# Basic Physics of Nuclear Medicine/Patient Dosimetry

This chapter overviews the **MIRD** method of estimating doses in
nuclear medicine and gives results of surveys of typical patient doses
for a small range of examinations. Doses from X-ray CT surveys are also
given for comparison purposes, and to aid with your appreciation of the
dosimetric impact of PET/CT and SPECT/CT.

## MIRD Calculations

The direct measurement of the absorbed
dose to
organs of the body from nuclear medicine procedures is rarely possible.
Most estimates depend on Monte Carlo
simulation. To compute a dose
distribution, many hundreds of thousands of virtual gamma rays
originating in numerous source organs must be traced through the body as
they interact with tissues by Compton
scattering
and photoelectric
absorption.
Contributions to the dose from Auger
electrons, internal conversion
electrons and beta
decays must also be included This latter part
of the simulation is usually quite straight-forward since these
radiations can be considered to be absorbed in the organ they originate
in.

The Medical Internal Radiation Dose
(MIRD) Committee in
the USA has provided a substantial body of data to assist in dose
estimation. The MIRD method of calculation allows estimation of the dose
to organs of significance from radioactivity distributed homogeneously
throughout a particular source organ. The method can be split into two
parts:

-   **Firstly**, some assumptions are made about or measurements are
    taken of the biological distribution of radioactivity throughout the
    body, taking into account both the biological and physical half-life
    of the labelled radionuclide.

:   The **cumulated activity**, *Ã*~*s*~, in any particular **source**
    organ is calculated by integrating the instantaneous activity over
    time. This data might be obtained from theoretical modelling (such
    as Compartmental
    Analysis)
    or from measurements using a gamma camera to measure the count rate
    as a function of time in the organ of interest - see the following
    figure:

!Estimation of the cumulated activity. The curve in this example could
for example represent the activity in part of the skeleton after
administration of
^99m^Tc-MDP.

:   Mathematically, this type of activity/time curve can be represented
    by the equation:

```{=html}
<div class="center">
```
$\tilde{A}_s = \int A_s (t) \cdot dt$

```{=html}
</div>
```

:   

    :   where *A*~*s*~(*t*) is the activity in the source organ, *s* at
        time, *t*.

-   **Secondly**, the absorbed dose to a target organ, *D*~*t*~, is
    calculated from:

```{=html}
<div class="center">
```
$D_t = \sum_{s} \tilde{A}_s \cdot S(t,s)$

```{=html}
</div>
```

:   where the summation over *s* is intended to account for
    contributions from all source organs to the target organ. The
    **S-factor**, *S*(*t*,*s*) is the mean absorbed dose to the target
    organ, *t*, from unit activity of the relevant radioisotope
    distributed homogeneously within the source organ, *s*. Note that
    its possible for the source and target organ to be the same entity.

## The S-Factor

The challenging part of the MIRD method is the calculation of the
S-factor because it depends on accurate knowledge of the radiations
emitted by the radionuclide. Although the MIRD publications assist by
providing representative values of S-factors for most organs and for a
variety of radionuclides, it is important to understand the methodology
and hence the limitations of this technique.

The S-factor for each radiation type can be broken down into component
factors:

```{=html}
<div class="center">
```
$S(t,s) = D \frac{f(t,s)}{m}$

```{=html}
</div>
```
where:

-   *D* is a measure of the total energy associated with the particular
    radiation type and is a physical entity known from the
    radioisotope\'s decay scheme,
-   *f*(*t*,*s*) is the **absorbed fraction** for the particular
    radiation emitted in the source organ, *s*, and absorbed by the
    target organ, *t*, and
-   *m* is the mass of the target organ.

The absorbed fraction represents the fraction of the total energy
emitted by radiation of a particular type that is absorbed in the target
organ. For beta particles, which have a short range in tissue, it can be
assumed that all the energy will be deposited in the source organ and
other target organs will not be irradiated. That is:

```{=html}
<div class="center">
```
$f(t,s) = 0\,\!$

```{=html}
</div>
```
Unless *t* = *s*, in which case:

```{=html}
<div class="center">
```
$f(t,s) = 1\,\!$

```{=html}
</div>
```
The determination of the S-factor is very simple in this case.

For gamma-rays, however, no such simple approach is possible since the
amount of energy deposited in the source organ and in the target organ
is dependent on:

-   the gamma ray energy, as well as
-   the size, shape and separation of the two organs in question.

