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**Traino AC ^{1*}, Piccinno M^{1}, Boni G^{2}, Bargellini I^{3} and Bozzi E^{3}**

^{1}Unit of Medical Physics, University Hospital Pisana, Italy

^{2}Unit of Nuclear Medicine, University Hospital Pisana, Italy

^{3}S.D Radiologia Vascular and Interventional, University Hospital Pisana, Italy

- *Corresponding Author:
- Traino AC

Professor, Unit of Medical Physics

University Hospital Pisana, Italy

**Tel:**+39 050992957

**E-mail:**[email protected]

**Received Date:** July 01, 2015; **Accepted Date:** January 11, 2016; **Published Date:** January 15, 2016

**Citation: **Traino AC, Piccinno M, Boni G, Bargellini I, Bozzi E (2016) Comparison
of Macrodosimetric Efficacy of Transarterial Radioembolization (TARE) by Using 90Y Microspheres of Different Density of Activity. J Phys Math 7:150. doi:10.4172/2090-0902.1000150

**Copyright:** © 2016 Traino AC, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Visit for more related articles at** Journal of Physical Mathematics

Purpose: Transarterial 90Y microspheres radioembolization is emerging as a multidisciplinary promising therapeutic modality for primary and metastatic cancer in the liver. Actually two different type of microspheres are used, whose main characteristic is the different density of activity (activity per microsphere). In this paper the effect due to the possible different distribution of the microspheres in a target is presented and discussed from a macrodosimetric point of view. Material and methods: A 100 g virtual soft-tissue target region has been builded. The administered activity was chosen to have a target average absorbed dose of 100 Gy and the number of 90Y microspheres needed was calculated for two different activity-per-microsphere values (2500) Bq/microsphere and 50 Bq/microsphere, respectively). The spheres were randomly distributed in the target and the Dose Volume Histograms were obtained for both. The cells surviving fractions (SF) for four different values of the radiobiological parameter α were calculated from the Linear - Quadratic model. Results: The DVH obtained are very similar and the SF is almost equal for both the activity-per- microsphere values. Conclusions: This macrodosimetric approach shows no radiobiological difference between the glass and resin microspheres. Thus the different number of microspheres seems to have no effect when the number of spheres is big enough that the distance between the spheres in the target can be considered small compared to the range of theÃ¯Â€Â β-particles of 90Y.

Microspheres; β-particles; Linear-quadratic model; TheraSphere

Radioembolization with ^{90}y **microspheres **via hepatic arterial
administration has been shown to be effective in the treatment of
primary and metastatic liver cancer (HCC), as well as in unresectable
colon carcinoma metastases [1-5] Radioembolization is a locoregional
liver directed therapy that involves transcatheter delivery of
microspheres embedded with ^{90}y. ^{90}y microspheres are injected into
the arterial supply of the liver, where they preferentially flow into hyper
vascularized tumor zones, with a higher irradiation of tumour tissue
compared to the normal liver parenchyma, with a consequent tumourtissue
necrosis. Actually ^{90}y can be delivered to the hepatic tumor
as either a constituent of a glass microsphere, TheraSphere®, or as a
biocompatible resin-based microsphere, SIR-Spheres®. TheraSphere®
was approved by the USA Food and Drug Administration for
unresectable HCC in December 1999 under a Humanitarian Device
Exemption. SIR-Spheres® was approved in March 2002 for colorectal
cancer metastatic to the liver in conjunction with continuous infusion
of intrahepatic floxuridine (FUDR) [6].

The characteristics of these two different kinds of^{90}Y microspheres
are summarized in **Table 1** [7]. From a dosimetric point of view,
the main difference between SIR-Spheres® and TheraSphere® is the
density of activity that in one case (SIR-Spheres® whose activity per
microsphere is ~50 Bq) is much lower than in the other (TheraSphere®
whose activity per microsphere is 2500 Bq).

^{90}Y-Microspheres |
||
---|---|---|

Material | Resin | Glass |

Sphere size (mm) | 20-60 | 20-30 |

Activity per sphere (Bq) | 40-70 | 2500 |

Specific gravity | Low | High |

Handling for dispensing | Required | Not required |

Splitting one vial for more patients | Possible | Not possible |

**Table 1:** Main characteristics of the two available kinds of ^{90}Y microsphere: Glass
spheres (TheraSphere^{®}) and resin spheres (SIR-Spheres^{®}).

In principle this difference could have an impact on the radiobiological effectiveness of the treatment [8], due to the much higher number of microspheres needed to have the same activity in the target tissue in one case (SIR-Spheres®) compared to the other (TheraSphere®). This because an higher number of microspheres could mean a more homogeneous distribution of activity (and consequently of target absorbed dose).

