Biomedical Engineering Reference
In-Depth Information
Now, in everyday oncology, most treatments use combinations of drugs that
exert their action in synergy on different targets. These drugs may act on phase
transitions only, but they may also act by inhibition of growth factor receptors (such
as cetuximab, or tyrosine kinase inhibitors), impinging on the speed
v
1
, depending
on age
x
at which
G
1
phase is run through. In this case, one may use, as in [
69
], an
extended version of model (
19
), where
∂
∂
)+
∂
∂
t
n
1
(
t
,
x
x
(
v
1
(
x
)
n
1
(
t
,
x
))+
d
1
(
t
,
x
)
n
1
(
t
,
x
)+
K
1
→
2
(
t
,
x
)
n
1
(
t
,
x
)=
0
(23)
Another possibility would be to introduce a non-proliferating, or quiescent, phase
G
0
exchanging cells with
G
1
and to represent the action of growth inhibitors by a
control of these exchanges.
In Sect.
7
, summing up [
27
], and following [
15
], we have focused on mathe-
matical models of tissue growth having in mind only the problem of limiting drug
toxicity to healthy cell populations to optimise cancer treatments. In the future,
making available models of the emergence of drug-resistant cell subpopulations
under drug pressure in a cell Darwinian perspective, we will simultaneously tackle
at the cell population level the constraints of drug resistance in tumour cells and of
toxicity to healthy tissues, to propose globally efficient combined therapies using at
least two complementary drugs.
In a multiscale perspective, integrating a representation of the vasculature around
a cancer cell population will also allow us to represent and optimise the action of
combined therapies associating cytotoxic and antiangiogenic drugs, as in [
49
,
84
].
To be relevant for actual clinical applications, models based on the representation
of evolving structured populations will also need to be integrated in a whole-body
level, from the infusion of drugs into the central compartment of general blood
circulation until the actions they exert at the peripheral sites on proliferating cell
populations. This has partly been done, but still without control, and in the case
of an avascular tumour, in [
31
]. Moreover, to take into account in a dynamic
way the constraint of limiting unwanted toxicity to healthy tissues, cell population
growth models will have to separately represent both tumour and healthy cell
populations, with therapeutic control, wanted or not, exerted on both, and possibly
with competition between the two populations, as is the case for space in the bone
marrow between leukaemic and normal haematopoietic cells at different stages of
their maturation.
Whole-body integration of different spatial scales of description of pharmaco-
logical control on tumour and on healthy cell populations should certainly go as
down as possible at the single cell level, including for instance nucleocytoplasmic
transport to model the control by p53 of the cell cycle in case of damage to the DNA,
as produced by cytotoxic drugs, and it must necessarily contain an intermediate
tissue level as the main level of description, for cancer is certainly a tissue disease,
which may be controlled only at the tissue, i.e., at the cell population level. Then
higher levels of integration: whole-body, and for the individualisation of treatments
(in particular adaptation of whole-body model parameters to clusters of patients),
population of individuals, must be considered, as sketched in [
38
].
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