Furthermore, we need to take into account not just the gamma-rays from
the nucleus of the radioisotope but also emissions from the whole atom,
i.e. emissions resulting from the electron shells when stimulated by
emissions from the nucleus. The situation for ^99m^Tc is illustrated in
the following table, as an example:

  Radiation                                             Radiations/Disintegration   Radiation Energy (keV)   Dose (keV/Disintegration)
  ----------------------------------------------------- --------------------------- ------------------------ ---------------------------
  Conversion electrons from M-shell, γ~1~               0.75                        1.63                     1.21
  γ~2~                                                  0.89                        140.5                    125
  Conversion electrons from K-shell, γ~2~               0.09                        119.5                    10.6
  Conversion electrons from L-shell, γ~2~               0.01                        137.5                    1.47
  Conversion electrons from M-shell, γ~2~               0.002                       140.0                    0.27
  Conversion electrons from N- and outer shells, γ~2~   0.0004                      140.4                    0.05
  Conversion electrons from K-shell, γ~3~               0.006                       121.6                    0.67
  Conversion electrons from L-shell, γ~3~               0.002                       139.6                    0.24
  Conversion electrons from M-shell, γ~3~               0.0003                      142.1                    0.05
  K~α1~ X-ray                                           0.04                        18.4                     0.74
  K~α2~ X-ray                                           0.02                        18.3                     0.39
  K~β~ X-ray                                            0.01                        20.6                     0.25
  K-Auger electron                                      0.02                        15.5                     0.32
  L-Auger electron                                      0.1                         2.2                      0.22

  : Adapted from the ENSDF Decay
  Data for
  ^99m^Tc (approximate values).

We can see in the table that a range of radiations are generated within
the atom as a whole. For instance, on the first line the energy of a
gamma-ray emitted by the nucleus is
given to an M-shell electron in
about 75% of one type of isomeric
transition giving it a maximum energy
of 1.63 keV, i.e. about 1.2 keV per nuclear disintegration. On the
second line, a gamma-ray resulting from another isomeric transition in
89% of instances emerges unscathed from the atom with an energy of 140.5
keV, or about 125 keV per disintegration. In a third case, in about 9%
of these latter isomeric transitions, an electron in the K-shell gains
energy of 119.5 keV, which is sufficient for it to overcome the binding
energy (about 21
keV)
of that shell and leave the atom. Notice that fluorescent
X-rays, resulting from electronic
transitions to fill vacancies in the K-shell are also produced - as well
as Auger electrons.

Part of a resultant MIRD table of S-factors for ^99m^Tc is reproduced
below as examples of typical values:\

  Target Organ       Liver as Source   Spleen as Source
  ------------------ ----------------- ------------------
  **Bladder Wall**   4.3 x 10^-5^      3.2 x 10^-5^
  **Stomach Wall**   5.1 x 10^-4^      2.7 x 10^-3^
  **Liver**          1.2 x 10^-2^      2.6 x 10^-4^
  **Lungs**          1.4 x 10^-4^      6.2 x 10^-4^
  **Pancreas**       1.1 x 10^-3^      5.1 x 10^-3^
  **Spleen**         2.5 x 10^-4^      8.9 x 10^-2^

  : The absorbed dose per unit cumulated activity, *S*(*t*,*s*), for
  ^99m^Tc (in mGy/MBq/hour)

The unit of the S-factor is typically mGy/MBq/hour. Note that
substantial discrepancies between actual and calculated values can be
expected depending on differences in anatomy and physiological function
between individual patients.

## The Dose in a Liver Scan

To illustrate how the table above can be used in a hypothetical
situation, suppose a liver scan is performed in which 37 MBq of
^99m^Tc-labelled sulphur colloid is administered to a patient. Suppose
also that it is found from metabolic modelling that:

-   80% of the cumulated activity goes to the patient\'s liver and
-   20% goes to their spleen.

When it is then assumed that the biological half-life for the colloid is
infinite in these two organs, which is a reasonable approximation, the
calculation of cumulated total activity is much simplified as
illustrated in the box below:

:   {\| class=\"toc\" style=\"background:transparent; text-align:left;\"

