. Functions ^^ଶand ^^ଷare linear interpolants defined between activity data sample pairs ^^^& ^^ଶand ^^ଶ& ^^ଷrespectively, depending MIR-2024-001WO 26-Sep-2025 Specification_Final upon the corresponding activity values. Both ^^ଶand ^^ଷdepend on ^^ଶand are therefore correlated even if the activity data samples themselves are statistically independent. Function ^^ସ1307 is a decaying monoexponential similar to that in Figure 12, except it is used to interpolate between ^^ଷand ^^ସand continues toextrapolate beyond ^^ସ to ^^ = ∞.As previously described, the total cumulative activity across the TAC may be determined by evaluating the cumulative activity modelled by each segment. As such, for segment ^^ there is a corresponding cumulative activity ^^^which contributes to the total, ^^^୭^. To obtain a value of uncertainty for ^^^୭^the uncertainty crosstalk between each ^^^and each other ^^^must be determined. Crosstalk may arise where the input functions are themselves statistically correlated, or where two segments share one or more input variables. In an embodiment of the invention whereby uncertainty is characterised by variances, this may be seen as calculating the covariance of each segment with respect to itself (i.e., its own variance) and with respect to the others. The variance of each may be determined as described in Figure 12. However, additional calculations may be required for cross-terms. In an embodiment of the invention, the covariance between ^^^and each ^^^may be conceived in the form of a covariance matrix ^^ 1308. This is illustrated in a pictorial format, with labels 1309 indicating which pair of segments give rise to which calculation type. Shown are 5 classes of calculation in the diagram key 1310, defined as follows: Linear segments which are self-covariant 1311, and may be cross- covariant with other linear 1312 or nonlinear 1313 segments. Nonlinear segments are also self-covariant 1314. If a pair of segments share no inputs and their inputs are independent, then there may also be no cross-covariance contributions from that pair 1315. A 6thclass, not shown in this example, is cross-covariance that arises from a pair of nonlinear segments. In this embodiment, the total variance is the sum of each entry in ^^ 1308. The importance of this description is that linear and nonlinear segments may require different treatment when calculating their ‘self-covariance’ (i.e., variance) or cross- covariances, depending on the statistical methodology used to determine the uncertainties involved. MIR-2024-001WO 26-Sep-2025 Specification_Final To continue from the example in Figure 12 based on Taylor’s theorem approximations, each linear segment’s variance 1311 is straightforward to calculate, since the first order Taylor series expansion is exact: 1Var[^^ଶ] =4 ^^^ଶ − ^^^^ଶ^Var[^^^] + Var[^^ଶ] + 2Cov[^^^, ^^ଶ]^.Evaluating this expression for normally distributed and independent activity values obtains Var[^^ଶ] = 14 ^^^2 − ^^1 where and ^^ଶare the standard deviations of activity values 1 and 2. Covariance between linear segments 1312 is equally straightforward. For example,the covariance between the two linear segments ^^ଶ and ^^ଷ which depend upon^^ത^^, ^ത^ଶ^ and ^^ത^ଶ,^ത^ଷ^ respectively is1Cov[^^ଶ, ^^ଷ] =4 ^^^ଶ − ^^^^^^^ଷ − ^^ଶ^^^ଶଶ.However, linear-nonlinear and nonlinear-nonlinear Taylor series expansion covariance estimators require further calculation up to a specified order, ^^. The linear-nonlinear and nonlinear-nonlinear series are different in general.For example, the covariance between the 3rd and 4th segment cumulative activities,^^ଷ and ^^ସ, is of the linear-nonlinear type 1313. Segment 3 depends upon meanactivity values ^ത^ଶand ^ത^ଷ, and segment 4 depends upon ^ത^ଷand ^ത^ସ. The Taylor series expansion covariance estimator for linear-nonlinear segment pairs which depend upon two activity values each, such as between ^^ଷand ^^ସin this example, has the form Then assuming independent normally distributed activity values, the 3rdorder covariance would then be Cov which uses the shorthand MIR-2024-001WO 26-Sep-2025 Specification_Final Although not shown in the example, nonlinear-nonlinear covariance calculations are also possible but are more complex to apply than linear-nonlinear due to crosstalk between the central moments of each segment.To illustrate, consider two segments A and B described by nonlinear functions ^^^ and^^^ and which depend upon two random variables each. Let these variables bedenoted ^^^^, ^^ଶ^ & ^^^^,^^ଶ^ with means ^^̅^^, ^̅^ଶ^ & ^^ത^^,^ത^ଶ^ and associated deviations^^^^, ^^ଶ^ & ^^^^, ^^ଶ^ respectively. The general Taylor series expansion for thecovariance between these two segments is then The method would then be applied in practice by either evaluating covariances between quantities ^^^and ^^^(which may be different quantities in general), or, as illustrated by the linear-nonlinear example, identifying ^^^in terms of ^^^. For example,setting ^^^^, ^^ଶ^ = ^^^^,^^ଶ^ and ^^^^, ^^ଶ^ = ^^^ଶ,^^ଷ^ would involve cross-covariancesbetween each of the ^^^quantities in addition to the self-covariance (i.e., variance) of^^ଶ.As can also be seen from this example, if ^^^and ^^^are different activity values whichare otherwise independent, Cov[^^^, ^^^] = 0, indicating entries in ^^ 1308 which do notcontribute 1315. The examples shown here are in terms of segments which depend upon two activity values each for simplicity, but segments may depend upon any number of activity values in which case equivalent principles apply. The Taylor method is one example method for determining the uncertainty in the total cumulative activity. Other methods may be used, such as statistical methods which involve explicit calculation of the transformed probability distribution of the cumulative activity arising from the input activities. The transformed probability distribution or its statistical properties may alternatively be empirically determined using Monte Carlo techniques. These may also be pre-calculated and tabulated so MIR-2024-001WO 26-Sep-2025 Specification_Final that uncertainty values are looked up using the activity values and associated uncertainties. Once each variance and covariance of segment pairs have all been calculated, by applying the Taylor method to the desired order, or otherwise, the total variance in cumulative activity for the associated TAC is then found by summing entries of ^^ 1308, The direct and explicit formulation of the cumulative dosimetric quantity data value and the associated uncertainty acts as a “white box” approach to the statistical characterization of uncertainty and commutative quantities. This facilitates trust in the calculations and interpretability of the resulting values and uncertainties. Prior art methods based on “best fit” indirect methods are unable to allow such analysis. Furthermore, the method as described works in generality without assuming normality. Due to the high degree of nonlinearity exhibited by the equations in RPT dosimetry it is expected that many quantities are not normally distributed. Instead, in this invention we are able to work with any input distributions and transform them according to the direct relationships to the outputs. This approach also avoids truncation to linear or quadratic approximations. The high degree of nonlinearity in the curves used in RPT dosimetry can mean that, for example, many terms would be needed in a Taylor series expansion to accurately approximate a statistical quantity. The example of figure 12 is able to calculate the covariance of the accumulated activity to any order of the indicated Taylor series, allowing arbitrarily high order calculations and associated analysis. Other non Taylor methods are also possible as described above. Figure 14 illustrates a simplified block diagram of an example of a system 1400 arranged to perform the methods for determining the value and associated uncertainty of time cumulative quantities as part of patient specific dosimetry as described above. In the illustrated example, the system 1400 comprises one or more user terminals 1401, for example comprising a workstation or the like, arranged to access datasets comprising