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\chapter{Erythrocyte MTX and 6MP metabolite levels} During the maintenance therapy of children with Acute Lymphoblastic Leukaemia the children receive weekly oral doses of methotrexate (MTX) and daily oral doses of 6mercaptopurine (6MP). The metabolites of MTX and 6MP are accumulated in the erythrocytes and the levels of metabolites in the erythrocytes serve as a surrogate measure of the levels of the metabolites in the diseased cells. The inter individual variation of the metabolisation of 6MP and MTX is substantial and previous studies have demonstrated that these differences are important for the rate of relapse such that patients with high metabolite levels show a decreased risk of relapse (\cite{lilleyman1994} and \cite{schmiegelow1995}). To gain insight into the processes generating the metabolite levels I will here formulate statistical models for the erythrocyte metabolite levels as a function of the doses and the characteristics related to the patients. When formulating appropriate models for the erythrocyte metabolite levels it is important to focus on the biology. In Section \ref{biology} I therefore give a short introduction to the biology and how the metabolites are accumulated in the erythrocytes. Next the available data are described in Section \ref{Data} and the class of statistical models I will use for analyses is described in \ref{Methods}. In Section \ref{emtxana} and \ref{e6tgnana} I apply the methods described in Section \ref{Methods} for each drug separately. Finally, I discuss the results and comment on the obtained models in Section \ref{discussion} . \section{Biology} \label{biology} Blood consists of leukocytes (white blood cells), erythrocytes (red blood cells) and platelets. The bone marrow supports stem cells which are large primitive undifferentiated cells. The stem cells differentiate to become one of these kinds of cells and only the mature cells are released into the blood stream. The leukocytes consist of five different types of white blood cells. In patients with ALL, precursors of the lymphocytes (lymphoblasts) continuously replicate themselves. The resulting leukemic clone does not function normally. %do not fight infections When the precursors of the lymphocytes form a clone, the DNA-sequences are replicated. When a patient is given 6MP and MTX, the replication of the DNA is disrupted, thereby controlling the proliferation of the lymphoblasts. The most important cytotoxic metabolite of 6MP is 6-thioguanin nucleotide (6TGN) which is incorporated in the replicated DNA sequences. Doer cellen saa? %isf. guanin The level of active metabolites in the lymphocytes within the bone marrow cannot easily be measured but 6TGN is also accumulated in the erythrocytes for which the level is relatively easily determined in a blood sample. The level of erthrocyte 6TGN is used as a surrogate measure of the level of 6TGN in the cells containing a nucleus and thereby as a surrogate measure of the influence of 6TGN on the DNA synthesis in the lymphocytes. MTX and methylated 6MP metabolites (MeMP) inhibit the purine de novo synthesis (i.e. the synthesis of the building blocks for the DNA synthesis). When the cells contain less purines, more 6TGN is incorporated in the replicated DNA sequences. MTX is also accumulated in the erythrocytes and the level of MTX in these cells (eMTX) similarly serves as a measure of the level of MTX in the cells containing a kernel and thereby as a measure of the influence of MTX on the DNA synthesis in the lymphoblasts. \\ The erythrocytes do not constitute a homogenous population. They have a life span of approximately 120 days and during that time a progressive ageing process is seen. The kinetics and metabolism of MTX and 6MP in the erythrocytes are qualitatively well described in the literature. For 6MP there is an extensive literature from several authors (e.g. \cite{rostami1995}, \cite{lennard1992}, \cite{lennard2001}) whereas for MTX most of the literature is due to Schr\o der (e.g. \cite{schroder1986}, \cite{schroder1989}). Below I shortly describe how the metabolites accumulate in the erythrocytes for each drug separately. \\ \subsection{Accumulation of MTX in erythrocytes}\label{sec:MTXbio} Due to accumulation, MTX is detectable in the erythrocytes for 2-3 months after the administration has been discontinued. The mature erythrocytes are not able to form MTX metabolites %polyglutamates but instead the metabolites are thought to be incorporated in the erythroid precursors of the bone marrow: \\ After a single oral dose of MTX, the serum MTX concentration reaches a peak after 1-2 hours. After 24 hours the serum MTX concentration will be almost 0. Initially the MTX concentration in the erythrocytes is kinetically similar but has a lower peak value (\cite{schroder1989}). \\ Three to five days after administration of a MTX dose, the concentration of MTX in the erythrocytes starts to rise and continues to increase for 10-14 days. This time delay in the MTX concentration in the ery\-thro\-cytes corresponds to the ery\thro\-cyte maturation time. \\ The erythroid precursors metabolise MTX to polyglutamates which are retained in the mature erythrocytes due to the size and loading (=ladning??) of the polyglutamates. However, during erythrocyte ageing, part of the MTX disappears from the cells through efflux. The long-chain MTX polyglutamates are retained in the erythrocytes until their age dependent destruction whereas the short-chain polyglutamates disappear and are thought to serve as a slow release MTX store. After 6-7 weeks no loss of MTX polyglutamates from the erythrocytes can be detected. During unaltered weekly oral MTX therapy a steady state MTX concentration in the erythrocytes is achieved. \cite{schroder1986} found that the steady state erythrocyte MTX concentration is obtained after at least 8 weeks of constant MTX dose for children on maintenance therapy. The level of MTX metabolites in the erythrocytes is measured in \ehx. \subsection{Accumulation of 6MP in the erythrocytes} \label{sec:6mpbio} After an oral dose of 6MP many potentially active metabolites are produced, the most important cytotoxic metabolite being 6TGN. The metabolites accumulate slowly within the erythrocytes and the e6TGN levels reflect the cumulative dose of 6MP and not the dose taken e.g. the day before the blood sample was taken. Whilst the e6TGN levels increase slowly during treatment, the plasma concentrations are low and fall to the lower limit of detection by 5 hours post-dose. %on a time scale of days and weeks . \cite{rostami1995} found that the 6TGN metabolites are found at the same level in all cell age groups indicating that the metabolites do not originate in the bone marrow as is the case for the MTX metabolites. The erythrocytes metabolise 6MP while in circulation. The inter individual variability is high due to differences in the activity of the enzyme thiopurine methyltransferase (TPMT). This enzyme methylates 6MP and some of the metabolites of 6MP. This enzyme is thus important for the intensity of the treatment with 6MP as well as the risk of toxicity. \\ The distribution of TPMT activity in the Caucasian population is trimodal: Approximately 89\% of the population have a high TPMT activity (homozygous, TPMT activity $>$ 14 U/ml erythrocytes), 11\% have intermediate levels of the activity (heterozygous) whereas 1 in 300 has no functional activity (TPMT activity $<$ 2 U/ml erythrocytes). Hvad er U? Several studies have demonstrated an inverse relation between TPMT activity and e6TGN (e.g. \cite{lennard1990} Lennard et al 1990 lancet) During unaltered daily oral 6MP therapy, steady state is obtained. The time until steady state depends on the TPMT activity such that the heterozygous patients quickly reach high erythrocyte levels whereas the homozygous patients have a much slower increase, reaching steady state levels after 3 weeks (Lennard 1992 siger 4 uger. Jeg kan desvaerre ikke faa adgang til KS ref). The level of 6TGN in the erythrocytes is measured in \ehmp.