Radiopharmaceutical Biodistribution and Dosimetry

Abstract

Nuclear medicine is a medical specialty, where diagnostic and or therapeutic radioisotopes are used to study the physiology of organs and the metabolism of various types of tumors. Pharmaceuticals labeled with radionuclides (radiopharmaceuticals) are studied at pre-clinical level before being used in humans. Animals (Rodents) are generally used to study the biokinetics of tracer in a group of predefined organs. The extrapolation of the results of these studies from animals to humans provides an estimate of the behavior of the radiopharmaceuticals and the irradiation delivered clinically. Nuclear Medicine is fundamentally based on Radiopharmaceuticals whose biodistribution in disease and healthy organ result in either images that are diagnostically useful or local irradiation of tissue that is therapeutically beneficial for treatment of tumors. In result, in most procedures the biodistribution is primarily dependent on clearance of the radiopharmaceuticals from the blood into organs, tissues or lesions. Radiation is harmful for living beings and hence radiation toxicity is required to assess for new radiopharmaceutical which can be calculated by following the methodology of Internal dose calculation. Basic principle of Internal dosimetry and calculation methodology are explained in this chapter.

1. Introduction

It has been well known that ionizing radiation is harmful to humans or living beings since the era of X-ray discovery by WC Roentgen in 1985. Application of ionizing radiation should minimize and or optimize according to its requirement while allowing its beneficial application. In 1924, radioactive materials as biological tracers’ were used by Georg de Hevesy and colleagues for radiotracer studies of the kinetics of Lead-210 (²¹⁰Pb) and Bismuth-210 (²¹⁰Bi) in animals. Iodine-131 (¹³¹I) and Technetium-99m (^99mTc) are the predominant radionuclides currently in diagnostic and therapeutic nuclear medicine studies [1]. Application of radiopharmaceuticals inside the human body that emit radiation photons which is detected by detectors available outside of the body to investigate the movements of body parts and help in finding functional information is interesting and revolutionary achievement of nuclear medicine technique. Nuclear Medicine procedures can be diagnostic; that is, studying structures and processes to diagnose diseases/tumors and guide medical response to potential human health issues. Almost 95% of Nuclear Medicine procedures are Diagnostic procedures, but radiopharmaceuticals used in nuclear medicine may also be used for the treatment of tumors as therapeutic procedures; that is, administering higher amounts of radiation doses with the aim of using radiation to kill tunours tissues in the body. From last one decade, use of therapeutic radiopharmaceuticals increased for the treatment of various tumors as many new therapeutic radiopharmaceuticals such as ¹⁷⁷Lu-DOTATATE, ¹⁷⁷Lu-PSMA617, ¹⁷⁷Lu-Rituximab etc. are innovated.

Incidence of thyroid cancer were high in the 1940s and 1950s in pediatric patients treated immediately after birth for thymus enlargement [2]. In a similar time period, higher amounts of radiation doses were given to patients suffering from spondylitis; the treatment was effective for treatment of spondylitis, but there was a radiation side effects which was associated with a high rate of leukemia. It was also observed that Radiologists and radiation therapists operating in the early years of radiation medicine suffered high rates of leukemia and pernicious anemia because of radiation awareness. In the early years, ²²⁶Ra was the principal radionuclide used in radiation therapy in which high-activity sources were placed on or near tumors to attempt to treat them. Modern external radiation therapy still employs a number of brachytherapy techniques involving different radionuclides and radiation-producing machines that deliver high doses of radiation to malignant tissues while minimizing dose to healthy body tissues. Therapeutic radiopharmaceuticals are generally administered intravenously or orally and are intended to deliver cytotoxic levels of radiation selectively to tumor sites. Specific targeted delivery is generally achieved with the use of a targeting moiety, such as a peptide or an antibody (¹⁷⁷Lu-DOTATATE, ¹⁷⁷Lu-Rituximab etc). Organ seeking radionuclides are naturally directed to a particular organ, reaching a desired organ without a ligand such as ¹³¹I for thyroid cancer and ¹⁵³Sm for bone palliation.

2. Radiopharmaceuticals

Radiopharmaceuticals contain radioisotopes and biological molecules where radioisotopes bound to biological molecules that are target specific organs, tissues or cells within the human body. These radioactive drugs can be used for the diagnosis and, increasingly, for the therapy of diseases. In nuclear medicine, more than 95% of the radiopharmaceuticals are used for diagnostic purposes, while the rest are used for therapeutic treatment. Radiopharmaceuticals should have minimal pharmacologic effect, because in most cases they are used in tracer quantities. Radiopharmaceuticals should be sterile and pyrogen free, and should undergo all quality control measures required of a conventional drug as they are administered to humans. A radiopharmaceutical may be a radioactive element such as ¹³³Xe, or a labeled compound such as ¹⁷⁷Lu-DOTATATE, ¹³¹I-iodinated proteins and ^99mTc-labeled compounds. Although the term radiopharmaceutical is most commonly used, other terms such as radiotracer, radio-diagnostic agent or radio-therapeutic agent, and tracer have been used by various groups. In the 1920s George de Hevesy coined the term radio-indicator or radiotracer, which introduced the tracer principle in biomedical sciences. A radiopharmaceutical term refers two terms and these are, a radionuclide and a pharmaceutical. Characteristics of these two terms radionuclide and pharmaceutical direct the use of radiopharmaceuticals. For designing a radiopharmaceutical, a pharmaceutical is first chosen on the basis of its preferential localization in a given organ or its participation in the physiologic function of the organ and this is verified by biodistribution of their pharmaceutical in concern organ or tissues or diseases. Then a suitable radionuclide either diagnostic or therapeutic radionuclide is tagged onto the selected pharmaceutical such that after administration of the radiopharmaceutical, radiations emitted from it are detected by a radiation detector of Gamma Camera or PET. The selection of pharmaceutical should be safe and nontoxic for human administration. Radiations from the radionuclide of choice should be easily detected by nuclear instruments, and the radiation dose to the patient should be minimal. Radiopharmaceutical must also be sterile, pyrogen free, safe for human use, and efficacious for a specific indication.

