Theoretical Analysis of Proton Therapy for Prostate Cancer

The dependence of high proton energies has been investigated for proton therapy, which are governed by essential physical factors such as ion ranges and stopping powers. In addition, the volume of prostate is another variable factor varies according to human age and types of tumor. The aim of this theoretical study is about bombardment the prostate tumor by normal incidence protons from Medical Cyclotron at room temperature and energy ranges 60-250 MeV. It was studied by means of calculating Stopping Powers, 3D Ion ranges (longitudinal, lateral and radial) and the total target damage as a function of proton energies, which are calculated by TRIM computer code. The electronic stopping powers were calculated by Bethe-Bloch model, which have showed good coincidence with the TRIM results with 0.99 correlation factor. The ionization process is predominated through track of protons in tissues of the prostate, which yields a steep increase in total stopping power with penetration distance leading to the Bragg peak close to the end of range of the proton beams. The skewness and kurtosis are calculated, the negative sign of skewness for all spectra indicated that left tail (towards the surface of incidence protons) is larger than right (away from the surface) leading to reduce side effects to the neighboring normal tissues. The positive value of kurtosis means that the spectra are peaked. This indicates that the precise dose localization is delivered to the tissues. Proton therapy offers the benefit of specified dose localization and has favorable dose-depth distributions, compared with photon beam radiotherapy. Theoretical Analysis of Proton Therapy for Prostate Cancer Buthainah Abdulmunem Ibrahim 147 Vol: 13 No:2 , April 2017 DOI: http://dx.doi.org/10.24237/djps.1302.183A P-ISSN: 2222-8373 E-ISSN: 2518-9255 The angular distribution of protons with different energies are studied to reach the tumor in any position in prostate, it is noticed that at angle of 45 degree, there is equidimensional ion ranges. The total target damage increases with proton energies with values (0.58 1.7) KeV/ion for ranges energy (60 250) MeV respectively. In order to reach the tumor, the proton beam direction could be changed in definite steps or turned on and off very quickly.Volumes of the different shapes of prostates change according to age and kinds of the tumor, which are prolate ellipsoid, prolate spheroid, or spherical shape. This leads to select the precise proton energy to prevent the spread of radiation outside the prostate.This theoretical study can be considered as a tool and an indication to determine the precise proton energy required for prostate cancer treatment to minimize the side effects. Proton therapy is a promising technology as a result of the rapid development of nuclear accelerators.

which have showed good coincidence with the TRIM results with 0.99 correlation factor.The ionization process is predominated through track of protons in tissues of the prostate, which yields a steep increase in total stopping power with penetration distance leading to the Bragg peak close to the end of range of the proton beams.The skewness and kurtosis are calculated, the negative sign of skewness for all spectra indicated that left tail (towards the surface of incidence protons) is larger than right (away from the surface) leading to reduce side effects to the neighboring normal tissues.The positive value of kurtosis means that the spectra are peaked.This indicates that the precise dose localization is delivered to the tissues.Proton therapy offers the benefit of specified dose localization and has favorable dose-depth distributions, compared with photon beam radiotherapy.

Background
Robert R. Wilson suggested in 1946, that energetic protons might be an effective treatment method [1], whilst he had been embroiled in the design of the Harvard Cyclotron Laboratory (HCL) [2].Therapy by this technology were performed up till now, and showed very highly uses and give excellent results.
Therapy of proton uses ionized radiation.As protons are charged particles, a pencil proton beam can be exactly guided towards the tumor.Protons, heavy particles so they penetrate with minimal prevalence and they slow down comparatively fast when entering biological tissues.accurate dose localization and suitable dose-depth distributions, in comparison with photon radiotherapy in which neighboring tissues to tumor may receive similar dose and can be damaged.Proton beams have acute slope increment in energy deposition at Bragg peak [3] and transport few dose to the healthy tissues shortly after the Bragg peak location [4].
Accelerators are the main part used for proton therapy to produce protons for energy ranges (60 to 250 ) MeV, so that deep-seated tumors in prostate in any depth can be treated [5].The proton beam causes damage of the DNA cells within the tumor [5].Adjusting proton energy during therapy maximizes killing tumors or stop reproduction of the cancerous cells.
The development of medical accelerator technology started to produce innovative designs and compact, high frequency, linear accelerators in order to reduce their costs, permitting more proton therapy centers to be accessible to as many hospitals as possible [6].
Notably, LIGHT (Linac for Image Guided Hadrons Therapy) is developed accelerator for proper treatment of cancer tissues with proton therapy [7].In addition, it also brings innovations in design and manufacturing to reduce production costs [8].
The essential physical factors such as stopping powers and ion ranges depend on the protons energy and properties of prostate tissues.In addition, the volume of prostate is another variable factor, which varies according to human age and types of tumor.