dosimetric quantity data and associated uncertainties at one or more time points, each representing a quantity of dosimetric interest MIR-2024-001WO 26-Sep-2025 Specification_Final associated with at least one radiopharmaceutical agent present within a volume of the patient, stored within, for example, a database 1402 or other data storage apparatus. In the illustrated example, a single database 1402 is illustrated. However, it will be appreciated that the user terminal 1401 may be arranged to access datasets from more than one data storage apparatus. Furthermore, in the illustrated example the database 1402 is illustrated as being external to the user terminal 1401. However, it will be appreciated that the user terminal 1401 may equally be arranged to access datasets stored locally within a local storage module illustrated at 1410 on one or more internal storage elements, such as the memory element illustrated at 1403 or the disk element illustrated at 1409. The user terminal 1401 further comprises one or more signal processing modules, such as the signal processing module illustrated generally at 1404. The signal processing module(s) is / are arranged to executing computer program code, for example stored within local storage module 1409. In the illustrated example, the signal processing module(s) 1405 is / are arranged to execute computer program code comprising one or more of the steps of the methods as set out above. The signal processing module 1404 in the illustrated example is further arranged to execute computer program code comprising one or more image display component(s) 1406; the image display component(s) 1406 being arranged to display in a meaningful manner results as described using the method above, to a user, for example on a display screen 1407 or the like. The system 1400 may further comprise one or more user input devices, such as illustrated generally at 1408, to enable a user to interact with computer program code etc. executing on the signal processing module(s) 1404. The present invention has been described with reference to the accompanying drawings. However, it will be appreciated that the present invention is not limited to the specific examples herein described and as illustrated in the accompanying drawings. Furthermore, because the illustrated embodiments of the present invention may for the most part, be implemented using electronic components and circuits known to those skilled in the art, details will not be explained in any greater extent than that considered necessary as illustrated above, for the understanding and appreciation of the underlying concepts of the present invention and in order not to obfuscate or distract from the teachings of the present invention. MIR-2024-001WO 26-Sep-2025 Specification_Final The invention may be implemented in a computer program for running on a computer system, at least including code portions for performing steps of a method according to the invention when run on a programmable apparatus, such as a computer system or enabling a programmable apparatus to perform functions of a device or system according to the invention. A computer program is a list of instructions such as a particular application program and / or an operating system. The computer program may for instance include one or more of: a subroutine, a function, a procedure, an object method, an object implementation, an executable application, an applet, a servlet, a source code, an object code, a shared library / dynamic load library and / or other sequence of instructions designed for execution on a computer system. Therefore, some examples describe a non-transitory computer program product having executable program code stored therein for automated contouring of cone-beam CT images. The computer program may be stored internally on a tangible and non-transitory computer readable storage medium or transmitted to the computer system via a computer readable transmission medium. All or some of the computer program may be provided on computer readable media permanently, removably or remotely coupled to an information processing system. A computer process typically includes an executing (running) program or portion of a program, current program values and state information, and the resources used by the operating system to manage the execution of the process. An operating system (OS) is the software that manages the sharing of the resources of a computer and provides programmers with an interface used to access those resources. An operating system processes system data and user input, and responds by allocating and managing tasks and internal system resources as a service to users and programs of the system. MIR-2024-001WO 26-Sep-2025 Specification_Final The computer system may for instance include at least one processing unit, associated memory and a number of input / output (I / O) devices. When executing the computer program, the computer system processes information according to the computer program and produces resultant output information via I / O devices. In the foregoing specification, the invention has been described with reference to specific examples of embodiments of the invention. It will, however, be evident that various modifications and changes may be made therein without departing from the scope of the invention as set forth in the appended claims and that the claims are not limited to the specific examples described above. Those skilled in the art will recognize that the boundaries between logic blocks are merely illustrative and that alternative embodiments may merge logic blocks or circuit elements or impose an alternate decomposition of functionality upon various logic blocks or circuit elements. Thus, it is to be understood that the architectures depicted herein are merely exemplary, and that in fact many other architectures can be implemented which achieve the same functionality. Any arrangement of components to achieve the same functionality is effectively ‘associated’ such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as ‘associated with’ each other such that the desired functionality is achieved, irrespective of architectures or intermediary components. Likewise, any two components so associated can also be viewed as being ‘operably connected,’ or ‘operably coupled,’ to each other to achieve the desired functionality. Furthermore, those skilled in the art will recognize that boundaries between the above described operations merely illustrative. The multiple operations may be combined into a single operation, a single operation may be distributed in additional operations and operations may be executed at least partially overlapping in time. MIR-2024-001WO 26-Sep-2025 Specification_Final Moreover, alternative embodiments may include multiple instances of a particular operation, and the order of operations may be altered in various other embodiments. However, other modifications, variations and alternatives are also possible. The specifications and drawings are, accordingly, to be regarded in an illustrative rather than in a restrictive sense. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word ‘comprising’ does not exclude the presence of other elements or steps then those listed in a claim. Furthermore, the terms ‘a’ or ‘an,’ as used herein, are defined as one or more than one. Also, the use of introductory phrases such as ‘at least one’ and ‘one or more’ in the claims should not be construed to imply that the introduction of another claim element by the indefinite articles ‘a’ or ‘an’ limits any particular claim containing such introduced claim element to inventions containing only one such element, even when the same claim includes the introductory phrases ‘one or more’ or ‘at least one’ and indefinite articles such as ‘a’ or ‘an.’ The same holds true for the use of definite articles. Unless stated otherwise, terms such as ‘first’ and ‘second’ are used to arbitrarily distinguish between the elements such terms describe. Thus, these terms are not necessarily intended to indicate temporal or other prioritization of such elements. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to advantage.