Radiopharmaceutical is a backbone of nuclear medicine, and its advances have the potential to affect imaging and radionuclide therapy developments and application protocols. Nuclear Medicine is fundamentally based on Radiopharmaceuticals whose biodistribution in organ, tissue or disease result in either images that are diagnostically useful or local irradiation of tissue that is therapeutically beneficial. All nuclear medicine procedures are dependent on the optimal biodistribution of radiopharmaceuticals in either for obtaining metabolic information from the images in diagnostic studies or for delivering maximally tolerated therapeutic doses of radiation to tumors in therapeutic studies. Hence, the biodistribution is primarily dependent on clearance of the radiopharmaceuticals from the blood into organs, tissues or lesions and it impact the overall efficacy Nuclear Medicine procedures.

Although several problems are associated with the clinical use of radiopharmaceuticals, important factors affecting the biodistribution of radiopharmaceuticals are:

1. Preparation and formulation of radiopharmaceutical.

2. Radiopharmaceutical administration techniques and procedures;

3. Pathophysiological and Biochemical changes;

4. factors caused by medical procedures; and.

5. factors associated with drug therapy or drug interaction.

In recent years, radiopharmaceuticals are re-emerging as attractive anticancer agents. To validate a radiopharmaceutical, it is desirous for the radiopharmaceutical to be target specific, very selective, and deliverable against tumors of a given, molecularly defined cancer for which it is intended to treat.

Development of new radiopharmaceuticals for clinical use typically follow complex drug-development sequences that expend considerable resources and time. Most of them are molecularly targeted radiopharmaceuticals for either diagnostic or therapeutic, and therefore, might only benefit a subgroup of cancer patients whose tumors express specific targets. Conventional drug-development sequences, which focus on preclinical in vitro and in vivo studies justifying early-phase I or II trials, and then if warranted, late-phase III trials without assessment of the target expression, are suboptimal in the clinical evaluation of radiopharmaceuticals. Radiopharmaceutical drug-development sequences therefore might benefit from ‘enrichment’ approaches that more reliably reduce patient resources and shorten trial timelines. Radiopharmaceutical validation might be considered one of those enrichment approaches.

Validation of radiopharmaceutical is basically a fundamental process whereby preclinical or clinical investigations demonstrate agent performance as being suitable for its intended clinical use. Successful validation improves efficiency in the drug-development sequence by increasing predictive power and by shortening timelines in which a treatment effect would be expected to be reasonably large.

It is well known that radiation can cause deleterious effects in living beings. It is therefore essential to assess these effects in humans for a given nuclear medicine procedure. The damaging effects arise from the absorption of energy in tissues and depend on a number of factors: these are-.

1. the activity of the administered radiopharmaceutical during nuclear medicine procedures.

2. the physical half-lives, biological half-lives and effective half-lives of the used radiopharmaceutical,

3. the spatial distribution of radiopharmaceutical and their metabolic fate in the subject,

4. the fraction of energy released per disintegration of radionuclide of radiopharmaceuticals from a source organ that is absorbed in the particular target volume of organ, and.

5. the shape of organ, composition of organ, and location of the source and target organs.

The physical characteristics of a radionuclide are well known and established which is available in tabular form. Biological information which depends on physiology of subjects can be obtained from various experimental studies in humans and animals or phantom model studies.

The ultimate test of the quality of a radiopharmaceutical is its biodistribution. Often the first indication that something might be wrong with a radiopharmaceutical is an unexpected pattern of biodistribution found during an imaging procedure.

Animal biodistribution studies are always performed during the development of a novel radiopharmaceutical before it is first administered to human for clinical trial. These studies may be done in animals with normal phenotypes but more increasingly are being performed in transgenic animals which have certain characteristics which mirror those of the ultimate human recipients of the tracer.

Biodistribution studies in animals may be performed by manufacturers of licensed radiopharmaceuticals as part of their Quality Assurance procedure before preparing a batch of kits for human applications.

Now a days, biodistribution studies mostly performed by imaging the animals on micro SPECT or PET imaging devices which avoid the killing of animals at certain times after administration of the radiopharmaceutical and measuring the distribution of the radioactivity in tissues by counting or autoradiographic techniques as used in conventional biodistribution studies. Once a radiopharmaceutical agent is administered to a patient, the biodistribution process occurs. This process consists of the substance’s absorption, distribution, metabolism and excretion. When the normal biodistribution pattern of a substance is known, any irregular pattern may suggest the presence of disease.

3. Internal dose calculation

Radiation dosimetry is the calculation of the absorbed dose in matter and tissue resulting from the exposure to ionizing radiation. It is broadly classified as external dosimetry and internal dosimetry. External dosimetry is the measurement of radiation dose from exposure of external sources of radiation which is used in external beam radiotherapy whereas internal dosimetry deals with the determination of the amount and spatial and temporal distribution of radiation energy deposited in tissue by radionuclides within the body. Internal dosimetry has been applied to the determination of tissue doses and related quantities for occupational exposures in radiation protection, and, diagnostic and therapeutic exposures in nuclear medicine.

Internal Radiation dose estimates are performed via calculations, not measurements. Usually, they are based on standardized models of the human body and often on standardized models of radiopharmaceutical behavior in the body as well. Internal dose calculations are basically depending on two components: biology components (refers the biodistribution and retention of the radiopharmaceuticals), quite complex and require special phantoms and models and physics components basically physical part (refers the energy transport and their deposition within the body), are typically well known and stored in look-up tables. In early ages, printed paper tables, look-up tables were used for dosimetry calculation which was quite tedious work. But now a days, dosimetry software such as OLINDA/EXM, DOSISOFT, NUKDOS etc. are developed where all the physical parameters are integrated in the software. The quantification of data from human or animal studies and treatment of it by a kinetic model, the analysis of which ultimately yields the numbers of disintegrations that have occurred in all significant source organs within the body are important and needed to collect these data for dosimetry calculation. Combination of these values with dose factors from the standardized phantoms (which give the dose to target regions per disintegration occurring in a source region) that yields the dose estimates that are of interest.

