Optimisation of Cancer Drug Treatments Using Cell Population Dynamics - Mathematical Methods and Models in Biomedicine - page 257

those that just slow down the cell division cycle, letting cells alive, but containing
tumour development, which we will define here as cytostatic. Note that “cytotoxic”
and “cytostatic” are terms on which consensus is not so widespread, hence this
necessary precision for our purposes.

2.1 Fate of Drugs in the Organism: Molecular

Pharmacokinetics- Pharmacodynamics

Anticancer drugs are delivered into the general circulation, either directly by intra-
venous infusion, or indirectly by oral route, intestinal absorption and enterohepatic
circulation ( i.e., entry in the general blood circulation from the intestine via the
portal vein towards the liver, and possibly back from the liver to the intestine via bile
ducts). Their fate, from introduction in the circulation until presence of an active
metabolite in the neighbourhood of their intracellular targets, can be represented
by pharmacokinetic (PK) compartmental ODEs for their concentrations. It is
also theoretically possible to represent this fate by spatial PDEs with boundary
conditions instead of exchange rules between compartments when data on spatial
diffusion of the drugs and some geometry of their distribution domain is known—
but this is seldom the case.
Then, in the cell medium, either an individual cell, or a mean intracellular
medium in a population of cells, pharmacodynamic (PD) differential equations
must be used to relate local drug concentrations with molecular effects on their
targets. At this level of description, it is a priori more relevant to describe by
physiologically structured than by spatially structured models the population of
cells under pharmacological attack, since anticancer drugs act mainly by blocking
the cell division cycle, which does not give rise to a spatially structured cell
population (apart from the very early stages of avascular spheroid tumour growth,
little geometry is relevant to describe a tumour seen under the microscope).

2.2 Cytotoxics and Cytostatics

Driving cells to their death may be obtained either by damaging the genome, or
more indirectly by impairing essential mechanisms of the cell division cycle, such
as enzymes thymidylate synthase (an enzyme that plays an essential role in DNA
synthesis and is one of the main targets of cytotoxic drug 5-FU) or topoisomerase
I (another essential enzyme of DNA synthesis, target of cytotoxic drug irinotecan).
The resulting damaged cell, unable to proceed until division into two viable cells, is
normally blocked at one or the other checkpoint, mainly G 1 / M (recall that

the cell division cycle is classically divided into four successive phases, G 1 , S for
DNA synthesis, G 2 ,and M for mitosis).

S or G 2 /