Within a closed system where all injected activity is conserved, the desired total activity of 90Y microspheres to be injected, A
Total (GBq) is:
$$A_{\text{Total}} = A_{\text{T}} + A_{\text{N}} + A_{\text{L}}$$
(1)
A
T is the total activity implanted within all tumor tissue, after shunting to nontumorous tissue and lung have occurred; A
N is the total activity implanted in all nontumorous tissue within the target arterial territory; A
L is the total activity implanted in lung due to tumor-to-lung shunting.
The tumor-to-lung shunt fraction (TLSF), is defined as:
$${\text{TLSF}} = \frac{{A_{\text{L}} }}{{A_{\text{T}} + A_{\text{L}} }}$$
(2)
Equation 2 is approximated by \(C_{\text{L}} /(C_{\text{T}} \; + \;C_{\text{L}} )\), where C
L and C
T are the total counts in lung and all tumor tissue respectively, quantified by scintigraphy. The TLSF assumes no lung shunt contribution from nontumorous tissue, and is therefore conceptually different from the “liver-to-lung shunt fraction” defined by the original partition model [8].
The ratio of total activity in tumor to nontumorous tissue, R, is defined as:
$$R = \frac{{A_{\text{T}} }}{{A_{\text{N}} }}$$
(3)
Equation 3 is approximated by\(C_{\text{T}} /C_{\text{N}}\), where C
N is the total counts in all nontumorous tissue quantified by scintigraphy. R is a ratio of activities, not of mean radioconcentrations and, therefore, is conceptually different from the “tumor-to-normal liver ratio” defined by the original partition model [8].
The critical step in predictive dosimetry requires the user to decide an appropriate intended tissue mean absorbed dose to be delivered to any one of the three dosimetric compartments, i.e., tumor, nontumorous tissue, or lung. In this example, let us give a value to the intended tumor mean absorbed dose, D
T (Gy), defined as:
D
T = 50 \(\left( {A_{\text{T}} /m_{\text{T}} } \right)\) by Medical Internal Radiation Dose (MIRD) schema, where “50” is the approximate absorbed dose coefficient of 1GBq of 90Y uniformly distributed throughout 1 kg of tissue [9], and m
T (kg) is the total mass of all tumors within the target arterial territory. Tissue mass (m) may be estimated by CT volumetry and its mean radiographic density on a calibrated system, with attention to accurate delineation of volumes-of-interest. Therefore, A
T may be expressed as:
$$A_{\text{T}} \; = \;\frac{{D_{\text{T}} m_{\text{T}} }}{50}$$
(4)
From Eqs. 3 and 4, the intended mean absorbed dose to non-tumorous tissue, D
N (Gy), of mass m
N (kg), is therefore:
$$D_{\text{N}} \; = \;\frac{{D_{\text{T}} m_{\text{T}} }}{{Rm_{\text{N}} }}$$
From Eqs. 2 and 4, the intended mean absorbed dose to lung, D
L (Gy), of mass m
L (kg), is therefore:
$$D_{\text{L}} \; = \;\left( {\frac{{D_{\text{T}} m_{\text{T}} }}{{m_{\text{L}} }}} \right)\left( {\frac{\text{TLSF}}{{1\; - \;{\text{TLSF}}}}} \right)$$
Applying Eqs. 2, 3 and 4 into Eq. 1:
$$A_{\text{Total}} \; = \;\frac{{D_{\text{T}} m_{\text{T}} }}{50}\; + \;\frac{{D_{\text{T}} m_{\text{T}} }}{50R}\; + \;\left( {\frac{{D_{\text{T}} m_{\text{T}} }}{50}} \right)\left( {\frac{\text{TLSF}}{{1\; - \;{\text{TLSF}}}}} \right)$$
In the simplest dosimetric scenario, all injected 90Y microspheres are completely implanted within tumor, i.e., both A
N and TLSF are zero (Fig. 2). Therefore, Eq. 1 is reduced to simply:
$$A_{\text{Total}} = A_{\text{T}} = \frac{{D_{\text{T}} m_{\text{T}} }}{50}$$
(5)
If nontumorous tissue is present within the target arterial territory (i.e., A
N >0), but there is no tumor-to-lung shunting (i.e., TLSF = 0), then Eq. 1 is reduced to:
$$A_{\text{Total}} \; = \;A_{\text{T}} \; + \;A_{\text{N}} \; = \;\frac{{D_{\text{T}} m_{\text{T}} }}{50\,}\; + \;\frac{{D_{\text{T}} m_{\text{T}} }}{50R}$$
If tumor-to-lung shunting is present (i.e., TLSF >0), but there is no nontumorous tissue within the targeted arterial territory (i.e., A
N
= 0), then Eq. 1 is reduced to:
$$A_{\text{Total}} \; = \;A_{\text{T}} \; + \;A_{\text{L}} \; = \;\frac{{D_{\text{T}} m_{\text{T}} }}{50}\; + \;\left( {\frac{{D_{\text{T}} m_{\text{T}} }}{50}} \right)\left( {\frac{\text{TLSF}}{{ 1\; - \;{\text{TLSF}}}}} \right)$$
(6)
In cases of multiple small or ill-defined tumor lesions which cannot be reliably quantified or delineated on imaging (e.g., diffuse lymphomatous infiltration), the user may choose to conceptually regard the entire target arterial territory as “tumor” (Fig. 3) and plan a single intended mean absorbed dose across the entire target arterial territory. Its dosimetry will be analogous to either Eqs. 5 or 6, depending on the TLSF.
Technology and innovations that may improve the safety and effectiveness of 90Y radioembolization to sites other than the liver are: (1) hybrid tomographic scintigraphy with integrated CT, i.e., SPECT/CT [7, 8] or PET/CT [10]; (2) antireflux catheters to minimize reflux of 90Y microspheres into nontarget tissue [11]; (3) Voxel dosimetry and dose-volume histograms to overcome inherent limitations of dosimetric planning based on mean absorbed doses [12]; (4) multi-isotope surrogates to qualitatively and quantitatively assess microsphere biodistribution within multiple target arterial territories [13, 14]; (5) future possibility of combined external beam radiotherapy with 90Y radioembolization.