In this paper a comparison of these two different densities of activity
is presented and discussed, showing that, neglecting other differences
between the two types of^{90}Y microspheres (different material and
consequent different specific gravity of SIR-Spheres® compared to
TheraSphere®, for example) the therapeutic effectiveness of the two** radioembolization **tools is almost the same from a macro**dosimetric **point of view.

A cubical target was simulated to test the expected difference
between the two different activities-per- sphere tools. The mass of the
target was 100 g, its density was 1.04 g/cm^{3}, that is the density of the soft
tissues [9]. The activity needed for an average target absorbed dose of
100 Gy was calculated by using the MIRD formalism:

where D(r_{T},∞)=100 Gy is the target absorbed dose; S(r_{T},r_{T} )=5.08 mGy/
MBq*h is the S-value for a self-irradiating 100 g spherical target treated
with^{90}Y; A_{0}=administered activity and λ=0.011 h-1 is the physical
decay constant of ^{90}Y. From Equation 1 it follows A_{0}=213 MBq.

The target volume was divided into N=21x21x21 square voxels of 2.21 mm size.

A number n_{sph} of^{90}Y embedded microspheres of the same size
were randomly distributed into the target, according with the equation:

Where δ_{a} represents two different densities of activity of 2500 Bq/
sphere and 50 Bq/sphere respectively. For an administered activity of
213 MBq there will be nsph =8.52 × 10^{4} ^{90}Y microspheres corresponding
to a density of activity δ_{a} =2500 Bq/sphere (glass spheres) and* nsph* =4.26 × 10^{6} ^{90}Y microspheres corresponding to δ_{a} =50 Bq/sphere
(resin spheres). The size was considered the same, 30μm, for both the
type of microspheres.

Software was built by using the open-source environment GNUOctave
to randomly distribute a number *nsph* of microspheres in
the target, to perform a 3D dosimetric calculation at the voxel level
by using the MIRD 17 method [10] and to show the Dose Volume
Histogram (DVH) corresponding to the different distributions of the ^{90}Y microspheres.

The absorbed dose di in each voxel was calculated, according to the MIRD 17 method, by using the equation:

where Ã_{h} is the cumulated activity in the ith-voxel and Si←h are the
dose conversion factors at the voxel level. The Si←h values for the voxel
size of 2.21 mm were taken [9] Note that Ah is the activity in each h
voxel, calculated by multiplying the number of microspheres randomly
placed in that voxel by the density of activity δ_{a}.

The Dose Volume** Histograms **for δ_{a} =2500 Bq/sphere and δ_{a} =50 Bq/sphere are shown in **Figure 1**. DVHs for the two values of δ_{a} considered are very similar.

The surviving fraction SF was calculated for each of the two values
of δ_{a} by using the Linear-Quadratic (LQ) model:

In Equation 4 β=/10 and the Lea-Catcheside factor G=0.023. This last factor for a mono-exponential decreasing dose-rate can be written as [11].

Where μ=ln(2)/ t_{rep} is the rate of repair of **sub-lethal damages **(the
repair half-time constant trep=1.5 h for tumor lesions was extracted
from Strigari [12] and λ=0.011h-1 is the physics decay rate of ^{90}Y. The
cells surviving fraction for four different values of α (α =1; 0.1; 0.01 and
0.001 Gy-1) is shown in **Table 2**.

Surviving Fraction | ||
---|---|---|

a (1/Gy) | 2500 Bq/sphere | 50 Bq/sphere |

1 | 5.90E-21 | 4.30E-27 |

0.1 | 1.02E-04 | 6.00E-05 |

0.01 | 0.32 | 0.32 |

0.001 | 0.89 | 0.89 |

**Table 2: **Cells surviving fractions for different values of a and different values of δ _{a} (2500 Bq/sphere and 50 Bq/sphere). The calculation was based on equation 4 with
a /b=10 and G=0.023.

From a macrodosimetric point of view, the different number of ^{90}Y
microspheres per unit mass could have an impact on the radiobiological
effect of the transarterial radioembolization therapy [8], due to the
different distribution of the microspheres in the treated target region.
The microspheres tend to be distributed as homogeneously as possible
via the microvascularization of the target zone. The homogeneous
distribution of the activity represents the better situation from a radiobiological point of view, because it causes an uniform absorbed
dose by the target. In this paper the hypothesis of a random distribution
of the microspheres in the target has been done, without considering
the trapping of the spheres in the blood vessels.

If the microspheres are rarefied in the target, meaning that the
average distance between spheres is higher than than the double range
of the β- of the radionuclide employed (^{90}Y in this case), the dose
distribution will be very unhomogeneous, leaving target zones where
the absorbed dose is zero **Figure 2**.

**Figure 2:** Representation of a rarefied distribution of microspheres in the
target. If the distance between two microspheres is bigger than the double
range of the β-particles there is a no-absorbed energy (and then noabsorbed
dose) zone. This means a very unhomogeneous absorbed dose
distribution in the target.

