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We study over-damped Brownian motion in various potential energy landscapes. Starting with one-dimensional systems, we derive the diffusion coefficient for motion in a piecewise-defined potential where the barrier height of each section is taken from a probability distribution. When the distribution is exponential the usual transition between diffusion and sub-diffusion is observed. The behaviour of the diffusion coefficient around the transition depends upon the shape of the energy barriers. A coarse-grained simulation scheme, where particles are moved between lattice sites located at the potential minima, is proposed. Good agreement with Brownian dynamics simulations is observed. Motion in one-dimensional rough potentials is studied, and a modified Langevin equation, valid on long time scales, is derived. This result is extended to higher dimensions and used to derive an expression for the effective diffusion coefficient. Comparison to that obtained from a lattice hopping model facilitates the construction of the multi-dimensional coarse-grained simulation scheme. Escape processes in multi-dimensional potentials are then studied. A framework to calculate the mean first-passage time is proposed and found to offer good agreement with simulations, even when the barrier to escape is small compared to the thermal energy. The framework attempts to capture the effect upon the motion of a varying profile in the direction(s) normal to the escape direction. Simulations reveal good agreement when the profile becomes more confining, but only moderate agreement when it becomes less so. Finally, we apply the above framework to a channel described by a confining parabolic potential whose curvature varies periodically along its length. The diffusion coefficient is derived under the assumption of rapid equilibration in the confining direction. Adding a periodic potential along the channel can enhance the rate of diffusion, depending upon its phase relative to the periodic curvature.

Aims and Objectives: Patient reported outcome measures (PROMs) are tools which seek to ascertain patients’ views of their symptoms, their functional status and their health- related quality of life, without interruption from a healthcare professional. Usually PROMs are questionnaires, they may include multiple choice components and/or free text answers. In order for the use of these tools to be considered reliable and valid in clinical practice, psychometric testing to provide evidence of reliability, validity and functionality should be undertaken. Electronic PROMs or ePROMs are such tools which are delivered electronically and completed on a computer or handheld device, often with responses uploaded onto the internet allowing remote completion and access of results. The ePAQ system is an ePROM platform which utilises an online electronic response system for completion of PROMs. The original ePROM for which the ePAQ system was developed is ePAQ-Pelvic Floor (ePAQ-PF). This is a pelvic floor questionnaire widely used in clinical practice with excellent evidence foe reliability, validity and functionality. This thesis aims to present a narrative on the development and utility of electronic patient reported outcome measures in gynaecology, including systematic literature reviews of existing tools prior to development/utilisation of ePROMs (papers 1 and 2), development and initial psychometric testing of two novel gynaecology ePROMs using the ePAQ system (papers 3 and 4) and discussion of the utility of ePROMs in gynaecology both as tools for clinical practice and in research (papers 5, 6 and 7). Methods: Two systematic reviews following PRISMA guidelines and registered prospectively on the PROSPERO database (CRD42017082508 and CRD42017084710) were undertaken. Paper 1 was a systematic review of non-invasive modalities used to identify women with anal incontinence following childbirth; to assess the existing PROMs for this purpose with a view to deploying the ePROM ePAQ-PF for this purpose in a future study. Paper 2 was a systematic review of PROMs, and their psychometric properties, used to assess body image in a urogynaecology patients. This was done to evaluate existing tools available, to inform development of a domain (area within a questionnaire) in ePAQ- PF to assess body image. The development and initial psychometric testing of a two novel gynaecology ePROMs based on the ePAQ system is described in papers 3 and three ethically approved retrospective cohort studies using data collected from ePAQ-PF as part of routine clinical practice are described in papers 5-7. Each of these papers deals with different symptom complexes and issues occurring in urogynaecology with the aim of presenting the utility of ePROMs in gynaecology both as clinical tools and research tools. In paper 5 the aim was to measure the prevalence of coital urinary incontinence (leakage of urine during sexual intercourse). In this study 2312 women completed ePAQ-PF in advance of their urogynaecology consultation. Logistic regression and Spearman’s rank correlation evaluated associations between types of coital incontinence and different types of urinary incontinence (urgency incontinence and stress incontinence). Mann-Witney test evaluated the relationship between coital incontinence and self-reported quality-of–sex-life and self -avoidance and partner-avoidance of sex using data from ePAQ-PF. A subgroup analysis was undertaken to analyse outcomes in 84 women with coital incontinence undergoing tension free vaginal tape (an operation to treat stress incontinence). In paper 6 the aim was to use data from ePAQ-PF to assess the relationship between pelvic organ prolapse symptoms, subjective outcomes of surgery and body mass index (BMI) in women undergoing vaginal hysterectomy for treatment of prolapse. Pre- and