Preclinical studies from animal model for radiation dose estimation always required for dosimetry correction but dose estimation based on human data are almost necessarily preferred, even though human based data are associated with some uncertainties. Data collection-based animal data is an essential and first step for new radiopharmaceuticals for their dose evaluation and must be followed by carefully designed and executed human studies that better establish the dose estimates. Collection of data is a very important overview document on data gathering and quantification for dosimetry. To determine the activity-time profile of the radioactivity in source regions, the following question should be solved which are-.

1. What are the source organs? (Identification of source organs).

2. How fast does the radiopharmaceuticals accumulate in these source organs? (Uptake of Radiopharmaceuticals).

3. How long does the radiopharmaceuticals remain in the source organs?

4. How much activity of radiopharmaceutical is in the source organs?

The above mention first question locate and identify the source organs, while the second and third questions relate to the appropriate number of imaging time points to be made in the source regions as well as the timing of these measurements. The fourth question explain quantification of images and/or sampling of tissues and excreta. Each source organ must be identified and its uptake and retention of radiopharmaceuticals as a function of time must be calculated. This provides the data required to calculate cumulated activity or residence time in all source organs. Each organ exhibiting significant radionuclide uptake should be evaluated directly where possible. The remainder of the body (total body minus the source organs) must usually be considered as a potential source as well. Mathematical models that describe the kinetic processes of a particular agent may be used to predict its behavior in organs where direct measurements are not possible, but where sufficient independent knowledge about the physiology of the organ is available to specify its interrelationship with the organs or tissues whose uptake and retention can be measured directly.

4. Clinical radiopharmaceutical dosimetry

Both diagnostic or therapeutic radiopharmaceuticals need to be estimated their dosimetry before their clinical use in humans to assess the radiation toxicity and overall effectiveness for the diagnosis or treatment of disease. The medical decision in order to treat a patient will depend on tumors and the organs at risk.

According to the article 56.1, of the Council Directive 2013/59/Euratom (The Council of the European Union, 2014), “For all medical exposure of patients for radiotherapeutic purposes, exposures of target volumes shall be individually planned and their delivery appropriately verified taking into account that doses to non-target volumes and tissues shall be as low as reasonably achievable and consistent with the intended radiotherapeutic purpose of the exposure”. In the article 56.6, the same document mentioned “Member States shall ensure that in the case of a patient undergoing treatment or diagnosis with radionuclides, the practitioner or the undertaking, as specified by Member States, provides the patient or their representative with information on the risks of ionizing radiation and appropriate instructions with a view to restricting doses to persons in contact with the patient as far as reasonably achievable.

Dosimetry information will also help to modulate the therapeutic activity, which means that depending on the dosimetry results the physician will prescribe more or less activity. This is called “personalized medicine”, where every patient is given what he or she required keeping in mind to protect critical organ and threshold radiation dose for critical organ. There are two types of situation where physician recommend the radionuclide therapy such as one cycle or single treatment and subsequent cycles.

when the radionuclide therapy consists in only one cycle of treatment and when cycles of treatment are repeated and close enough so that the results obtained on one cycle can be used to plan subsequent cycles.

In the one cycle of treatment, patient may follow a preparation process. Then, a low amount of activity will be administered to the patient to proceed with the dosimetry measurements. In the case of thyroid cancer cell, a saturation effect, called stunning is well known, then tracer activities as low as 35 MBq can be used to perform a pre-therapeutic dosimetry study.

For the subsequent cycle treatment situation, Nuclear Medicine Physicist will estimate absorbed doses to certain organ at risk for the first therapy cycle. Under the assumption that organs at risk will have same biokinetics among all treatment cycles, a dosimetry extrapolation can be done in order to calculate the activity that can safely be administered for subsequent cycles. This administration scheme could be implemented for PRRT patients. However now a day’s patients receive the fixed activity for each cycle of treatment (7.4 GBq per cycle, five cycles of treatment subject to follow maximum cumulated absorbed dose delivered of 23 Gy to Kidney for stopping radionuclide therapy) [3].

Clinical dosimetry is an evolving area in which different patient pathologies are explained and the treatment is optimized during the time due to new equipment, new radiopharmaceuticals, more professional staff, dosimetry software availability (to acquire, to reconstruct, to correct images), new regulations, etc. In fact, implementing clinical dosimetry in practice is quite a demanding task. This is why different dosimetry approaches have been proposed, using mostly academic software as research tools, even though commercial software is becoming increasingly available.

The most famous and accepted radiopharmaceutical calculation scheme was proposed by the Medical Internal Radiation Dose (MIRD) Committee.

4.1 MIRD schema for absorbed dose determination

MIRD committee is part of the Society of Nuclear Medicine & Molecular Imaging (SNMMI). It develops standard methods, models, assumptions, and mathematical schemas for assessing internal dosimetry from administrated radiopharmaceuticals.

The Medical Internal Radiation Dose (MIRD) Committee started its publications in 1968 with the MIRD Pamphlet No. 1: Schema for absorbed-dose calculation for biologically distributed radionuclides. This first document was revised in 1975 and further publications published in 1988 and 1991 containing examples. In 2009, the MIRD Pamphlet No. 21 [4] proposed a new nomenclature, intended to conciliate MIRD and ICRP terminology. The main aims of the MIRD committee is to propose means to compute absorbed doses, several publications are intended to explain the complexity of nuclear medicine imaging quantification. In 1999 the MIRD Pamphlet No. 16 [5] showed quantification of images using planar images. In the same year the MIRD No. 17 [6] showed dosimetry calculation methodology for non-uniform activity distributions at voxel level. In 2012 the MIRD Pamphlet No. 23 [7] explained the quantification of SPECT images targeting for patient-specific 3D-dosimetry. In 2016 the MIRD Pamphlet No. 26 [8] was published, a joint document between the EANM and MIRD Committee and explained SPECT quantification for ¹⁷⁷Lu radionuclide.

