**2. Internal radiation-generating devices**

The requisite technology to construct internal radiation-generating devices (IRGDs) is being developed (e.g., electron accelerators powered by lasers [28]). These devices are optical cavities [28] whose size depends on the laser's wavelength. The utilization of shorter wavelength lasers leads to devices of the size envisioned for IRGDs [1–3, 6].

Refs. [1–6] provide calculations for the range of heavy ions in water. By selecting appropriate ion and energy combinations, specific target irradiation locations are preferentially irradiated. The capability to localize dose in the target is a positive feature that makes heavy ions an attractive tool for external beam therapy and supports their potential use in an IRGD. By adjusting the beam energy and radiation type, an IRGD has the capability to selectively irradiate the tumor.

### **2.1. Candidate radiation types**

Internal devices could incorporate pions, muons, photons, electrons, protons, and heavy ions to deposit energy into tumors. Ranges on the order of a centimeter are achieved using 10–20 MeV pions and muons, 30–40 MeV protons, 100–200 MeV alpha particles, and energies on the order of 90 MeV/nucleon for 12C, 16O, 20Ne ions, and heavier ions [1–6].

#### **2.2. IRGD characteristics and arrangement**

This chapter considers two approaches that have the potential to significantly minimize the dose to healthy tissue while maximizing the dose delivered to the target tissue. The first technique utilizes internal radiation-generating devices that are in their conceptual development phase, and the second is an enhancement of the 90Y microsphere approach that has been suc-

Heavy ions, neutrons, protons, and other radiation types have numerous applications for treating a variety of cancers [1–3, 6, 9–14]. To date, these techniques have focused on beams originating outside the body. These external beams selectively irradiate the tumor mass, but still deliver some dose to healthy tissue. This chapter investigates the possibility of using radiation-generating devices that would be implanted within a tumor to preferentially irradiate its volume and develops their requisite characteristics to permit the selective irradiation of tumors. These devices are postulated to have a size on the order

Microspheres offer a unique approach that has the potential to impact tumor cells by disrupting their vascular structure. A number of authors [15, 16] have proposed a therapy approach that prevents the development of the tumor's vascular supply. Vascular disruption agents incorporate both chemotherapy [17, 18] as well as radiotherapy [18–27]. Radiotherapy vascular disruption techniques utilizing 90Y microspheres, including anti-angiogenic and radioembolization therapies, are used to treat liver cancers [18–23]. Other radionuclides (e.g., 32P) are under investigation, but radiation types other than high-energy beta particles are not under

The requisite technology to construct internal radiation-generating devices (IRGDs) is being developed (e.g., electron accelerators powered by lasers [28]). These devices are optical cavities [28] whose size depends on the laser's wavelength. The utilization of shorter wave-

Refs. [1–6] provide calculations for the range of heavy ions in water. By selecting appropriate ion and energy combinations, specific target irradiation locations are preferentially irradiated. The capability to localize dose in the target is a positive feature that makes heavy ions an attractive tool for external beam therapy and supports their potential use in an IRGD. By adjusting the beam energy and radiation type, an IRGD has the capability to selectively irradi-

Internal devices could incorporate pions, muons, photons, electrons, protons, and heavy ions to deposit energy into tumors. Ranges on the order of a centimeter are achieved using 10–20 MeV pions and muons, 30–40 MeV protons, 100–200 MeV alpha particles, and energies on the order

length lasers leads to devices of the size envisioned for IRGDs [1–3, 6].

of 90 MeV/nucleon for 12C, 16O, 20Ne ions, and heavier ions [1–6].

cessfully utilized to treat liver cancers by disrupting the tumor's vasculature.

of 10−6 m [1–3, 6].

214 Radiotherapy

active consideration [22].

ate the tumor.

**2.1. Candidate radiation types**

**2. Internal radiation-generating devices**

The feasibility of using IRGDs for therapy applications is illustrated using a cubic Cartesian configuration. This configuration is repeated to irradiate various tumor sizes. A unit cell concept is arbitrary, but simplifies the calculation of absorbed dose to the tumor site.

The cubic Cartesian configuration utilizes 27 devices arranged in three planes with nine devices in each plane. The coordinates of the devices are written in terms of a scaled dimension ξ:

$$
\xi = \frac{\mathbf{R}}{\mathbf{d}} \tag{1}
$$

where d is the internal device grid spacing and R is the maximum ion range. This approach facilitates a general discussion and eliminates adjustments for specific ion-energy combinations.