In this work, bombardment of the prostate tumor by normal incidence protons from Medical
Cyclotron at room temperature and energy ranges 60-250 MeV.It was studied by means of calculating Stopping Powers, 3D Ion ranges (longitudinal, lateral and radial) and the total target damage as a function of proton energies, which are calculated by TRIM computer code [9] by using computer simulation for transport of protons in matter [10].The electronic stopping powers were calculated by using Bethe-Bloch model, which have showed good agreement with the TRIM results with 0.99 correlation factor.prostate, it is noticed that at angle of 45 degree, there is equidimensional ion ranges.The total target damage increases with proton energies with values (0.58 -1.7) KeV/ion for ranges energy (60 -250) MeV respectively.In order to reach the tumor, the proton beam direction could be changed in definite steps or turned on and off very quickly.
Many studies were done for calculating the volume of prostate, some of them show that, the common shapes of human prostate are: prolate ellipsoid or prolate spheroid [11]

Objective
The aim of the study is to reduce the side effects to healthy tissues of proton therapy for prostate cancer.The selection of specific energy and direction of protons have protected the healthy tissues from radiation.This is also achieved through precise calculation of prostate volume.

Stopping power
The ion is slowed down mainly by outer electrons of atoms of medium at high energy, and it moves nearly in a straight path.When the ion is slowed enough, the collision with the nucleus would be more probable.Finally, the nuclear stopping power was dominating the slowing down process [12] The total stopping powers are equal to the energy loss ( E ) per unit path length ( x), as shown by [13].The total stopping power depends on the energy and type of the incident radiation and on the properties of the substance through which it passes.Since the production of an ion pair requires specific amount of energy, the ionization density is proportional to the total stopping power.
Generally total stopping powers are increased toward the end of ion ranges and reached a maximum, the Bragg peak soon before the energy drops to zero.The curve that describes the stopping power versus the target depth is called the Bragg curve which represents major practical importance for proton therapy.Electronic energy loss has calculated by using Bethe formula given by [13]: Where, E,  1 , energy, mass and velocity of projectile respectively.
N-Atomic density of target.
me , emass and charge of the electron.
Z1, Z2 -the atomic number of the projectile and the target.
Then, reduced nuclear stopping power is given by: Where,   = For  ≤ 30 ln ()

2𝜖
For  > 30 The reduced energy is given by: The total stopping power S (E) is given by [13]: When the target is composed of more than one element, it is assumed that each component contributes to stopping power, for compound     , where x + y =1, then the stopping power is given by the following equation : Where,      are the stopping powers of each target atom A and B respectively [13].
Theoretically simulation methods by computer to calculate the motion of ions in the material, are now the predominant way of treating stopping powers [14].

Ion ranges
The range, R of an energetic projectile with energy   is determined by the rate of energy loss along the path of the projectile until stopping the projectile (  =0) [13].
The general three dimensional ion ranges (Longitudinal, Lateral and Radial) are showed in figure (1).

Figure (1): three dimensional ion ranges
Conventional methods used to compute ion ranges are based on the binary collision approximation (BCA) [10].The well known BCA simulation program is, TRIM computer code based on the ZBL nuclear stopping and interatomic potential [9].

Volume of prostate
One of the factors that reduce side effects is the precise measuring of the prostate size to maintain healthy cells from radiation, that's why there are many studies about the prostate volume.Estimates of prostate volume for various scanning modalities have been used.
Average gland sizes have calculated by the contoured ultrasound, ellipsoid ultrasound, and erMRI methods which are 33.99,37.16, and 39.62 cc, respectively [15].equations and models can facilitate further studies about prostate growth and may enable early diagnosis of benign prostate hyperplasia (BPH) [16].The prostate volume has been estimated with transrectal ultrasound.Theoretically the volume is calculated by prolate ellipsoidal size formula [17] .The volume of the prostate was calculated by using TRUS.The height of the prostate is more precisely determined by using transaxial than mid sagittal scanning [18].Simple formula determined prostate volume (Prolate ellipsoid & prolate spheroid), based on prostate diameters, the results provide only marginally inferior to planimetry, which are preferable because they are simpler to perform in the clinic and are associated with less inconvenience for patient [11].

Results and Discussion
The elemental compositions of human prostate (W&WJ were shown in table ( 1) ) [9]:

Conclusions
The conclusions of this study have indicated that, the ranges of proton ions in prostate tissues were increased with increasing proton energies.As well as, the total damage of the prostate increased due to increase the proton energy.
Bragg effect means that, few side effects transferred to the neighboring vital tissues.High accuracy in calculating the size of the prostate have led to select the appropriate energy of proton beams and their directions according to the depth of tumors, which keep the radiation within the prostate volume to reduce the side effects to the healthy cells.
The angular distribution of proton beams leads to decrease the longitudinal ranges (depths of tumor) with increasing the angle of proton incidence.On contrary, lateral and radial ion ranges (area of tumor) was increased, so that the protons direction could be changed at definite steps, in order to reach the tumors in any position.
The vertical incidence of proton beams with high energy treat the distal depth tumors in prostate tissues, but the angular distribution of the proton beams treat the near depth tumors to the prostate surface.
This theoretical study can be considered as a tool and an indication to select the precise proton energy required for prostate cancer treatment and to minimize the side effects.
Proton therapy is a promised technology as a result of the fast development of particle accelerators.