4.2 Theoretical concept of absorbed dose and biokinetics of radiopharmaceuticals

Absorbed dose (D) is the energy (E) absorbed in a particular mass of tissue, divided by the tissue mass (m):

$$\mathit{D}=\frac{\mathit{E}}{\mathit{m}}$$E1

In radionuclide therapy:

E = number of radionuclide disintegrations in a particular volume × energy emitted per disintegration of the radionuclide × fraction of emitted energy that is absorbed by a particular (target) mass.

Number of radionuclide disintegrations in a particular volume for E depends on the half-life of the radionuclide and its spatial and temporal distribution. Number of radionuclide disintegrations is analogous to Cumulated Activity (Ã) which is the amount of activity in the source organ and the time over which it presents in source organ. Distribution of radionuclides is typically obtained by imaging or sampling. Images collected at different times after injection of the radionuclides/radiopharmaceuticals are used to estimate the amount or concentration of radioactivity in a specific region. The level of activity obtained at different times after injection, plotted against time, gives a time-activity curve for a particular organ. The integral of this curve gives the total number of disintegrations or the cumulated activity (Ã) for the region.

Energy emitted per disintegration of the radionuclide is the total energy (e.g., gamma, beta particle, Auger electron, or alpha particle) emitted per disintegration of the radionuclide. This is a characteristic of the radionuclide and is independent of all other factors involved in calculating absorbed dose.

Fraction of emitted energy that is absorbed by a particular target volume depends on the emission type of radiation, energy of radiation photons, and also the geometry and characteristics of the source and target organs which provide a net factor and this factor used to converts the total energy emitted in a particular source organs to that absorbed in the organs or in other organs. This absorbed fraction factor is conventionally calculated using the anthropomorphic phantom studies but it is determined generally by Monte Carlo calculation. The spectrum of emission types will determine the fraction of energy emitted by a particular radionuclide that is absorbed by a particular target mass. Radionuclide emissions may be broadly categorized according to their absorption properties. Particulate emissions, such as beta or alpha particles are generally absorbed within the tissue of origin because of short range. Photons, depending on their energy, will deposit energy in both the source tissue and other adjacent and nonadjacent tissues. Various methods are used for calculation of internal dose.

5. MIRD committee schema

Internal dose calculation in nuclear medicine (NM) is normally used the techniques, equations, and resources provided by the Medical Internal Radiation Dose Committee of the society of NM. To yield the absorbed dose to the target, the absorbed energy (E) is divided by the mass of the target which is symbolically expressed in the form of following Eq. (2).

$${\mathit{D}}_{\mathit{T}\leftarrow \mathit{S}}=\frac{{\stackrel{\sim }{\mathit{A}}}_{\mathit{S}}\times \mathit{∆}\times {\mathit{\phi }}_{\mathit{T}\leftarrow \mathit{S}}}{{\mathit{M}}_{\mathit{T}}}$$E2

Where ${\stackrel{\sim }{\mathit{A}}}_{\mathit{S}}$ cumulated activity in source region S; Δ energy emitted by the radionuclide per disintegration; ${\mathit{\phi }}_{\mathit{T}\leftarrow \mathit{S}}$ fraction of energy emitted by the radionuclide in source region S that is absorbed in the target region, T; and ${\mathit{M}}_{\mathit{T}}$ mass of region T.

The Eq. (2) is the starting point for most current approaches to absorbed dose estimation. This equation describes the dose contribution to a target region from a single region. The derivation as well as the conceptual framework used to arrive at this expression is attributed to the early work of the MIRD Committee, which also established the most commonly used practical approach for estimating absorbed dose. The MIRD Committee reduced Eq. (1) into a product, the cumulated activity in a source region and S, the absorbed dose to a target region per unit cumulated activity in the sources given by single Eq. (3).

$$D=\stackrel{\sim }{A}\times S=A_0\times \tau \times S$$E3

$\tau$ is the residence time which is simply equal to Ã/A₀ and S is given by-.

$$S=\frac{k{\sum }_i{n}_i{E}_i{\varphi }_i}{m}$$E4

There are various anthropomorphic body models which have been used for determination of absorption fraction or S-value. Current generation of anthropomorphic phantoms began with the development of the Fisher-Snyder phantom which employed a combination of geometric shapes e.g. spheres, cylinders, cones, etc. to create a reasonably accurate representation of the body [6, 9, 10, 11, 12, 13, 14, 15]. Monte Carlo computer programs is used to simulate the creation and transport of photons through these various structures in the body [13]. Cristy and Eckerman modified the adult male model and developed models for a series of individuals of different size and age [16, 17, 18, 19, 20].

A generalized expression for calculating internal dose, which may describe the equations shown in publications by different authors especially in OLINDA dosimetry software, can be calculated by the following equation:

$$D=N\times \mathit{DF}$$E5

N is the number of nuclear transitions that occur in source region S analogous to Ã_S, and DF is a “dose factor” analogous to S factor.

6. Implementation of clinical dosimetry

The dosimetry calculation steps or dosimetry chain is related with the phases that are associated to analyze all images and data in a Gamma Camera or SPECT/CT or PET/CT system, where nuclear medicine physicist can calculate the absorbed dose for a specific organ/tissue. The dosimetry calculation chain is addressed collection of data, arranging the data and analyzing the data for dose calculation. There is few software that has been created for this purpose, some are open-source software, other from commercial companies. The graphical view of dosimetry calculation chain is shown in Figure 1.