[0002] MIR-2024-001WO 26-Sep-2025 Specification_Final References [1] Siegel, J. A., et al. (1999). ‘MIRD pamphlet no.16: Techniques for quantitative radiopharmaceutical biodistribution data acquisition and analysis for use in human radiation dose estimates’. Journal of Nuclear Medicine, 40(2), 37–61 [2] Gear, J. I., et al. (2018) ‘EANM practical guidance on uncertainty analysis for molecular radiotherapy absorbed dose calculations’ European Journal of Nuclear Medicine and Molecular Imaging. https: / / doi.org / 10.1007 / s00259-018-4136-7 [3] Landaw, E. M., & DiStefano, J. J. (1984) ‘Multiexponential, multicompartmental, and noncompartmental modeling. II. Data analysis and statistical considerations’, American Journal of Physiology-Regulatory, Integrative and Comparative Physiology https: / / doi.org / 10.1152 / ajpregu.1984.246.5.R665 [4] Kletting, P., et al. (2013) ‘Molecular radiotherapy: The NUKFIT software for calculating the time‐integrated activity coefficient’, Medical Physics https: / / doi.org / 10.1118 / 1.4820367 [5] Ivashchenko, O. V., et al. (2024) ‘Time-Activity data fitting in molecular Radiotherapy: Methodology and pitfalls’, Physica Medica [6] Li, W. B. (2018) ‘Internal Dosimetry’, Japanese Journal of Health Physics https: / / doi.org / 10.5453 / jhps.53.72 [7] Joint Committee for Guides in Metrology (2008) ‘JCGM 100:2008 Evaluation of measurement data – Guide to the expression of uncertainty in measurement’. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, 2008. Available at: www.bipm.org / en / publications / guides

