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Estimating dose painting effects in radiotherapy: a mathematical model.

Alfonso JC, Jagiella N, Núñez L, Herrero MA, Drasdo D - PLoS ONE (2014)

Bottom Line: As a consequence, when radiotherapy is used as a treatment of choice, radiation dosimetries are prescribed under the assumption that the malignancy targeted is of a homogeneous nature.It is also shown that, when compared with homogeneous dose distributions as those being currently delivered in clinical practice, such heterogeneous radiation dosimetries fare always better than their homogeneous counterparts.Finally, limitations to our assumptions and their resulting clinical implications will be discussed.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, Faculty of Mathematics, Universidad Complutense de Madrid, Madrid, Spain.

ABSTRACT
Tumor heterogeneity is widely considered to be a determinant factor in tumor progression and in particular in its recurrence after therapy. Unfortunately, current medical techniques are unable to deduce clinically relevant information about tumor heterogeneity by means of non-invasive methods. As a consequence, when radiotherapy is used as a treatment of choice, radiation dosimetries are prescribed under the assumption that the malignancy targeted is of a homogeneous nature. In this work we discuss the effects of different radiation dose distributions on heterogeneous tumors by means of an individual cell-based model. To that end, a case is considered where two tumor cell phenotypes are present, which we assume to strongly differ in their respective cell cycle duration and radiosensitivity properties. We show herein that, as a result of such differences, the spatial distribution of the corresponding phenotypes, whence the resulting tumor heterogeneity can be predicted as growth proceeds. In particular, we show that if we start from a situation where a majority of ordinary cancer cells (CCs) and a minority of cancer stem cells (CSCs) are randomly distributed, and we assume that the length of CSC cycle is significantly longer than that of CCs, then CSCs become concentrated at an inner region as tumor grows. As a consequence we obtain that if CSCs are assumed to be more resistant to radiation than CCs, heterogeneous dosimetries can be selected to enhance tumor control by boosting radiation in the region occupied by the more radioresistant tumor cell phenotype. It is also shown that, when compared with homogeneous dose distributions as those being currently delivered in clinical practice, such heterogeneous radiation dosimetries fare always better than their homogeneous counterparts. Finally, limitations to our assumptions and their resulting clinical implications will be discussed.

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Estimates on the total number of CSCs at the end of the recurrence tumor stage.Number of CSCs at the end of the recurrence tumor stage (where about 106 cells is again obtained) and the corresponding standard deviations after performing 20 simulations in each case (with different seeds of a random number generator) are shown. (A) For averaged homogeneous therapies corresponding to heterogeneous therapies consisting of 2.5 Gy, 2.9 Gy and 3.3 Gy in the inner sphere and 2.0 Gy in the rest of the tumor for the cases ,  and  (left, middle, right) assuming the low migration rate and CSC cycle durations equal to 48 h, 72 h and 96 h (see Table 4). (B) For heterogeneous therapies consisting of 2.5 Gy, 2.9 Gy and 3.3 Gy in the inner sphere and 2.0 Gy in the rest of the tumor (Top) and the corresponding averaged homogeneous therapies (Bottom) for the cases ,  and  (left, middle, right) with the high migration rate and CSC cycle durations equal to 48 h, 72 h and 93 h (see Table 5). In all cases (A, B, C), a standard scheduling (30 sessions along 6 weeks separated by 24 hours intervals except for weekends) was applied. Notice that the vertical coordinate is represented in a logarithmic scale. See Tables in the Document S1 for further details and Movies S3, S4, S5, S6, S7 and S8 for some examples of simulations represented in (A), (B) and (C).
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pone-0089380-g009: Estimates on the total number of CSCs at the end of the recurrence tumor stage.Number of CSCs at the end of the recurrence tumor stage (where about 106 cells is again obtained) and the corresponding standard deviations after performing 20 simulations in each case (with different seeds of a random number generator) are shown. (A) For averaged homogeneous therapies corresponding to heterogeneous therapies consisting of 2.5 Gy, 2.9 Gy and 3.3 Gy in the inner sphere and 2.0 Gy in the rest of the tumor for the cases , and (left, middle, right) assuming the low migration rate and CSC cycle durations equal to 48 h, 72 h and 96 h (see Table 4). (B) For heterogeneous therapies consisting of 2.5 Gy, 2.9 Gy and 3.3 Gy in the inner sphere and 2.0 Gy in the rest of the tumor (Top) and the corresponding averaged homogeneous therapies (Bottom) for the cases , and (left, middle, right) with the high migration rate and CSC cycle durations equal to 48 h, 72 h and 93 h (see Table 5). In all cases (A, B, C), a standard scheduling (30 sessions along 6 weeks separated by 24 hours intervals except for weekends) was applied. Notice that the vertical coordinate is represented in a logarithmic scale. See Tables in the Document S1 for further details and Movies S3, S4, S5, S6, S7 and S8 for some examples of simulations represented in (A), (B) and (C).