\| rowspan=\"5\" style=\"vertical-align:top; padding-right:5px;\" \|
$\tilde{A}_{\text{liver}}$ \| $= \int A(t) \cdot dt$ \|- \|
$= \int A_0\ \text{exp} \left ( \frac{-0.693t}{T_\frac{1}{2}} \right ) \cdot dt$
\|- \| $= A_0 \cdot 1.44 \cdot T_{\frac{1}{2}}$ \|- \|
$= 0.8 \cdot 37 \cdot 1.44 \cdot 6.03 \cdot \text{MBq.h}\,\!$ \|- \|
$= 256.6\ \text{MBq.h}\,\!$ \|- \|   \|\|   \|- \| rowspan=\"2\"
style=\"vertical-align:top; padding-right:5px;\" \|
$\tilde{A}_{\text{spleen}}$ \|
$= 0.2 \cdot 37 \cdot 1.44 \cdot 6.03\ \text{MBq.h}\,\!$ \|- \|
$= 64.1\ \text{MBq.h}\,\!$ \|- \|   \|\|   \|- \| rowspan=\"2\"
style=\"vertical-align:top; padding-right:5px;\" \|
$D_{\text{liver}}\,\!$ \|
$= (1.2 \cdot 10^{-2} \cdot 256.6) + (2.6 \cdot 10^{-4} \cdot 64.1)\ \text{mGy}\,\!$
\|- \| $= 3.2\ \text{mGy}\,\!$ \|}

Note that the liver dose arises almost exclusively from the presence of
radioactivity in the liver and that the activity in the spleen
contributes little to this dose - just 5%.

In similar way, the dose to the spleen can be calculated to be
`<span style="color:red;">`{=html}5.8 mGy`</span>`{=html}. Note that
even though less activity accumulates in the spleen the absorbed dose is
higher. This apparent paradox can be resolved however when you recall
that the absorbed dose is the energy absorbed **per unit mass**.

The International Commission on Radiological Protection (**ICRP**) have
published more accurate organ absorbed doses derived on the basis of
knowledge of physiological data for what is known as the **Reference
Man** and from the MIRD data. Note that the absorbed doses to the liver
and to the spleen in the following table are
`<span style="color:red;">`{=html}2.74`</span>`{=html} and
`<span style="color:red;">`{=html}2.85`</span>`{=html} mGy,
respectively - somewhat lower than we calculated in our simple,
hypothetical situation above.

  Target Organ        w~T~    Absorbed Dose (mGy)                                      w~T~.H~T~ (mSv)
  ------------------- ------- -------------------------------------------------------- -----------------
  **Gonads (F)**      0.2     0.081                                                    0.016
  **Red Marrow**      0.12    0.41                                                     0.049
  **Colon**           0.12    0.07                                                     0.008
  **Lung**            0.12    0.2                                                      0.024
  **Stomach**         0.12    0.23                                                     0.028
  **Bladder**         0.05    0.04                                                     0.002
  **Breast**          0.05    0.1                                                      0.005
  **Liver**           0.05    `<span style="color:red;">`{=html}2.74`</span>`{=html}   0.137
  **Oesophagus**      0.05    0.1                                                      0.005
  **Thyroid**         0.05    0.03                                                     0.0015
  **Bone Surfaces**   0.01    0.24                                                     0.0024
  **Spleen**          0.025   `<span style="color:red;">`{=html}2.85`</span>`{=html}   0.071
  **Remainder**       0.05    0.21                                                     0.005

  : Data for estimation of effective dose, *E*, for a liver scan using
  37 MBq ^99m^Tc labelled colloid, where *w*~*T*~ is the tissue
  weighting factor and *H*~*T*~ is the equivalent dose for tissue, *T*.

Note that an **effective dose** of 0.35 mSv can be obtained by summing
the values in the right hand column of the table.

Finally, note that a radiation weighting factor, *w*~*R*~, of unity has
been assumed for simplicity throughout the above discussion for all the
radiation energies arising from the decay of ^99m^Tc.

## Typical Nuclear Medicine Doses

The following table lists the effective dose from a number of nuclear
medicine procedures (adapted from ICRP 53):