[0003] MIR-2024-001WO 26-Sep-2025 Specification_Final Glossary Absorbed dose – The amount of ionising energy deposited per kilogram of tissue. Activity – Radioactivity; The number of radioactive decays per second. Administration – Supplying a radiopharmaceutical to the patient, by injection, inhalation, implantation, or otherwise. BED – Biologically effective (absorbed) dose, indicates biological impact of absorbed dose on tissues. CT – Computed tomography, 3D X-ray-based imaging modality. Cumulative activity – See TIA. Cycle – A single course or fraction of treatment typically involving a single injection of radiopharmaceutical. More cycles may be administered once the previous has decayed away. Dosimetry – The process of evaluating absorbed dose due to exposure to ionising radiation. DRC – Dose rate curve, a graphical representation of the rate of absorbed dose deposition within a specified region or location over time. Half-life – A physical property of a radionuclide which corresponds to the period of time taken for half of a sample of the radionuclide to decay. Molecular radiotherapy – A type of RPT with an emphasis on delivering therapeutical levels of ionising radiation to internal regions of the body by use of one or more RPs. MRI – Magnetic resonance imaging, imaging modality based on magnetisation. PET – Positron emission tomography, a 3D imaging modality based on beta-positive radioactive decay. Planar scintigraphy – Acquisition of a 2D image using one or more gamma cameras. Radiopaque – The quality of being sufficiently attenuating to X-rays as to be visible in an X-ray image. RP – Radiopharmaceutical, a pharmaceutical which is radioactive. RPT – Radiopharmaceutical therapy. SPECT – Single photon emission tomography, a 3D imaging modality based on gamma decay. Surrogate – An indirect measurement used to infer another, in this case, activity. Theranostics – Diagnostic and therapeutic nuclear medicine (combined). MIR-2024-001WO 26-Sep-2025 Specification_Final TAC – Time-activity curve, a graphical representation of the activity within a specified region or location over time. TIA – Time-integrated activity, the total number of radioactive decays within a specified location, region, or volume. Referred to in generality as cumulative activity. Timepoint – A measurement or derived activity sample obtained at a given time, such as a SPECT-CT acquired 4 hours after administration of a radiopharmaceutical.