post-operative data from ePAQ-PF were collected prospectively from 60 women undergoing vaginal hysterectomy for prolapse. Of these, 20 were normal weight (BMI 18.5 – 24.9), 20 were overweight (BMI 25 – 29.9) and 20 were women with obesity (BMI 30 – 34.9). The relationship between BMI and symptom scores for prolapse, impact on vaginal symptoms on quality of life and ‘overall change in condition’ was assessed. Pre- and post-operative symptom scores were compared using repeated mixed ANOVA test for BMI as a categorical variable (Normal, Overweight and Obese). Spearman’s rank order correlation test was carried out to evaluate BMI as a continuous variable. All women underwent vaginal hysterectomy using a standardised technique. ePAQ-PF uses a free test question to assess the concerns and treatment goals of patients completing this ePROM. All patients are asked: ‘Considering the issues that currently concern you the most, what do you hope to achieve from any help, advice or treatment?’. The objectives of the study presented in paper 7 were to undertake a content analysis of the free-text concerns and goals recorded by patients completing this item in ePAQ-PF and measure how these related to self-reported symptoms and health-related quality-of-life (HRQOL) data also recorded using ePAQ-PF. In total, 1996 consenting patients completed ePAQ-PF. Content analysis was undertaken of the free-text item responses. Key content themes were identified by the lead researcher, and three researchers read and coded all recorded responses. Student’s t test was used to compare ePAQ-PF domain scores for patients reporting concerns in the relevant domain with those who did not. Results: Paper 1: 109 studies were included from 1602 screened articles. 36 studies utilising 15 different PROM instruments were identified. Mean response rates were 92% up to six weeks after childbirth. Non-personalised assessment modalities (PROMs) were associated with reporting of higher rates of anal incontinence compared to patient interview at all periods of follow up after childbirth, this was statistically significant between six weeks and one year after childbirth (p<0.05). Paper 2: 17 studies were included from 3207 screened articles. Seven different PROMs used to assess body image in a urogynaecological population were identified. Two of these PROMs (Genital Self-Image Scale-20 and Body Image in Pelvic Organ Prolapse questionnaire) had good psychometric evidence for use but this was only in the context of women with prolapse. Evidence for validity and reliability was limited for the other five PROMs identified. Paper 3 (development/testing of ePAQ-Vulva): Factor analysis identified five principal components. These were reviewed and amended to provide a putative domain structure of six domains. Internal reliability of these domains was assessed using Cronbach’s alpha, producing values of 0.715 to 0.917. Inter-rater reliability of the picture items produced a Kappa statistic of 0.405. Spearman’s rank showed moderate correlation between multiple choice answers and free-text concerns (r=0.364 – 0.462) in three of the six domains (Pain, Sex and Dyspareunia). Paper 4 (development/testing of ePAQ-Menstrual, Pain and Hormonal (ePAQ-MPH)): Exploratory factor analysis identified 18 domains (Cronbach’s α >0.7) and 30 redundant items. Test-retest analysis found acceptable intra-class correlations of 0.6–0.9 (p<0.05). Eight domains were compared with Menstrual Distress Questionnaire showing moderate or strong correlation in seven domains. Ten domains were compared with Women’s Health Questionnaire, six of which showed moderate correlation. Mean QQ-10 Value and Burden scores were 76 and 25, respectively (SD=15.8 and 15.5). The mean completion time for ePAQ-MPH was 31 minutes. Confirmatory factor analysis of the revised version 2 instrument with 15 domains showed good model fit. Paper 5: Prevalence of coital incontinence in the cohort was 30%. Symptoms of both urgency incontinence (p<0.005) and stress incontinence (p<0.005) were significantly and independently associated with both types of coital incontinence (orgasm & penetration). In women with coital incontinence compared with those without, there was significant self- avoidance of sex (p<0.0005), partner-avoidance of sex (p<0.0005) and impaired quality-of- sex-life due to sexual problems (p<0.005). Subgroup analysis of 84 women undergoing TVT showed significant improvement in all coital incontinence symptoms three months post- operatively. Paper 6: Overall, 93% of women reported improvement in their condition. The main finding was that ‘Overall change in condition’ was negatively correlated with increasing BMI (rs= - 0.324, p=0.028). Irrespective of BMI, significant improvements were observed in symptoms of prolapse and vaginal symptoms impact on health-related quality of life at three-months post operation. Paper 7: 63% of participants who completed the questionnaire, recorded at least one free- text item. Content analysis identified 1560 individual concerns coding into the 19 ePAQ-PF domains. Symptom scores were significantly higher for patients reporting free-text concerns in 18 domains (p<0.05) indicating convergent validity of ePAQ-PF. Additional concerns relating specifically to body image were recorded by 11% of patients. Conclusions: This narrative thesis presents good evidence for the use of ePROMs in gynaecology, both as clinical and research tools. Electronic patient reported outcome measures in gynaecology have an important role in supporting self- expression and increasing disclosure of potentially taboo or embarrassing symptoms. Their use as research tools is valuable allowing symptom complexes to be explored and outcomes after interventions measured accurately. Further research and development of ePROMs in gynaecology will be needed to support the NHS Long Term Plan.