In the case described in this paper, doing the hypothesis of a
random distribution of the ^{90}Y microspheres in the target, for a 100 g
target treated with an activity of 213 MBq, which corresponds to a target
absorbed dose of 100 Gy, the average density of ^{90}Y microspheres is
0.852 spheres/mm^{3} if δ_{a} =2500 Bq/sphere and 42.6 spheres/mm^{3} if δ_{a} =50 Bq/sphere. Remembering that the range of the β- particles of ^{90}Y
is about 11 mm in the soft tissues, this means that the β- Particles
of the ^{90}Y are close also for δ_{a} =2500 Bq/sphere, compared to their
range. Thus for the glass microspheres (δ_{a} =2500 Bq/sphere) there are
low high-activity spheres for unit mass, compared to an higher number
of low-activity resin microspheres (δ_{a} =50 Bq/sphere). In both cases
the effect of the microspheres is almost homogeneous in the volume
considered, because the average distance among the spheres is lower
than the range of the β- particles of ^{90}Y **Figure 3**.

**Figure 3:** 2D representation of the target region, divided into cubical voxels
of 2.21 mm size. The 90Y microspheres are randomly distributed in the voxels. The average
number of glass microspheres per voxel is 9.2; the average number of resin
microspheres per voxel is 459.8. The microspheres are closer than the β-
range of the 90Y (maximum range: 11 mm; average range: 2.5 mm)

In **Table 3** the average density (number of spheres/mm^{3}) of ^{90}Y
glass and resin microspheres (δ_{a}=2500 Bq/sphere and δ_{a} =50 Bq/sphere
respectively) needed for an average target absorbed dose of 100 Gy is
shown for different target mass values. The average number of spheres
per mm3 of target has a very low variation depending on target mass.
This means that the macrodosimetric effect of the glass and resin ^{90}Y
microspheres is almost the same in the target, because the microspheres
are very close respect to the range of the β- particles of ^{90}Y. This seems
true for all the possible treated masses, if the required target average
absorbed dose is 100 Gy.

TARGET MASS (g) | AMINISTERED ACTIVITY (MBq) | AVERAGE NUMBER OF GLASS SPHERES/mm^{3} |
AVERAGE NUMBER OF RESIN SPHERES/mm^{3} |
---|---|---|---|

40 | 86 | 0.866 | 43.3 |

80 | 170 | 0.854 | 42.7 |

100 | 213 | 0.853 | 42.6 |

300 | 626 | 0.835 | 41.7 |

400 | 833 | 0.833 | 41.7 |

500 | 1041 | 0.833 | 41.7 |

100 | 2059 | 0.825 | 41.2 |

2000 | 4026 | 0.805 | 40.3 |

**Table 3: **Density (number of spheres/mm^{3}) of glass and resin microspheres (δ_{a} =2500 Bq/sphere and δ_{a} =50 Bq/sphere respectively) for different masses of softtissue target. The administered activity corresponds to an average target absorbed dose of 100 Gy; the density of the soft-tissue is 1.04 Kg/dm^{3}.

The random distribution of the microspheres in the whole
target is only a hypothesis. The real situation is different because
the microspheres are vehiculated into the target by the arterial
system: this means that the distribution of the spheres in the target
is unhomogeneous in principle. In the real situation the ^{90}Y activity needed to have a certain absorbed dose (es.100 Gy) in a target volume
(es. 100 g) is forced in a volume smaller than the target (arterial system
in the target is smaller than the whole target). This means that there
is the same number of microspheres (8.52 × 10^{4} ^{90}Y microspheres
corresponding to a density of activity δ_{a} =2500 Bq/sphere and 4.26x106
corresponding to δ_{a} =50 Bq/sphere) randomly distributed in a volume
lower than 100 g. For this reason the ^{90}Y microspheres are much closer
than the situation described in this paper, thus the macrodosimetric
differences due to the different number of resin and glass microspheres
in the target are probably lower.

In this paper the macrodosimetric effect due to the different number of 90Y microspheres per unit mass in a target submitted to the radioembolization procedure is treated. From this point of view, it seems that the different number of microspheres doesn't have any effect on the distribution of the target absorbed dose due to the small distance among the spheres compared to the range of the particles of 90Y. This result seems to be in agreement with those described by Gulec in their paper [13], where, starting from a microdosimetric approach, they don't find any difference in the absorbed dose due to the different number of microspheres in the target.

The **microdosimetic **effects due to the different density of activity
(activity per sphere) between glass and resin microspheres, already
treated in literature [13,14] is beyond the scope of this paper. Also the
probable radiobiological effect due to the different specific gravity of
the microspheres (due to the different material), which almost surely affects the distribution of the microspheres in the target, is not taken
into consideration in this paper.

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