Claims

MIR-2024-001WO 26-Sep-2025 Specification_Final Claims 1. A method for analysing dosimetry data as part of a patient-specific dosimetry in radiopharmaceutical therapy (RPT), comprising: obtaining a dataset comprising of one or more dosimetric quantity data values and associated uncertainties at one or more timepoints each representing a quantity of dosimetric interest associated with at least one radiopharmaceutical agent present within a volume of the patient; selecting a dosimetric quantity time representation curve (TRC) model comprised of one or more curves which contiguously span from the time of administration of the radiopharmaceutical; , wherein each of the one or more curves is directly calculated from the dosimetric quantity data values determining one or more parameters associated with at least one of the one or more curves comprising the selected TRC model; determining from the one or more curves a mathematical function which directly relates the time cumulative quantity to the dosimetric quantity data values; calculating the cumulative dosimetric quantity data value using the mathematical function; calculating the uncertainty associated with the cumulative dosimetric quantity data value using the mathematical function by a method of propagation of uncertainty; and returning the cumulative dosimetric quantity data value and associated uncertainty as an output; using the output of the cumulative dosimetric quantity data value and associated uncertainty in at least one of: the planning, adjustment, or assessment of dosimetry data for future radiopharmaceutical therapy, or the planning, adjustment or assessment of future radiotherapy dosages, for one or more patients.MIR-2024-001WO 26-Sep-2025 Specification_Final 2. The method as claimed in claim 1 wherein the one or more patients comprises at least one of: the patient of the patient specific dosimetry RPT, one or more different patients.

3. The method as claimed in claim 1 or claim 2 wherein the dosimetric quantity is activity, and the one or more curves comprising the TRC model is a time- activity curve utilised to determine cumulative activity.

4. The method as claimed in any preceding claim wherein the dosimetric quantity is absorbed dose rate and the one or more curves comprising the TRC model is a dose rate curve utilised to determine absorbed dose.

5. The method as claimed in any preceding claim wherein the dosimetric quantity data value relates to radioactivity present in a patient volume.

6. The method as claimed in any preceding claim wherein the mathematical function is an integrated function, determined analytically or numerically, in order to perform propagation of uncertainty.

7. The method as claimed in claim 6 wherein the propagation of uncertainty is by means of a statistical method utilising the dosimetric quantity data values and associated uncertainties and the associated mathematical function.

8. The method as claimed in claim 7 wherein the statistical method is a Taylor series expansion which approximates one or more statistical moments of the time cumulative quantity 9. The method as claimed in any preceding claim wherein the TRC model comprises one or more curves.

10. The method as claimed in claim 9 wherein the one or more curves comprising the TRC model span from the time of radiopharmaceutical administration to the time at which all radioactivity is taken to be effectively decayed in a contiguous fashion.MIR-2024-001WO 26-Sep-2025 Specification_Final 11. The method as claimed in claim 9 or claim 10 wherein at least one of the curves comprised by the TRC are nonlinearly related to the associated dosimetric quantity data values.

12. The method as claimed in any preceding claim wherein the TRC model is assessed for quality and utilized to adjust inclusion of dosimetric quantity data values or the curves which are comprised by the TRC.