Mentions: Tables 4 and 5 reveal that tumor recurrence occurs in all cases for a homogeneous therapy delivering the corresponding average dose (). Besides, the number of CSCs in the tumor at the end of the radiotherapy treatment decreases with and CSC cycle duration (see Figure 9, and Tables in the Document S1 provided). In the case of low migration, for the heterogeneous therapies failing to achieve tumor control, the number of CSCs remaining alive at the end of the recurrence tumor stage is 107, 1785 and 4457 respectively, with the corresponding standard deviations being 8.53, 78.31 and 232.67 (see Figure 9 (A) to compare with the corresponding averaged homogeneous therapies). These values correspond to the cases , and with a CSC cycle duration of 48 h. In Figure 9 (B), the number of CSCs at the end of the recurrence tumor stage is provided in the case of high migration for the heterogeneous therapies delivering 2.5 Gy (for the case ), 2.9 Gy (for ) and 3.3 Gy (for ) in the inner region, and 2.0 Gy in the rest of the tumor. Notice that, even when tumor control cannot be achieved with the heterogeneous therapies, the corresponding averaged homogeneous therapies always have more CSCs at the end of the recurrence tumor stage (see Figure 9 (C)). Moreover, in some cases that number of CSCs is larger than before the treatment started, resulting in more radioresistant tumors after treatment (see Document S1 for further details).


Estimating dose painting effects in radiotherapy: a mathematical model.

Alfonso JC, Jagiella N, Núñez L, Herrero MA, Drasdo D - PLoS ONE (2014)