Figure 1.

Clinical dosimetric chain.

In general, the following steps required to be considered for dose calculation in almost all the dosimetry software.

6.1 System calibration factor

Calibration factor is a most important parameter that needs to be considered for absolute quantification. The calibration factor can be derived from the sensitivity of the SPECT/CT system.

The system calibration factor must be measured at some time before or after radiopharmaceutical administration in a separate experiment. The count rate per unit activity (in units of, e.g., cpm/MBq) represents the calibration factor.

A standard of known activity of the same radionuclide to be used for administration to subjects, usually a few tens of MBq in a suitable container. The standard should be counted in air for a fixed time (e.g., 5 minutes) at a source-to-collimator distance that approximates that of the patient midline distance used for the imaging study.

In principle the acquisition for calibration factor should be done using the same protocol used for patient imaging. Normally a phantom is used for that purpose. The calibration factor basically used to relate the number of counts within the image per voxel with the quantified activity per voxel.

Patient image acquisition: Depending on the availability of system, software and dosimetry protocol, images are acquired which must include section of the patient body, where critical organs and/or tumors are present. Normally several times point measurements are needed. At least three imaging time points over the physical half-life of radionuclide/radiopharmaceuticals are recommended to acquire for the best curve-fitting.

Corrections: Corrections like attenuation, scatter and partial volume corrections are implemented on every time points imaging to improve the counts. These corrections improve the quantitative accuracy in internal dosimetry which impact the dosimetry calculation.

6.2 Dead time correction

This correction must be done when high-count rates are present. Gamma camera is a para-lizable system, a second event occurring within the dead time due to the first event will not be recorded but will also initiate a pile-up effect. This means that not only will be recorded counting rate be less than the true counting rate but that, at high sample activities, the recorded counting rate will begin to decrease. Two source method proposed by Cherry [21, 22, 23] is used to correct the dead time correction.

6.3 Background correction

Background count is one which is originated from activity in the subject’s body that is outside of desired source region on image, it might be scattered radiation from region of interest. Thus, scaling factor may be needed to correct the number of counts in background ROI. Alternatively, one may simply subtract the number of counts per pixel in Background ROI from the number of counts per pixel in the source ROI.

6.4 Organ overlapping correction

Organ overlapping can occurs for some organs or tumors, and this is the major drawback for planar quantification. For example, right kidney and liver are frequently partially superimposed on planar images.

M. Stabins propose the two approximation approaches. One approximation: for pairs organs, such as kidneys and lungs, is to quantify the activity in one of the organs in which there is no overlap, then double the number of counts obtained in this organ to estimate the counts in the two organs. The second approximation: is to draw an ROI over the organ region in scans where there is overlap, count the number of pixels and record the count per pixel, then use a ROI from another image in which there is no overlap; record the number of pixel from this new image, then multiply the count rate per pixel from the first image by the number of pixels in the second image.

6.5 Scatter correction

Scatter correction can be done by either using scatter correction technique such as dual or triple energy window methods during acquisition of images. It can also be corrected by using processing software after acquisition of images.

Scatter correction must be applied to determine the amount of scatter photons included into the main energy window at its contribution to the total amount of counts within this energy window. The scatter counts will degrade the quality of the acquired image and it will affect the quantification.

In Energy window method one, two or more energy windows additionally to the main photo-peak energy window are implemented. Hence, one can estimate either the complete energy spectrum of scatter counts, or at least the integral of that spectrum from the lower energy cut-off of the photo-peak window to the upper-energy cut-off of that window, subtraction of the scattered counts, pixel by pixel, is required to correct it [6].

The dual-energy window (DEW), using just one energy window below the main, both with the same width. An assumption is made, considering that the number of scattered photons in the “low energy” window is proportional to the number of scattered photons in the main energy window. The number of primary photons is given by:

$${\mathit{C}}_{\mathit{\text{Primary}}}={\mathit{C}}_{\mathit{\text{Total}}}-\mathit{\kappa }.{\mathit{C}}_{\mathit{\text{scatter}}}$$E6

Where κ is a constant value, found to be 0.5 for ^99mTc.

Triple Energy Window (TEW) method employs two energy windows close to the main energy window. The number of scattered photons can be determined as follows:

$${\mathit{C}}_{\mathit{\text{Scatter}}}\cong \left(\frac{{\mathit{C}}_{\mathit{\text{left}}}}{{\mathit{W}}_{\mathit{S}}}+\frac{{\mathit{C}}_{\mathit{\text{Right}}}}{{\mathit{W}}_{\mathit{s}}}\right).\frac{{\mathit{W}}_{\mathit{m}}}{2}$$E7

Where C_left and C_Right are the acquired count from the two energy windows W_s, placed above and under the main energy window W_m. Then the amount of scatter counts can be estimated from the trapezoidal region having a left height of $\frac{C_{\mathit{\text{left}}}}{W_S}$, a right height of $\frac{C_{\mathit{\text{Right}}}}{W_s}$, and a base of W_m. Figure 2 shows an illustration of this trapezoidal correction.

Figure 2.

The graphical representation of trapezoidal correction.

Therefore, using the result from Eq. (6), the count of primary photons is given by:

$${\mathit{C}}_{\mathit{\text{Primary}}}={\mathit{C}}_{\mathit{\text{Total}}}-\mathit{\kappa }.{\mathit{C}}_{\mathit{\text{scatter}}}$$E8

6.6 Attenuation correction (transmission method)

Attenuation compensation is required to maintain the intensity of photon which were lost during interaction of photons with tissues in body which impair the detection. Quantification from images are influenced by attenuation of photons.

In the conjugate view, the attenuation correction can be done by using a transmission factor (T_f). The attenuation is measured by acquisition of a separate transmission scan sometimes using a ⁵⁷Co sheet source, or flood phantoms (using ^99mTc or ideally the isotope used for emission image acquisitions.

