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Affine vector fields in 4-dimensional Lorentz manifolds have recently been investigated in some detail by Hall and da Costa. The picture is completed in this thesis by studying the zeros of affine vector fields. Hall and da Costa show that the problem of finding affine vector fields in non-degenerately reducible 4-dimensional Lorentz manifolds can be reduced, with one exceptional case, to the problem of finding homothetic vector fields in lower dimensional manifolds. This means that the study of affine vector fields with zeros in 4-dimensional Lorentz manifolds is aided by investigating proper homothetic and Killing vector fields with zeros in 2- or 3-dimensional manifolds. To this end proper homothetic vector fields with zeros are investigated in 2- and 3-dimensional Manifolds using techniques similar to those used by Hall. It is shown that in the 2-dimensional case the zero is necessarily isolated, whereas in the 3-dimensional case the zero set may either be isolated or 1-dimensional. In the latter case the manifold is shown to be a 3-dimensional plane wave space-time, and all of the affine and conformal vector fields that it admits are found. These results are then used to determine the nature of the zero sets of affine vector fields in 4-dimensional Lorentz manifolds. The algebraic structure of the Riemann, Ricci and Weyl tensors at such zeros is also described. This work is extended by studying affine vector fields, and their zero sets, in 3-dimensional Lorentz manifolds. An investigation of the zero sets of affine vector fields in 3- and 4-dimensional positive-definite manifolds is included for comparison.

Neuraxial blockade is used to provide analgesia for labour and anaesthesia for caesarean section in approximately one third of deliveries in the UK (more than 200 000 per year)8. Although neuraxial blockade is considered lower risk than general anaesthesia9, it is frequently complicated by tremor and a rise in body temperature ("epidural fever")12. Anecdotally the tremor is extremely unpleasant and epidural fever is associated with adverse neonatal neurological outcome13. Despite the harmful nature of these adverse effects little is known about either condition: the incidence of tremor is not known, the mechanisms underlying both tremor and epidural fever are unclear and their impact upon patient satisfaction has not been evaluated. In a series of experiments this PhD aimed to investigate the cause and the impact of both conditions. In the first study (chapter 3) the subjective incidence and severity of tremor and its impact upon maternal satisfaction was evaluated with a post-delivery questionnaire completed by 644 patients. Chapter 4 contains three pilot studies and a feasibility study, which prepared the ground for the main work of chapters 5 and 6. Chapter 5 investigated the hypothesis that the tremor associated with epidural extension is non-thermoregulatory shivering. In the first study of this chapter the tremor and electromyography frequency profiles of cold stress-induced shivering were defined. Tremor and surface electromyography were recorded in 40 healthy subjects as they undertook a cold stress protocol using a water-circulating mattress and blanket. In the second study tremor, surface electromyography, body temperature and perceived body temperature were recorded in 20 patients before and after epidural extension for emergency caesarean section. The tremor and electromyography frequency profiles were compared to those of cold stress-induced shivering to establish whether or not epidural extension tremor is shivering. Additionally, patients' body temperatures (real and perceived) were compared before epidural extension and at the onset of tremor to determine whether or not the tremor is thermoregulatory. The final data chapter (chapter 6) tested the hypothesis that epidural fever is a consequence of blockade of active cutaneous vasodilation. Body temperature, cutaneous heat flux and skin blood flow were recorded before and after epidural extension in 19 patients. Changes in cutaneous vasomotor tone were inferred from the pattern of variation in skin temperature, cutaneous heat flux and skin blood flow. Chapter 6 also includes a case study of a patient who was excluded from the previous study, which documents the effects of an attempted instrumental delivery upon body temperature. The main findings are: (1) the incidence of tremor following obstetric neuraxial blockade is 48% and it is associated with reduced patient satisfaction; (2) the tremor associated with epidural extension for emergency caesarean section is non-thermoregulatory shivering generated by a perceived reduction in body temperature; and (3) following epidural extension body temperature rises due to a reduction in cutaneous heat loss, which is compatible with the blockade of active vasodilation hypothesis.

