Radiotherapy and risks of tumor regrowth or inducing second cancer
© Springer-Verlag 2011
Received: 13 February 2011
Accepted: 27 July 2011
Published: 18 August 2011
Considerable research is aimed at determining the mechanism by which tumor cures, or regrows or second cancer develops, to be predictable and controllable. The wide range of doses, from low to very high, estimated statistically is responsible for such risks. A mathematical model is presented that describes both: the growth due to lower or over irradiated doses or the post therapy relapse of human cancer, and the shrinkage due to either of over irradiated doses, or appropriate irradiated doses. Simulations of the presented model showed that the initial tumor energy, administered dose energy, and their subsequent summation of tumor regrowth energy are always balanced with summation of Whole Body Cell Energy Burden during all treatment phases. Tumor regrows if its energy is higher than that of the dose, or if the increase of dose energy from that of the tumor is less than the one required to complete its shrinkage path. Patient-specific approaches that account for variations in tumor energies should enable more accurate dose estimates and, consequently, better protection against either lower or over irradiation that could lead to tumor regrowth and increase risks of second cancer.
KeywordsCuring time Summation of tumor growth energy Whole Body Cell Energy Burden Lower irradiated dose treatment Over irradiated dose treatment
This relation enables us to test all the background of medical dosimetry experiments that, based on the statistical analysis as well as prior successful treatments, had been conducted in different schools of medicine. In an effort to assist in the understanding of recurrent cancer and the energy balance processes that mediate this disease, this approach provides a framework for using mathematical techniques to study novel therapeutic strategies aimed at controlling this disease and tries to relate the cancer therapeutic drugs course of phase I prior the treatment to tumor response of phases II and III.
2 Methods and materials
2.1 Mathematical model
2.2 Lower irradiated dose treatment
2.3 Over irradiated dose treatment
2.4 Estimating the WEPT from the tumor response through the LIDT or the OIDT
Checking the postulates of this approach:
Numerical simulations of Eqs. (2.1.1)–(2.1.19) are performed to investigate the tumor’s response to radiotherapy for various parameter values. The fit of the mathematical model to the experimental data [2.2-, 2.3-, 2.4-] is based on the tumor’s response to radiotherapy according to the balance of the dose released energy and the summation of tumor energy. During shrinkage stage, these energies are in equilibrium, and once balance is violated, tumor will be grown. During growing stage, summation of tumor growth energy , results from the balance between initial tumor energy E0.Tumor, initial drug energy E0.Doses, and, finally, summation of Whole Body Cell Energy Burden ∑WBCEB, such that . Negative or positive sign (∓) to cover all types of treatments with respect to dose energy: negative for the OIDT and positive for the LIDT. Despite OIDT may cure the primary tumor in certain cases as shown in 2.4- for the higher dose (18.5 MBq), it contributes in increasing WBCEB to levels higher than that tolerated. The best fit of the model to the experimental data allows for the estimation of the cure or the regrowth at both low and high radiation doses to be used for optimization of radiotherapy protocols.
3.1 Effects of changing model parameters
The stability of the conclusions of the modeling study was investigated by varying the radiobiologic and pharmacokinetic parameters associated with tumor response. The effects on tumor response of varying the radiobiologic parameters lower and over the initial tumor energy were covered. In all cases, cure responses were for WEPT and OIDT, which satisfied the model energy balances of Eq. (2.1.7), whereas remission responses were similar for all LIDT and OIDT that satisfied Eq. (2.1.1). This was done for both macroscopic and microscopic tumors. It should be noted that the tumor response model is applicable for all kinds of cancer radiotherapies. All variations of radiobiologic factors are explained in only four parameters (a) initial tumor energy, (b) initial dose energy, (c) summation of Whole Body Cell Energy Burden and (d) summation of tumor energy, which arises as a result of the unbalance between the sums of the first two parameters against the third one. The possibility of adaptation of shrinkage pathway is considered by changing the parameter of the drug released energy to maintain the equation of energy balances of this model. Notice that when ΔE Doses → 0, which represents the amount by which the dose energy differs from that of WEPT, its resultant which is the difference in the summation of tumor energy of either OIDT or LIDT from that of WEPT too, which is the optimal targeted cancer radiotherapy. Moreover, the model relates all types of tumor response to the difference between energies of OIDT or LIDT from that of WEPT, with the capability to predict the tumor pathway. This was done to keep the number of model parameters at a minimum, but at same time, this simulation shows that the model and so the tumor responses are completely controlled by energy balances. In addition, it is clear that there are specific times for which tumor response energy exceeds the difference of OIDT energy from that of WEPT, resulting in net growth. Further information regarding interval time of the tumor response, whether cure or regrowth, can be derived on the basis of the n half-life times needed for WBCEB to reach the NBR. During the regrowth period, the curve of tumor energy of OIDT surpasses that of WEPT resulting in a balance point at which the model predicts the level of tumor energy that can be reached above the curve of tumor energy of WEPT. The model also predicts that tumor relapse is associated with a decrease in released dose energy from the supposed quantity needed to allow the tumor to continue its shrinkage pathway.
In such a case, tumor regrowth energy will vanish. Such an approach, unifying short- and long-term models, has some advantages over currently existing methods, as discussed in the previous articles (Moawad 2010; 2011). Reasons for tumor regrowth are either underestimation or overestimation of the administered dose. For underestimation, Emad Moawad showed that exposure to certain levels of radiation of energy less than that of the biological culture allows harmful nuclear transmutation in biological cultures, which contributes in their growth and, consequently, different kinds of cancerous tumors where growth energy gained is equivalent to energy gained of such elemental transmutations (Moawad 2011). While overestimation is the second reason for tumor regrowth or second cancer, it can be a reply for several questions like why might secondary rectal cancer rates be higher in prostate cancer patients who had conservative treatment (Harlan et al. 2001b). Rajendran et al. showed the statistical analysis to dose assessment by ignoring patient-specific factors and using standard models is responsible for a wide range of doses and, consequently, second cancer risks (Rajendran et al. 2004). Hence, significant differences are observed between the tumor response due to the physical approach and those obtained from the statistical standard models. This shows that ignoring patient-specific factors and tumor size that was handled by WEP and depending on statistical models, lead to either underestimation or overestimation of the true tumor energy of individual patients (Fisher 1994). Therefore, patient-specific approaches that account for variations in tumor sizes along with its growth doubling time should enable more accurate dose estimates and, consequently, better protection against lower or over irradiation that could lead to tumor growth or serious normal tissue toxicities and increasing the risks of second cancer.
Radiotherapy and its subsequent are an energy balance process; tumor regrows if its energy is higher than that of the dose, or if the increase of dose energy from that of the tumor is less than the required one to complete its shrinkage path. Patient-specific approaches that account for variations in tumor energies should enable more accurate dose estimates and, consequently, better protection against either lower or over irradiation that could lead to tumor regrowth and increase risks of second cancer.
Conflict of interest
The author declares that there is no conflict of interest concerning this paper.
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