The transmission factor T_f can be expressed as follows:

$${\mathit{T}}_{\mathit{f}}=\frac{{\left[\frac{\mathit{dN}}{\mathit{dt}}\right]}_{\mathit{Roi},\mathit{\text{object}}}}{{\left[\frac{\mathit{dN}}{\mathit{dt}}\right]}_{\mathit{Roi},\mathit{no}-\mathit{\text{object}}}}$$E9

Region of interest (ROI) is drawn on images acquired with object and without object.

In a whole-body scan, keep same bed speed for both scans.

If the isotope for transmission and isotope for emission images are different then a correction must be applied due to differences in linear attenuation coefficients between radionuclides with their energies. In this case, the transmission factor can be scaled and corrected as mention in below Eq. (10).

$${\mathit{T}}_{\mathit{f}}={\mathit{e}}^{(\frac{\mathit{\mu }}{{\mathit{\mu }}_{\mathit{\text{Measured}}}}ln\left({\mathit{T}}_{\mathit{\text{Measured}}}\right)}$$E10

Where μ is the linear attenuation coefficient associated to the injected radionuclide, μ_measured and T_measured are the attenuation coefficient and the transmission factor of the radionuclide used for the transmission scan, respectively.

Chang method which is an analytical method assuming homogeneous density and using a fixed linear attenuation coefficient to correct attenuation may be used. Chang method is applied after reconstruction, considering each pixel of the image, however, this method is assuming a constant attenuation coefficient. This method is not used nowadays, because of the hybrid SPECT/CT technology available in the nuclear medicine departments. The impact of Chang method in attenuation correction can be seen in Figure 3.

Figure 3.

Effect of Chang attenuation correction on SPECT images of a 20-cm diameter cylinder.

In SPECT/CT where inbuilt CT images used for attenuation correction, attenuation map is generated from CT images of patient. Because of heterogeneity in tissue composition in the human body, the estimation of an accurate and patient-specific attenuation map for nonuniform attenuation compensation is necessary. Attenuation map is a voxel-by-voxel representation of the linear attenuation coefficients at the SPECT photon energy. Generally, these maps have lower noise, better spatial resolution, better contrast and are faster and easier to acquire [7, 22]. The attenuation map is expressed by the matrix of CT numbers associated with each pixel in a tomographic slice in CT images. The CT number can be defined as it is shown in Eq. (11).

$$\mathit{CT}\#=\left(\frac{\mathit{\mu }}{{\mathit{\mu }}_{{\mathit{H}}_2\mathit{O}}}-1\right)\ast 1000$$E11

Where μ is the linear attenuation coefficient of the medium and μ_H2Ois the linear attenuation coefficient of water. CT number units are Hounsfield Units (HU). Because linear attenuation coefficients are energy-dependent, the CT numbers at the x-ray energy must be scaled to the energy of the radioisotopes used for images.

The International Atomic Energy Agency (IAEA) in their book dedicated to Nuclear Medicine teachers and students [22, 23, 24, 25, 26] proposed to generated the attenuation map μ(ℎ) considering the attenuation coefficients for water and bone as follows (ℎ = Hounsfield units):

$$\mathit{\mu }\left(\mathit{h}\right)=\frac{1000+\mathit{h}}{1000}{\mathit{\mu }}_{\mathit{\text{water}}}\mathit{\text{for}}\mathit{h}\le 0$$

$$\mathit{\mu }\left(\mathit{h}\right)={\mathit{\mu }}_{\mathit{\text{water}}}+\frac{\mathit{h}}{{\mathit{h}}_{\mathit{\text{bone}}}}\left({\mathit{\mu }}_{\mathit{\text{bone}}}-{\mathit{\mu }}_{\mathit{\text{water}}}\right)\mathit{\text{for}}0<\mathit{h}<{\mathit{h}}_{\mathit{\text{bone}}}$$

$$\mathit{\mu }\left(\mathit{h}\right)=\frac{\mathit{h}}{{\mathit{h}}_{\mathit{\text{bone}}}}{\mathit{\mu }}_{\mathit{\text{bone}}}\mathit{\text{for}}\mathit{h}<{\mathit{h}}_{\mathit{\text{bone}}}$$

6.7 Kinetic analysis

The bio-kinetics of a radiopharmaceutical can be addressed knowing the relationship of the activity (or number of counts) per time point. By plotting this relationship among all pairs (time, activity), a time activity curve (TAC) can be generated. Figure 4 shows a theoretical representation of a TAC. Estimating the area under the TAC will produce the time-integrated activity (TIA), which was also known as cumulated activity, in units (Bq.S). Essentially this is a measure of the total number of disintegrations occurring in an organ source containing the radiopharmaceutical.

Figure 4.

A theoretical representation of a TAC.

After gathering a series of whole-body scans or SPECT images at various time points based on selected radiopharmaceuticals that estimate uptake, retention, and/or excretion of radiopharmaceuticals, the next step is to interpret these measurements in such a way as to design a kinetic model that can be used to estimate the number of disintegrations occurring in source organ. In general, three types analysis can take place depending of complexity of data-

1. Direct-Integration Method

   Direct integration in which directly integrate under the actual measured values by a number of methods. It does not give very much information but it does allow to calculate the number of disintegrations rather easily. The most common method used is the trapezoidal method, simply approximating the area by a series of trapezoids.

