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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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Spatial distribution of CSCs for a heterogeneous tumor with the high migration rate.From left to right tumor stage when radiation therapy is started (about 106 cells in total) with the high migration rate, 3D transversal cut in the middle of the tumor, region where 80% of CSCs are located (yellow) and region where 90% of total cells (CCs and CSCs) are located (yellow and blue). (A) For the case  and (B) for  considering CSC cycle duration equal to 48 h. Depicted in dark and light green (respectively, dark and light red) are proliferating and quiescent CCs (respectively, proliferating and quiescent CSCs). Dead cells are represented in black.
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pone-0089380-g006: Spatial distribution of CSCs for a heterogeneous tumor with the high migration rate.From left to right tumor stage when radiation therapy is started (about 106 cells in total) with the high migration rate, 3D transversal cut in the middle of the tumor, region where 80% of CSCs are located (yellow) and region where 90% of total cells (CCs and CSCs) are located (yellow and blue). (A) For the case and (B) for considering CSC cycle duration equal to 48 h. Depicted in dark and light green (respectively, dark and light red) are proliferating and quiescent CCs (respectively, proliferating and quiescent CSCs). Dead cells are represented in black.

Mentions: On the other hand, when the high migration rate is considered, CSCs are not fully concentrated in an inner region of the tumor (see Figure 5 for and CSC cycle duration equal to 48 h). However, we can define an inner region where at least 80% of CSCs are located (see Figure 6). When asymmetric division probability and CSC cycle duration are allowed to change in the parameter range considered, this inner region approximately represents between 21% to 40% of the volume where 90% of cells, both CCs and CSCs, are located (see Table 3, and Figures in the Document S1 provided). In this case, the diameter of the tumor for all cases is about 5294 µm (with a standard deviation of 778 µm over 20 simulations performed for each parameter set considered). In Tables 2 and 3 the number of CSCs just before treatment starts is shown, so that its dependence with migration rate, asymmetric division probability and CSC cycle duration can be observed. Actually, the number of CSCs existing before treatment starts is a key factor to estimate tumor resistance to radiation therapy, as we will recall below.


Estimating dose painting effects in radiotherapy: a mathematical model.

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

Spatial distribution of CSCs for a heterogeneous tumor with the high migration rate.From left to right tumor stage when radiation therapy is started (about 106 cells in total) with the high migration rate, 3D transversal cut in the middle of the tumor, region where 80% of CSCs are located (yellow) and region where 90% of total cells (CCs and CSCs) are located (yellow and blue). (A) For the case  and (B) for  considering CSC cycle duration equal to 48 h. Depicted in dark and light green (respectively, dark and light red) are proliferating and quiescent CCs (respectively, proliferating and quiescent CSCs). Dead cells are represented in black.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC3935877&req=5

pone-0089380-g006: Spatial distribution of CSCs for a heterogeneous tumor with the high migration rate.From left to right tumor stage when radiation therapy is started (about 106 cells in total) with the high migration rate, 3D transversal cut in the middle of the tumor, region where 80% of CSCs are located (yellow) and region where 90% of total cells (CCs and CSCs) are located (yellow and blue). (A) For the case and (B) for considering CSC cycle duration equal to 48 h. Depicted in dark and light green (respectively, dark and light red) are proliferating and quiescent CCs (respectively, proliferating and quiescent CSCs). Dead cells are represented in black.
Mentions: On the other hand, when the high migration rate is considered, CSCs are not fully concentrated in an inner region of the tumor (see Figure 5 for and CSC cycle duration equal to 48 h). However, we can define an inner region where at least 80% of CSCs are located (see Figure 6). When asymmetric division probability and CSC cycle duration are allowed to change in the parameter range considered, this inner region approximately represents between 21% to 40% of the volume where 90% of cells, both CCs and CSCs, are located (see Table 3, and Figures in the Document S1 provided). In this case, the diameter of the tumor for all cases is about 5294 µm (with a standard deviation of 778 µm over 20 simulations performed for each parameter set considered). In Tables 2 and 3 the number of CSCs just before treatment starts is shown, so that its dependence with migration rate, asymmetric division probability and CSC cycle duration can be observed. Actually, the number of CSCs existing before treatment starts is a key factor to estimate tumor resistance to radiation therapy, as we will recall below.

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