Autonomic dysfunction is a common presentation of various neurological disorders and has a heterogeneous aetiology and pathophysiology. PoTS is a very common form of orthostatic intolerance characterized by excessive increases in heart rate during orthostatic stress without orthostatic hypotension and is often associated with the Joint Hypermobility Syndrome (JHS); the most common heritable disorder of connective tissue. However, information is still limited in PoTS with regards to the clinical presentation and quality of life, pathophysiology, the responses to treatment and possible genetic contributions. As part of this thesis a novel autonomic function scoring scale was generated and validated to quantify the degree of autonomic impairment (CAF score), which was able to differentiate patients with different autonomic disorders and quantify the degree of autonomic overactivity in patients with PoTS. An autonomic and quality of life self-administered questionnaire (AQQoL) was also developed in order to assess a range of autonomic symptoms, allied features, familial autonomic dysfunction and the relative quality of life in a large cohort of patients with autonomic disorders. This instrument was found to be helpful in detecting autonomic, non-cardiovascular and quality of life impairments in patients with autonomic disorders and could inform future longitudinal studies in patients with a wide range of autonomic disorders. PoTS might be a genetic disorder with a likely multifactorial and polygenic pathophysiology and possible variable expressivity. Using the AQQoL and further investigations 21 families with PoTS and JHS were described for the first time. In order to further understand the pathophysiology of PoTS and JHS, peripheral small nerve fibre function and morphology, using the skin biopsy technique, were evaluated. A subgroup of patients with PoTS and JHS have an underlying small fibre neuropathy and associated abnormalities of Collagen IV in basement membranes and blood vessels in the skin indicating that multiple pathophysiological mechanisms could coexist in the same patients and that the skin biopsy is a valuable tool to differentiate PoTS sub-groups. Diagnosing PoTS can be challenging and tests, in addition to the traditional orthostatic stressors, such as liquid meal challenge, modified exercise and heat challenge tests, can be of value in the assessment of these patients. In particular, the liquid meal challenge test is also helpful in determining whether drugs such as the somatostatin analogue, Octreotide, can reduce postural tachycardia and symptoms of orthostatic intolerance pre- and post-prandially. Similarly, for the first time, the beneficial effect of 50 mcg of Octreotide on orthostatic hemodynamic responses before and after food ingestion in PoTS was shown. PoTS is a complex multi-system disorder that may cause significant autonomic morbidity and impairment of quality of life. The pathophysiology is heterogeneous and in our patient cohort is likely to be linked to connective tissue disorders, such as JHS and genetic factors. A more extensive autonomic assessment, including the evaluation of hemodynamic responses to daily stimuli, may be important for establishing definitive diagnostic criteria for PoTS. The management of these patients needs a multi-step pharmacological approach and in the most severe cases requires specific targeting, with medications such as Octreotide for example, which might be beneficial in reducing postural tachycardia and orthostatic intolerance.

The autonomic nervous system innervates and influences every organ in the body through two major efferent pathways; the sympathetic and parasympathetic nervous systems. Autonomic dysfunction, especially orthostatic hypotension (OH) and olfactory dysfunction, are commonly present in a variety of neurological disorders, particularly, multiple system atrophy (MSA) and allied disorders, such as Parkinson’s disease (PD) and Pure Autonomic Failure (PAF) and can significantly impact quality of life and cause significant morbidity. Similarly, non-motor symptoms have been increasingly recognized in PD. The overlapping autonomic features of PD, PAF and MSA, e.g., OH, can sometimes make it difficult to differentiate a diagnosis between these conditions. The further evaluation of autonomic function, e.g., cardiovascular, olfactory and gastrointestinal function, in patients with primary chronic autonomic failure disorders could offer better diagnostic accuracy, improve the understanding of disease progression and inform the development of treatments. Cardiovascular autonomic function screening tests are commonly used to confirm a diagnosis of autonomic failure, e.g., orthostatic hypotension, but OH is not often reliable for distinguishing between PD and MSA. Novel indices of cardiovascular autonomic function in patients with chronic autonomic failure have therefore been evaluated as well as the severity of olfactory dysfunction and other non-motor (e.g., daily activities and depression) symptoms in MSA, PD and PAF. Results demonstrated that baroreflex sensitivity and blood pressure recovery time (BRPT) in response to the Valsalva Manoeuvre are useful for differentiating MSA from PD with autonomic failure (PD+AF). BPRT was also significantly prolonged in PD patients compared to healthy controls. In addition, an association of BPRT and disease duration in PD also suggests that this index may be useful for monitoring disease progression in PD. Other findings indicated that assessing olfactory function is also helpful for distinguishing between PD, MSA and PAF. A greater degree of depression and impairment of daily activities in MSA relative to PD and PAF were also evident. In order to further investigate the presenting symptoms and features of PAF, a time when diagnosis is often still unclear, and other disorders, such as MSA, can be suspected, the clinical characteristics and laboratory investigations, in a large cohort of PAF patients were examined. Results indicated that abnormal white matter lesions are prevalent in PAF. Furthermore, gastrointestinal symptoms were also evident in PAF and can also occur in other autonomic disorders, e.g., MSA. Using electrogastrography, impaired indexes of gastric motility were also evident in PAF.