2. Least-square Analysis

   An alternative to direct integration of a data set is to attempt to fit curves of a given shape to the data. The curves are represented by mathematical expressions that can be directly integrated. The most common approach is to attempt to characterize a set of data by a series of exponential terms, as many systems are well represented by this form, and exponential terms are easy to integrate. In general, the approach is to minimize the sum of the squared distance of the data points from the fitted curve. The curve will have the form:

   $$A_t=a_1{e}^{-b_{1t}}+a_2{e}^{-b_{2}t}+\dots$$E12

   The difference of the square between each point and the result of the fitted curve at that point and minimizing this quantity by taking the derivative of this expression with respect to each of the unknowns, a_i and b_i, and setting it equal to zero. Once the ideal estimates of a_i and b_i are obtained, the integration of A(t) from zero to infinity is expressed as:

   $${\int }_0^{\infty }A\left(t\right)d\left(t\right)=\frac{a_1}{b_1}+\frac{a_2}{b_2}+\dots$$E13

   Here the units of coefficients a_i are the same as the units of activity and the integration of it is the cumulated activity and the units of the b_i are time⁻¹. If the coefficients are the fractions of the administered activity or radiopharmaceuticals, then the area under the curve represents the normalized cumulated activity (e.g. Bq-h/Bq).

3. Compartmental Analysis

   Biological system where a group of compartments interconnected through transfer rate coefficient. Cumulated activity of the various compartments requires a system of coupled differential equations expressing transfer of the radiopharmaceutical between compartments and elimination from the system. The result to the time-activity curve for each compartment will be a sum of exponentials, not obtained by least-squares fitting each compartment separately, but obtained by varying the transfer rate coefficients between compartments until the data are well fit by the model.

Absorbed dose calculation: There are several ways to calculate absorbed dose, for instance, the analytical, local energy deposition, dose point kernel, dose voxel kernels, Monte Carlo and Tabular approaches. All these methods will produce different types of outputs, average absorbed dose, absorbed dose maps and voxel-based absorbed dose in which absorbed dose volume histogram can be generated.

6.8 Activity quantification

Activity quantification is very important and this should be determined for a particular ROI/VOI/Structure before Time Activity Curve estimations can generated.

7. Planar imaging

Nowadays, most nuclear medicine department have a single- or dual-head imaging system. These systems can be used to image one section of the patient-body or the patient whole-body. Static, dynamic images or whole-body images can be acquired with these systems. Also, in the case of whole-body images an auto-contour can be activated to generate images as close as possible of the patient.

According to MIRD Pamphlet 16, “this method will be greatest for radiopharmaceuticals distributed in a single region or isolated regions that do not overlap (non-superimposed) in the planar projection”. Figure 5 shows an illustration to introduce the quantification situation.

Figure 5.

Quantification scenario in planar imaging.

In the conjugate view, an object with thickness τ is placed at depth δ. Here, it is assuming of no activity in the medium surrounding the object is considered, and also the medium and the object have same physical properties and no scatter radiation is presented. A differential slice of activity dA, with thickness dr is placed at distance r. Then, this differential of activity is expressed as-.

$$\mathit{dA}={\mathit{C}}_{\mathit{A}}\mathit{dt}$$E14

The amount of activity per unit thickness in the object is:

$${\mathit{C}}_{\mathit{A}}=\frac{\mathit{A}}{\mathit{\tau }}$$E15

The rate of photons detected from this differential thickness in the anterior and posterior views are:

$$\text{Anterior},\frac{{\mathit{d}}^2{\mathit{N}}_{\mathit{A}}}{{\mathit{d}}_{\mathit{t}}{\mathit{d}}_{\mathit{r}}}=\mathit{\kappa }{\mathit{C}}_{\mathit{A}}{\mathit{e}}^{-\mathit{ur}}⟹\frac{\mathit{d}{\mathit{N}}_{\mathit{A}}}{\mathit{dt}}=\mathit{\kappa }{\mathit{C}}_{\mathit{A}}{\int }_{\mathit{\delta }}^{\mathit{\delta }+\mathit{\tau }}{\mathit{e}}^{-\mathit{ur}}\mathit{dr}$$E16

$$\text{Posterior},\frac{{\mathit{d}}^2{\mathit{N}}_{\mathit{P}}}{{\mathit{d}}_{\mathit{t}}{\mathit{d}}_{\mathit{r}}}=\mathit{\kappa }{\mathit{C}}_{\mathit{A}}{\mathit{e}}^{-\mathit{ur}}⟹\frac{\mathit{d}{\mathit{N}}_{\mathit{P}}}{\mathit{dt}}=\mathit{\kappa }{\mathit{C}}_{\mathit{A}}{\int }_{\mathit{\delta }}^{\mathit{\delta }+\mathit{\tau }}{\mathit{e}}^{-\mathit{ur}}\mathit{dr}$$E17

Where ξ is the planar calibration factor of the gamma-camera system, μ is the linear attenuation coefficient. Then the geometric mean of the two count rates is.

$${\left(\frac{\mathit{dN}}{\mathit{dt}}\right)}_{\mathit{\text{geom}}}=\sqrt{\frac{\mathit{d}{\mathit{N}}_{\mathit{A}}}{\mathit{dt}}}\frac{\mathit{d}{\mathit{N}}_{\mathit{P}}}{\mathit{dt}}=\mathbf{K}\mathit{A}\frac{sinh\left(\frac{\mathit{\mu \tau }}{2}\right)}{\left(\frac{\mathit{\mu \tau }}{2}\right)}\sqrt{\mathfrak{H}}$$E18

The attenuation of the emitted photons ($\mathfrak{H}$) through the entire thickness of the medium is given by:

$$\mathfrak{H}\mathfrak{=}{\mathit{e}}^{-\mathit{\mu h}}$$E19

Finally, for the object, the activity can be expressed as follows:

$$\mathit{A}=\frac{1}{\mathit{\kappa }\sqrt{\mathfrak{H}}}{\left(\frac{\mathit{dN}}{\mathit{dt}}\right)}_{\mathit{\text{geom}}}\left(\frac{\frac{\mathit{\mu \tau }}{2}}{sinh\left(\frac{\mathit{\mu \tau }}{2}\right)}\right)=\frac{1}{\mathit{\kappa }\sqrt{\mathfrak{H}}}{\left(\frac{\mathit{dN}}{\mathit{dt}}\right)}_{\mathit{\text{geom}}}$$E20

Where ξ is called the self-attenuation factor of the activity contained in the object.

