**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 autocontour 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.

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-.

$$dA = \mathcal{C}\_A dt\tag{14}$$

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

$$\mathbf{C}\_{A} = \frac{A}{\pi} \tag{15}$$

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

**Figure 5.** *Quantification scenario in planar imaging.*

*Radiopharmaceuticals - Current Research for Better Diagnosis and Therapy*

$$\text{Anterior, } \frac{d^2 N\_A}{d\_t d\_r} = \kappa \mathcal{C}\_A e^{-ur} \Longrightarrow \frac{d N\_A}{dt} = \kappa \mathcal{C}\_A \int\_{\delta}^{\delta + \tau} e^{-ur} dr \tag{16}$$

$$\text{Posterior, } \frac{d^2 N\_P}{d\_t d\_r} = \kappa \mathcal{C}\_A e^{-ur} \Longrightarrow \frac{d N\_P}{dt} = \kappa \mathcal{C}\_A \int\_{\delta}^{\delta + \tau} e^{-ur} dr \tag{17}$$

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.

$$
\left(\frac{dN}{dt}\right)\_{\text{geom}} = \sqrt{\frac{dN\_A}{dt}} \frac{dN\_P}{dt} = \mathbf{K}A \frac{\sinh\left(\frac{\mu\mathbf{r}}{2}\right)}{\left(\frac{\mu\mathbf{r}}{2}\right)} \sqrt{\mathfrak{H}} \tag{18}
$$

The attenuation of the emitted photons (H) through the entire thickness of the medium is given by:

$$\mathfrak{H} = e^{-\mu \hbar} \tag{19}$$

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

$$A = \frac{1}{\kappa \sqrt{\mathfrak{H}}} \left( \frac{dN}{dt} \right)\_{\text{geom}} \left( \frac{\frac{\mu \tau}{2}}{\sinh \left( \frac{\mu \tau}{2} \right)} \right) = \frac{1}{\kappa \sqrt{\mathfrak{H}}} \left( \frac{dN}{dt} \right)\_{\text{geom}} \tag{20}$$

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 Aj , is given by the general expression.

$$A\_{j} = \frac{1}{\kappa \sqrt{\mathfrak{S}}} \left( \frac{dN}{dt} \right)\_{geom} \left( \frac{\frac{\mu\_{j}\tau\_{j}}{2}}{\sinh \left( \frac{\mu\_{j}\tau\_{j}}{2} \right)} \right) \tag{21}$$

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.

**Figure 6.** *An overlaying source region in planar imaging.*

## **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.

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 Aj is given as:

$$A\_j = \sqrt{\frac{I\_A I\_P}{\varepsilon^{-\mu\_f}}} \left(\frac{f\_j}{C}\right)$$

$$f\_j = \frac{\mu\_j t\_j / 2}{\sin\left(\frac{\mu\_j f\_j}{2}\right)}$$

Where IA and IP 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<sup>e</sup> 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 (μj) and source thickness (tj) (i.e., source self-attenuation correction).

#### **Figure 7.**

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