Estimates on the total number of CSCs at the end of the recurrence tumor stage.Number of CSCs at the end of the recurrence tumor stage (where about 106 cells is again obtained) and the corresponding standard deviations after performing 20 simulations in each case (with different seeds of a random number generator) are shown. (A) For averaged homogeneous therapies corresponding to heterogeneous therapies consisting of 2.5 Gy, 2.9 Gy and 3.3 Gy in the inner sphere and 2.0 Gy in the rest of the tumor for the cases ,  and  (left, middle, right) assuming the low migration rate and CSC cycle durations equal to 48 h, 72 h and 96 h (see Table 4). (B) For heterogeneous therapies consisting of 2.5 Gy, 2.9 Gy and 3.3 Gy in the inner sphere and 2.0 Gy in the rest of the tumor (Top) and the corresponding averaged homogeneous therapies (Bottom) for the cases ,  and  (left, middle, right) with the high migration rate and CSC cycle durations equal to 48 h, 72 h and 93 h (see Table 5). In all cases (A, B, C), a standard scheduling (30 sessions along 6 weeks separated by 24 hours intervals except for weekends) was applied. Notice that the vertical coordinate is represented in a logarithmic scale. See Tables in the Document S1 for further details and Movies S3, S4, S5, S6, S7 and S8 for some examples of simulations represented in (A), (B) and (C).
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pone-0089380-g009: Estimates on the total number of CSCs at the end of the recurrence tumor stage.Number of CSCs at the end of the recurrence tumor stage (where about 106 cells is again obtained) and the corresponding standard deviations after performing 20 simulations in each case (with different seeds of a random number generator) are shown. (A) For averaged homogeneous therapies corresponding to heterogeneous therapies consisting of 2.5 Gy, 2.9 Gy and 3.3 Gy in the inner sphere and 2.0 Gy in the rest of the tumor for the cases , and (left, middle, right) assuming the low migration rate and CSC cycle durations equal to 48 h, 72 h and 96 h (see Table 4). (B) For heterogeneous therapies consisting of 2.5 Gy, 2.9 Gy and 3.3 Gy in the inner sphere and 2.0 Gy in the rest of the tumor (Top) and the corresponding averaged homogeneous therapies (Bottom) for the cases , and (left, middle, right) with the high migration rate and CSC cycle durations equal to 48 h, 72 h and 93 h (see Table 5). In all cases (A, B, C), a standard scheduling (30 sessions along 6 weeks separated by 24 hours intervals except for weekends) was applied. Notice that the vertical coordinate is represented in a logarithmic scale. See Tables in the Document S1 for further details and Movies S3, S4, S5, S6, S7 and S8 for some examples of simulations represented in (A), (B) and (C).
Mentions: Tables 4 and 5 reveal that tumor recurrence occurs in all cases for a homogeneous therapy delivering the corresponding average dose (). Besides, the number of CSCs in the tumor at the end of the radiotherapy treatment decreases with and CSC cycle duration (see Figure 9, and Tables in the Document S1 provided). In the case of low migration, for the heterogeneous therapies failing to achieve tumor control, the number of CSCs remaining alive at the end of the recurrence tumor stage is 107, 1785 and 4457 respectively, with the corresponding standard deviations being 8.53, 78.31 and 232.67 (see Figure 9 (A) to compare with the corresponding averaged homogeneous therapies). These values correspond to the cases , and with a CSC cycle duration of 48 h. In Figure 9 (B), the number of CSCs at the end of the recurrence tumor stage is provided in the case of high migration for the heterogeneous therapies delivering 2.5 Gy (for the case ), 2.9 Gy (for ) and 3.3 Gy (for ) in the inner region, and 2.0 Gy in the rest of the tumor. Notice that, even when tumor control cannot be achieved with the heterogeneous therapies, the corresponding averaged homogeneous therapies always have more CSCs at the end of the recurrence tumor stage (see Figure 9 (C)). Moreover, in some cases that number of CSCs is larger than before the treatment started, resulting in more radioresistant tumors after treatment (see Document S1 for further details).

Bottom Line: As a consequence, when radiotherapy is used as a treatment of choice, radiation dosimetries are prescribed under the assumption that the malignancy targeted is of a homogeneous nature.It is also shown that, when compared with homogeneous dose distributions as those being currently delivered in clinical practice, such heterogeneous radiation dosimetries fare always better than their homogeneous counterparts.Finally, limitations to our assumptions and their resulting clinical implications will be discussed.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, Faculty of Mathematics, Universidad Complutense de Madrid, Madrid, Spain.

ABSTRACT
Tumor heterogeneity is widely considered to be a determinant factor in tumor progression and in particular in its recurrence after therapy. Unfortunately, current medical techniques are unable to deduce clinically relevant information about tumor heterogeneity by means of non-invasive methods. As a consequence, when radiotherapy is used as a treatment of choice, radiation dosimetries are prescribed under the assumption that the malignancy targeted is of a homogeneous nature. In this work we discuss the effects of different radiation dose distributions on heterogeneous tumors by means of an individual cell-based model. To that end, a case is considered where two tumor cell phenotypes are present, which we assume to strongly differ in their respective cell cycle duration and radiosensitivity properties. We show herein that, as a result of such differences, the spatial distribution of the corresponding phenotypes, whence the resulting tumor heterogeneity can be predicted as growth proceeds. In particular, we show that if we start from a situation where a majority of ordinary cancer cells (CCs) and a minority of cancer stem cells (CSCs) are randomly distributed, and we assume that the length of CSC cycle is significantly longer than that of CCs, then CSCs become concentrated at an inner region as tumor grows. As a consequence we obtain that if CSCs are assumed to be more resistant to radiation than CCs, heterogeneous dosimetries can be selected to enhance tumor control by boosting radiation in the region occupied by the more radioresistant tumor cell phenotype. It is also shown that, when compared with homogeneous dose distributions as those being currently delivered in clinical practice, such heterogeneous radiation dosimetries fare always better than their homogeneous counterparts. Finally, limitations to our assumptions and their resulting clinical implications will be discussed.

Show MeSH
Related in: MedlinePlus