Now, considering a situation in which many overlaying source regions are presented, such as the case demonstrated in Figure 6, the activity for a source region jth A_j, is given by the general expression.

Figure 6.

An overlaying source region in planar imaging.

$${\mathit{A}}_{\mathit{j}}=\frac{1}{\mathit{\kappa }\sqrt{\mathfrak{H}}}{\left(\frac{\mathit{dN}}{\mathit{dt}}\right)}_{\mathit{\text{geom}}}\left(\frac{\frac{{\mathit{\mu }}_{\mathit{j}}{\mathit{\tau }}_{\mathit{j}}}{2}}{sinh\left(\frac{{\mathit{\mu }}_{\mathit{j}}{\mathit{\tau }}_{\mathit{j}}}{2}\right)}\right)$$E21

The Figures 5 and 6 are ideal case, most of the time patient images are degraded by different physical effects, for example, dead time, background, organ overlapping, scatter and attenuation.

8. Absorbed dose calculation approaches

In radiopharmaceutical dosimetry, the absorbed dose can be calculated using S-values from a reference phantom model.

In targeted radionuclide therapy, the objective is to assess patient-specific dosimetry. Patients are different from reference models used in phantom in terms of total-body weight and size, organs masses, etc. Also, depending on the emission that is within the source, the radiation transport algorithm implemented for absorbed dose calculation may differ. Therefore, considerations regarding the size of the source and targets vs. radiation range are key aspects for the selection of absorbed dose calculation algorithms. Targeted radionuclide Therapeutic patient data sets are represented in 2D (pixel maps) or 3D (voxel maps) images in which the provided information will vary according to the biokinetics of the radiopharmaceutical product inside an organ.

9. Case studies: dose calculation using OLINDA/EXM software

Radiation absorbed dose of organs will be calculated with the help of series (minimum three series) of post therapy whole Body planar images acquired. Figure 7 Shows the Anterior and Posterior Images of post therapy scan with ¹⁷⁷Lu-DOTATATE. A Region of Interest (ROI) could be drawn over the Kidneys, liver, spleen and tumors and counts were extracted.

Figure 7.

The anterior and posterior images of post therapy scan with ¹⁷⁷Lu-DOTATATE.

An important consideration in the extracting of counts from planar images is the drawing of appropriate background ROIs for organs. ROI is drawn outside the body images and subtracted its counts from outside the body is relatively easy (comparison with drawing ROIs for internal body structures). Background ROIs are just small circular or elliptical regions that are placed in an area that seems “reasonable” in representing counts that are underlying the image at all imaging time points where the ROI for the organ or whole body is drawn. Any reasonable placement of the background ROI in the image field will give an estimate of this background count rate.

Numerical values of counts from ROIs drawn over organs in post therapy images were extracted with the help of The ImageJ software (Open-source software). The ImageJ software displayed the counts of ROI over organs as the images at various times can be loaded into the software where the below given formulae was implemented [25, 26]. The source activity A_j is given as:

$$A_j=\sqrt{\frac{I_A.I_P}{e^{-{\mu }_{e}t}}}\left(\frac{f_j}{C}\right)$$

$$f_j=\frac{{\mu }_j{t}_j/2}{sin\left(\frac{{\mu }_{j.}{t}_j}{2}\right)}$$

Where I_A and I_P are the counts over a given time for a given ROI in the anterior and posterior images, t is the patients thickness over the ROI, μ_e is the effective linear attenuation coefficient for the selected radionuclide/radiopharmaceuticals, camera, and the collimator (LEAP), C is the system calibration factor (counts/time per unit activity), and the factor f represents a correction for the source region attenuation coefficient (μ_j) and source thickness (t_j) (i.e., source self-attenuation correction).

10. Stepwise methodology for the calculation of radiation absorbed dose using OLINDA/EXM1 software

1. A. Step-1

2. Analyze the series of patient images, times at which the images are acquired at various time point are calculated. These time points can be calculated simply by spreadsheet program by just subtracting one time from another.

3. B. Step-2

4. I_A and I_P were calculated as explained above.

5. C. Step-3

6. The system calibration factor “C” can be calculated as explained in Calibration Factor paragraph.

7. D. Step-4

8. Activity in the source organs and fraction of administered activity in the source organs were calculated. The percentage of administered activity (% IA) at each time point of images of various organs and tumors were calculated and used in OLINDA/EXM software for absorbed dose calculation.

9. E. Step-5

10. Total number of disintegrations of source organs can be calculated with the help of percentage of injected activity at various time points. Depending on the data collected i.e. % IA of organs, mono-exponential or bi-exponential curve can be fitted in kinetic input form of OLINDA/EXM software and total number of dis-integration can be calculated selecting the particular organs. For tumor and pituitary organs “remainder body” was selected and curve was fitted for the calculation of total number of disintegration (cumulated activity).

11. F. Step-6

12. Radiation absorbed dose of source organs can be calculated using the total number of disintegration of source organs from Step-5 and S-value of selected radionuclide in OLINDA/EXM software.

13. First radionuclide will be selected in OLINDA/EXM for data processing as shown in Figure 8. Then, adult male or adult female will be selected according to patient’s data for Kidney, Liver and Spleen but Sphere model can be used for the tumors as shown in Figure 9.

14. Figures 10–12 of OLINDA/EXM software is shown the fitting the curve for calculation of cumulated dose or total number of disintegrations to dose calculation using the s-value from the software.

Figure 8.

The selection of radionuclide in OLINDA EXM 1 software.

Figure 9.

The selection of models in OLINDA EXM 1 software.

Figure 10.

Data fitting curve in OLINDA EXM 1 software.

Figure 11.

Input of cumulated activity in OLINDA EXM 1 software.

Figure 12.

Display of calculated absorbed dose in OLINDA EXM 1 software.