The female reproductive hormone oestrogen influences cardiovascular and thermoregulatory control. A dramatic decline in oestrogen during the menopause causes cardiovascular and thermoregulatory dysfunction resulting in hot flushes (HFs). HFs consist of feelings of intense heat with rapid increases in cutaneous vasodilation and sweating that severely affect quality of life and increase cardiovascular disease risk. Treatment using hormone replacement therapy for HFs is contraindicated in some symptomatic females meaning an alternative strategy is warranted. Exercise training may reduce HFs; however no study to date has examined the physiological mechanisms that cause changes in the frequency and severity of HFs following a period of exercise training. Exercise training is known to enhance thermoregulatory efficiency via an earlier core temperature onset for cutaneous vasodilation and sweating in pre-menopausal females. Exercise training is also known to positively impact vascular function in the conduit, cutaneous and cerebral vessels and thus can also decrease cardiovascular risk in symptomatic post-menopausal females. Heat acclimation interventions target the same thermoregulatory and cardiovascular physiological mechanisms, and may also be beneficial. The primary aim of this thesis was to (i) examine whether exercise training reduces objectively measured HFs via improving cardiovascular and thermoregulatory dysfunction in symptomatic post-menopausal females, and to (ii) assess the efficacy of an exercise-independent stimulus in improving thermoregulatory and cardiovascular function in pre-menopausal females. Twenty-one symptomatic post-menopausal females completed a 16-week exercise training intervention (n=14, 52±4y, 29±6 kg/m2) or a no-exercise control intervention (n=7, 52±6y, 30±7 kg/m2). Cardiorespiratory fitness (VO2peak) and brachial artery endothelial function was assessed using flow-mediated dilation (FMD). Participants underwent a passive heat stress in a water-perfused suit (~48ºC) to obtain core temperature thresholds and sensitivities for cutaneous vascular conductance (CVC) and sweat rate at two sites (chest and forearm). Middle cerebral artery velocity (MCAv) was measured at rest and throughout the heat stress. All measurements were repeated following the intervention period. HFs reduced by 39 HF•wk (95% CI= 31, 47) following exercise training compared to no change in control. HF-severity reduced by 101 (AU) (95% CI= 80, 121) following exercise training compared to no change in control. VO2peak and FMD improved (P<0.05), along with a lower core temperature following exercise training [0.14ºC (95% CI=0.03, 0.20; P=0.04)]. Sweat rate and CVC body/core temperature thresholds occurred ~0.22ºC earlier alongside an increase in sweating sensitivity, at both sites, following exercise training. Resting MCAv was 3.12 cm/s (95% CI, 1.20, 5.01; P=0.03) higher, with decreases in MCAv attenuated during heat stress, following exercise training. HFs recorded in symptomatic females during the passive heat stress prior to and following the exercise training (n=9) or no-exercise control (n=6) intervention were used to assess changes in thermoregulatory and (cerebro)vascular responses during an acute HF. HFs were objectively identified and divided into eight equal segments, with each segment representing 12.5% of HF duration, for analysis. Exercise training decreased HF duration by 63s (95% CI, 14, 113; P=0.08) compared to a negligible decrease of 17s (95% CI, -43, 66) following control. Chest sweat rate decreased by 0.04 mg•cm2•min-1 (95% CI, 0.02, 0.06; P=0.01) during HFs after exercise training compared to no change in control (P>0.05). This was accompanied by a reduction in chest skin blood flow of 26 AU (95% CI, 21, 30; P=0.01) during HFs following exercise training compared to no change in control (P=0.10). MCAv was attenuated by 3.4 cm/s (95% CI, 0.7, 5.1; P<0.001) during a HF following exercise training compared to control [0.6 cm/s (95% CI, -0.7, 1.8; P=0.93)].Eighteen pre-menopausal females (25±8y) were assigned to 3x30-min of cycling exercise (70% HRmax) or warm water immersion (42ºC) to the level of the sternum for 8-weeks. FMD (P=0.003) and VO2peak (P<0.001) improved following both interventions. Core body temperature reduced by 0.14ºC (95% CI, 0.04, 0.23; P=0.004) following both interventions. Sweat rate mean body temperature thresholds at the chest and forearm occurred 0.10ºC (95% CI=-0.14, 0.33, P<0.001) and 0.19ºC (0.12, 0.23ºC, P<0.001) earlier following the interventions, alongside an increase in sweat rate sensitivity of 1.18 mg•cm2•min-1 (95% CI= 0.68, 1.67; P<0.001) following water immersion compared to 0.28 mg•cm2•min-1 (95% CI= 0.23, 0.78) following exercise training. CVC core temperature thresholds occurred ~0.20ºC earlier at the chest and forearm (P<0.001). Resting MCAv was 2.30 cm/s (95% CI=1.20, 3.34; P<0.001) higher, with decreases in MCAv attenuated during heat stress, following both interventions. The findings from this thesis suggest that reductions in the frequency and severity of HFs with exercise training are mediated by improvements in thermoregulatory function, alongside cerebral, conduit and cutaneous adaptation. This coincided with objective reductions in HF severity following exercise training, with attenuation in the physiological perturbations observed during an acute HF. Consequently, interventions that target thermoregulatory function may be useful in reducing post-menopausal HFs. In keeping with the exercise mediated physiological changes, warm water immersion training also elicits similar favourable thermoregulatory, conduit- and cerebrovascular adaptations to a period of moderate intensity exercise training in pre-menopausal females. Immersion therapy may therefore be applicable to HF-symptomatic post-menopausal females.