Includes bibliography. / The aim of this thesis was to investigate the feasibility of using the shape of the umbilical flow waveform, obtained clinically with Doppler ultrasound, to monitor the condition growth impaired foetuses. This aim was addressed via the following . 1. Survey the literature to obtain information regarding : a) the foetal blood flow distribution for normal foetuses. b) the effect of placental pathology and maternal hyperoxygenation in compromised foetuses. 2. Model the foetal circulation to investigate the effect, on the umbilical flow waveform, of physiological changes resulting from placental insufficiency. 3. Perform a theoretical and practical assessment of Doppler ultrasound by considering its suitability in monitoring foetal condition, through alterations in the umbilical blood flow waveform shape. 4. Clinically gather and analyse umbilical blood flow waveforms from foetuses currently on a trial to investigate appropriate protocols for the assessment of maternal hyperoxygenation.