13. The method as claimed in any preceding claim wherein the volume is one or more of: a volume within the patient comprising: parts of the body, organs, sub-regions within organs, tissues, lesions, tumours, sites of microscopic disease; or a volume based on biological material; or the volume represents abstract fractional quantities including metabolic compartments of materials associated with metabolization of the radiopharmaceutical agent.

14. The method as claimed in any preceding claim wherein at least one dosimetric quantity data value is derived from measurements using at least one of nuclear medicine sensors; medical imaging techniques, well counter sensors and dosimeter sensors.

15. The method as claimed in any preceding claim wherein the uncertainty for the dosimetric quantity data value is derived from measurements using at least one of: nuclear medicine sensors, medical imaging techniques, well counter sensors and dosimeter sensors.

16. The method as claimed in claim 14 or claim 15 wherein the nuclear medicine sensors comprise one or more of: positron emission tomography (PET), single photon emission computed tomography (SPECT), planar scintigraphy, or dosimeter sensors.MIR-2024-001WO 26-Sep-2025 Specification_Final 17. The method as claimed in any preceding claim wherein at least one dosimetric quantity data value is derived using surrogate quantities measured using other medical imaging sensors.

18. The method as claimed in any preceding claim wherein the associated uncertainty for the patient treatment data value is derived from measurements using surrogate quantities measured using other medical imaging sensors.

19. The method as claimed in claim 17 or claim 18 wherein other medical imaging sensors include one or more of: computed tomography (CT) and magnetic resonance imaging (MRI) sensors.

20. The method as claimed in any preceding claim wherein at least one dosimetric quantity data value is retrieved from the patient’s historical data.

21. The method as claimed in any preceding claim wherein the associated uncertainty for the dosimetric quantity data value is derived from at least one of: the patient’s historical data, prior data.

22. The method as claimed in any preceding claim wherein at least one of the dosimetric quantity data values and associated uncertainties are assessed for quality and excluded from further processing to be part of the output when they do not meet a quality threshold.

23. The method as claimed in claim 22 wherein the quality assessment involves comparison of the dosimetric quantity data values and / or associated uncertainties to at least one of: biological constraints, physical constraints, the patient’s historical data, patient population data, other TRC model candidates for the volume.

24. The method as claimed in claim 23 wherein the comparison for the quality assessment of at least one of: the patient treatment data values and the associated uncertainty is performed by an operator or automated process.MIR-2024-001WO 26-Sep-2025 Specification_Final 25. The method as claimed in any preceding claim wherein determination of the uncertainty associated with the time cumulative quantities comprises at least one of: physical half-life of any radionuclides, derived quantities which preclude determination of one or more dosimetric quantity values, or other intermediate quantities such as mathematical parameters of any curves which are comprised by the TRC.

25. A system for determining the value and uncertainty in patient treatment data as part of a patient-specific dosimetry in radiopharmaceutical therapy (RPT), comprising: a database for storing patient data, a display for displaying information: a processor configured to perform the following steps: obtaining a dataset from the database comprising of one or more dosimetric quantity data values and associated uncertainties at one or more timepoints each representing a quantity of dosimetric interest associated with at least one radiopharmaceutical agent present within a volume of the patient; selecting a dosimetric quantity time representation curve (TRC) model comprised of one or more curves which contiguously span from the time of administration of the radiopharmaceutical; determining one or more parameters associated with at least one of the one or more curves comprising the selected TRC model where each of the one or more curves is directly calculated from the dosimetric quantity data values; determining from the one or more curves a mathematical function which directly relates the time cumulative quantity to the dosimetric quantity data values; calculating the cumulative dosimetric quantity data value using the mathematical function;MIR-2024-001WO 26-Sep-2025 Specification_Final calculating the uncertainty associated with the cumulative dosimetric quantity data value using the mathematical function by a method of propagation of uncertainty; and returning the cumulative dosimetric quantity value and associated uncertainty as an output, to be displayed on the display; wherein the output of the cumulative dosimetric quantity data value and associated uncertainty is used in at least one of: the planning, adjustment, or assessment of dosimetry data for future radiopharmaceutical therapy, or the planning, adjustment or assessment of future radiotherapy dosages, for one or more patients.

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