+----------+----------+----------+----------+----------+----------+
| Exa      | Rad      | Activity | Organ    | Absorbed | E        |
| mination | iopharma | (MBq)    |          | Dose     | ffective |
|          | ceutical |          |          | (mGy)    | Dose     |
|          |          |          |          |          | (mSv)    |
+==========+==========+==========+==========+==========+==========+
| **Bone   | ^99      | 740      | Bone\    | 46\      | 4.2      |
| Scan**   | m^Tc-MDP |          | Bladder  | 38       |          |
+----------+----------+----------+----------+----------+----------+
| **Heart  | ^201^Tl- | 120      | Testes\  | 68\      | 26(M)    |
| Wall**   | Thallous |          | Colon\   | 44\      | 16(F)    |
|          | Chloride |          | Kidney   | 65       |          |
+----------+----------+----------+----------+----------+----------+
| **Inf    | ^67^Ga   | 150      | Bone\    | 94\      | 15       |
| ection** | -Gallium |          | Colon\   | 25\      |          |
|          | Citrate  |          | Red      | 31\      |          |
|          |          |          | Marrow\  | 14\      |          |
|          |          |          | Adrenal  | 15       |          |
|          |          |          | Glands\  |          |          |
|          |          |          | Spleen   |          |          |
+----------+----------+----------+----------+----------+----------+
| **Re     | ^99m     | 150      | Bladder  | 9.3      | 0.73     |
| nogram** | ^Tc-DTPA |          |          |          |          |
+----------+----------+----------+----------+----------+----------+
| **Liver  | ^99m^Tc  | 74       | Liver\   | 5.2\     | 0.7      |
| Scan**   | -Sulphur |          | Spleen   | 5.6      |          |
|          | Colloid  |          |          |          |          |
+----------+----------+----------+----------+----------+----------+
| **       | ^99      | 74       | Lung\    | 4.9\     | 0.8      |
| Lung-Per | m^Tc-MAA |          | Liver    | 1.2      |          |
| fusion** |          |          |          |          |          |
+----------+----------+----------+----------+----------+----------+
| **Lu     | ^        | 20       | Lung     | 2.2      | 0.3      |
| ng-Venti | 99m^Tc-T |          |          |          |          |
| lation** | echnigas |          |          |          |          |
+----------+----------+----------+----------+----------+----------+
| *        | ^99m^    | 185      | Colon\   | 8.0\     | 1.9      |
| *Thyroid | Tc-Perte |          | Stomach\ | 4.8\     |          |
| Scan**   | chnetate |          | Thyroid  | 4.1      |          |
+----------+----------+----------+----------+----------+----------+
| *        | ^131^    | 150      | Bladder\ | 91\      | 9.2      |
| *Thyroid | I-Sodium |          | Stomach  | 5        |          |
| Scan**   | Iodide   |          |          |          |          |
+----------+----------+----------+----------+----------+----------+
| **PET    | ^18^     | 180      | Bladder\ | 29\      | 3.4      |
| Scan**   | F-2-Deox |          | Heart    | 11       |          |
|          | yglucose |          |          |          |          |
+----------+----------+----------+----------+----------+----------+

Note that typical effective doses from ^99m^Tc scans are of the order of
a few mSv. Also note the high effective dose from a ^201^Tl scan -
arising in part because of the high uptake of activity in the testes -
and also those from ^67^Ga and ^131^I. The administered activities
listed in the table are consistent with the most commonly used
activities found in a survey of Australasian Nuclear Medicine practices
conducted in 2000.

## Typical Doses in X-Ray CT

The radiation dose delivered to the patient in X-ray CT is determined by
factors which include the radiation energy and intensity
characteristics, the size of the patient, the efficiency of the
radiation detectors as well as factors derived from the specific form of
image acquisition used (axial versus helical scanning, for example).

The absorbed dose is far from uniform within the patient - being
greatest at the skin and a factor of about three lower in the centre of
the irradiated region. Typical values for skin absorbed doses range from
about 5 mGy to 50 mGy. Head scan absorbed doses are usually higher than
body scan doses because of the substantial attenuation in the skull. In
addition, the lens of the eye can receive a relatively large dose,
typically 50 to 100 mGy, and if repeat examinations are undertaken the
deterministic limit for cataract induction may be exceeded. Protocols,
using appropriate gantry angulation, should be developed to minimise the
possibility for direct irradiation of the eye. Likewise, relatively
large uterine doses may arise from abdominal or pelvic CT scans and this
may be a concern in scanning women of child bearing age.

A number of surveys have been published in recent years in which the
effective dose from CT scans have been estimated - see the table below.
The data indicates that the effective dose is typically 2 to 20 mSv with
the higher values relating to CT scans of the abdomen and pelvis and the
lower values relating to the head and cervical spine. This variation is
largely a reflection of the number of radiosensitive organs that may be
irradiated by the primary beam. The dose variation between countries is
a different matter!

  Examination        New Zealand   Australia   United Kingdom
  ------------------ ------------- ----------- ----------------
  **Head**           2.2           2.7         1.8
  **Chest**          9.8           10.7        7.8
  **Abdomen**        11.6          17.5        7.6
  **Liver**          6.5           13.4        7.2
  **Lumbar Spine**   5.0           5.4         3.3
  **Pelvis**         7.2           11.2        7.1

  : CT effective doses (mSv)

Notice that effective doses from nuclear medicine procedures are of a
similar order of magnitude, but generally lower, than that from CT
examinations. To assist with your comparison: the effective dose from a
chest X-ray is about 0.02 mSv, while that
from a mammogram is about 0.4 mSv and from an
intravenous pyelogram (**IVP**)
its about 3 mSv. How does this last figure compare with the dose from a
renogram? You might like to speculate on the reasons for the large
difference as an exercise to further develop your understanding of this
topic.