The 27 devices reside at the locations (x, y, z): (0, 0, z), (ξ, 0, z), (ξ, − ξ, z), (0 − ξ, z), (−ξ, − ξ, z), (−ξ, 0, z), (−ξ, ξ, z), (0, ξ, z), and (ξ, ξ, z) for z = -ξ, 0, and ξ. Utilizing additional devices enhances the delivery of dose in a more uniform manner.

IRGDs should incorporate a number of characteristics to facilitate the dose delivery to the target volume. In general, the IRGDs should have the capability to (1) irradiate 4π steradians, (2) deliver various ion-energy combinations, (3) be controlled in real time, (4) rapidly change the radiation type, energy, and fluence, (5) produce a variable fluence to deliver a uniform dose, (6) position itself at a desired location, (7) monitor the delivered dose profile using positron emission tomography or other techniques to verify that it is preferentially irradiating the tumor volume, and (8) have the capability to be removed from the body.

Delivering a uniform absorbed dose (D) requires careful control of the fluence, ion type, and energy (E). These parameters are varied during the irradiation time (T) to deliver a uniform dose within the unit cell:

$$\begin{aligned} \text{dose within the unit cell:}\\ \text{dose within the unit cell:}\\ \text{D} &= \sum\_{i=1}^{\text{N}} \int \int \int \int \frac{1}{\rho(\mathbf{x}\_{i}, \mathbf{y}\_{i}, \mathbf{z}\_{i})} \left( - \frac{\text{dE}(\mathbf{x}\_{i}, \mathbf{y}\_{i}, \mathbf{z}\_{i}, t)}{\text{d}\mathbf{r}(\mathbf{x}\_{i}, \mathbf{y}\_{i}, \mathbf{z}\_{i})} \right) \\ & \quad \times \Phi(\mathbf{x}\_{i}, \mathbf{y}\_{i}, \mathbf{z}\_{i'}, t) \, \text{d $\mathbf{x}\_{i}$  dy $\_{i} dz\_{i}$ dt} \end{aligned} \tag{2}$$

where r(xi , yi , zi ) is the distance measured from each device, Φ˙(*xi* , *yi* , *zi* , *t* ) is the time-dependent fluence rate, *N* is the number of implanted devices, and *i* labels the individual device [1–3, 6].

#### **2.3. Absorbed dose calculations**

Eq. (2) is used to calculate the absorbed dose from internal radiation-generating devices within a Cartesian lattice. Stopping powers are determined using the methodology outlined in Refs. [1–6], and energy-dependent cross sections are obtained from Shen et al's parameterization [29] or models [1–6].

As an initial example of the internal device concept, a spectrum of eight proton groups (i.e., 10, 20, 30, 40, 50, 60, 70, and 80 MeV) is selected to be the output of the device. A spectrum of energies facilitates the irradiation of the entire tumor volume. A uniform distribution of proton dose requires a continuous proton energy distribution. The 27 proton generating devices are distributed in a 10 × 10 × 10 cm volume of water. Each device is assumed to radiate isotropically. The results of irradiating this water volume with 27 internal devices generating an output of 10, 20, 30, 40, 50, 60, 70, and 80 MeV protons are illustrated in **Figure 1**. The fluence at each proton energy is selected to be the same.

**Figure 1.** Normalized absorbed dose distribution from 27 internal radiation-generating devices producing a spectrum of eight proton groups (i.e., 10, 20, 30, 40, 50, 60, 70, and 80 MeV protons). The absorbed dose is proportional to the plotted circle radius.

Since the total absorbed dose of **Figure 1** is the superposition of a number of manifolds (i.e., the various isodose surfaces), the structure of the surface is governed by the proton output spectrum, fluence, attenuating medium characteristics, ion stopping power, and reaction cross section as noted in Eqs. (1) and (2). **Figure 1** represents the three-dimensional absorbed dose profile. In **Figure 1**, the dose at each point is proportional to the plotted circle radius.

**Figure 1** illustrates the symmetry of the absorbed dose distribution associated with the 27 internal radiators. Although the distribution is not uniform, the IRGDs effectively irradiate the target volume. The average dose to the target 10 × 10 × 10 cm volume depends on the IRGD proton spectrum. For example, proton energy groups of 10 MeV; 10 and 20 MeV; 10, 20, 30, and 40 MeV; and 10, 20, 30, 40, 50, 60, 70, and 80 MeV produce to an average dose over the target volume of 5.89 × 10−6, 5.75 × 10−4, 3.00 × 10−2, and 9.79 × 10−2 relative to the peak dose, respectively.

Increasing the number of proton energy groups between 10 and 80 MeV range will continue to increase the average absorbed dose to the tumor site. The discussion of the characteristics of the detailed three-dimensional absorbed dose profile illustrates the complexity of therapy planning when implementing a new technology.
