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Lymphocyte migration through peripheral lymphoid tissue represents an important part of the function of the immune system, but it is still poorly understood. Under normal conditions, it has been estimated that about one- fourth of the blood lymphocytes that arrive at postcapillary venules will

successfully migrate through the inter-endothelial space into lymph node tissues. The remaining blood lymphocytes return to the central blood vessels through the venous system. Furthermore, the majority of lymphocytes appearing in the efferent lymph are derived from the blood. It has been calculated that

approximately 5% of the lymphocytes in lymph are derived from cell division in the lymph node or from entry into it via afferent lymph vessels (Hall and Morris, 1962; Hall and Morris, 1965b). Any changes in the blood-borne lymphocyte population would be expected to have an effect on the lymphocyte population in efferent lymph if the calculation that approximately 95% of this is derived directly from the circulating blood is accurate. This information has influenced the

experimental design of the present study. An experimental protocol that can demonstrate the relationship between the lymphocyte profile (ie concentration) in both blood and lymph simultaneously would be more advantageous for any attempt at modelling. To achieve this, the injection of labelled lymphocytes into the blood circulation and the monitoring of those cells in both blood and lymph

has been used to track labelled lymphocytes. This was followed by construction of mathematical models to describe the kinetics of lymphocyte migration within lymph node tissue.

As the present study was intended to concentrate on the events involved in lymphocyte migration, the sheep model was selected because of its advantages compared with in vitro or small animal models which have been described in section 1.5.1. A major goal of this thesis was to compare alternative approaches to modelling the events of lymphocyte migration in lymphoid tissue. From their starting point, these experiments were planned to obtain enough informative data to construct suitable models while avoiding physiological assumptions whenever possible. This modelling approach was considered to have substantial

advantages compared with modelling from retrospective data. In the latter situation, informative data may be unavailable since the original experiments were directed to achieve other goals. There are three main approaches followed

in this thesis. A compartmental model is an example of a classical biological model, which still requires many assumptions and availability of physiological values from other known sources. In fact, all of the published models previously developed to describe lymphocyte migration and summarised above in this section are purely compartmental analysis-based models. The second approach will be to model in the time domain using the technique of system identification. This is a new trend in modelling which has not been used very much by

biological scientists. The third approach will be an attempt to combine two modelling techniques, namely the frequency and time domain analysis together, to give a clear picture of lymphocyte migration.

In lymphocyte migration experiments, compromise between the aims of the experiment and constraints imposed by the modelling procedures is required at several points. Almost all of the experimental procedures will be performed in the laboratory with experimental animals. Physiological data collection in lymphocyte studies is subject to possible complications introduced by dealing with animal and lymphocyte preparations. There are ethical constraints inherent in long-term experiments with conscious animals. The process of sampling and data

collection is likely to require a few weeks from the start for each individual experiment. Furthermore, continuation of this process requires ongoing, manual input to keep the experiment progressing smoothly. Failure of maintenance or any technical interruption may cause an involuntary cessation of the experiment. Unlike studies in some other biomedical fields, for example the neurosciences, data on lymphocyte recirculation can not be acquired continuously in a short period of time by using computer-aided devices. The results of lymphocyte migration experiments require more time to collect and process to obtain a unique discrete data pattern. This is a significant distinguishing feature compared with the short time scale of experiments in neurological sciences (which might take only a few seconds to a few minutes to collect the sample). Data acquired from those studies can include a great number of data points within a short experimental time, depending on the speed of sampling frequency and the ability of recording devices used in those studies.

Finally lymphocyte migration experiments present a set of uneven-discrete data which extend over an experimental period of about 10 days. This introduces a further difficulty in processing the actual data since the basic principle of the signal may have to be determined as a pre-requisite to proceeding to further stages of analysis. Firstly, signals should be in an appropriate pattern to be characterised as evenly discrete data. Secondly, the number of items of data

should be sufficient to satisfy the modelling procedure. Clearly, if the data set is small, there will be a tendency to have a large variation (error) in the models. To achieve those requirements, the actual data must be processed (ie interpolated) by using a linear interpolation26 algorithm to get a constant sampling interval.