METHODS: The governing equations of fluid flow have been transformed in the form of ordinary differential equations. These equations have been solved by two methods namely, shooting method and three-stage Lobatto IIIa formula.
RESULTS: The effects of different parameters on temperature, velocity, concentration profiles, skin friction coefficient, Sherwood number, and reduced Nusselt number were obtained and presented graphically. It was noticed that four solutions existed at definite ranges of the parameters for high suction over both surfaces for the first time. The results of the stability analysis revealed that only the first solution is more stable and possess physical reliability compared to the remaining solutions.
CONCLUSION: The graphs also indicated that the fluid velocity decreases as the thermophoresis parameter increases but the opposite behavior observed for both temperature and concentration profiles in the first solution. Furthermore, it was detected that the concentration profile declined at the higher values of the Brownian motion parameter.
SUMMARY ANSWER: High-throughput flagellar waveform tracking and analysis enable measurement of experimentally intractable quantities such as energy dissipation, disturbance of the surrounding medium and viscous stresses, which are not possible by tracking the sperm head alone.
WHAT IS KNOWN ALREADY: The clinical gold standard for sperm motility analysis comprises a manual analysis by a trained professional, with existing automated sperm diagnostics [computer-aided sperm analysis (CASA)] relying on tracking the sperm head and extrapolating measures. It is not currently possible with either of these approaches to track the sperm flagellar waveform for large numbers of cells in order to unlock the potential wealth of information enclosed within.
STUDY DESIGN, SIZE, DURATION: The software tool in this manuscript has been developed to enable high-throughput, repeatable, accurate and verifiable analysis of the sperm flagellar beat.
PARTICIPANTS/MATERIALS, SETTING, METHODS: Using the software tool [Flagellar Analysis and Sperm Tracking (FAST)] described in this manuscript, we have analysed 176 experimental microscopy videos and have tracked the head and flagellum of 205 progressive cells in diluted semen (DSM), 119 progressive cells in a high-viscosity medium (HVM) and 42 stuck cells in a low-viscosity medium. Unscreened donors were recruited at Birmingham Women's and Children's NHS Foundation Trust after giving informed consent.
MAIN RESULTS AND THE ROLE OF CHANCE: We describe fully automated tracking and analysis of flagellar movement for large cell numbers. The analysis is demonstrated on freely motile cells in low- and high-viscosity fluids and validated on published data of tethered cells undergoing pharmacological hyperactivation. Direct analysis of the flagellar beat reveals that the CASA measure 'beat cross frequency' does not measure beat frequency; attempting to fit a straight line between the two measures gives ${\mathrm{R}}^2$ values of 0.042 and 0.00054 for cells in DSM and HVM, respectively. A new measurement, track centroid speed, is validated as an accurate differentiator of progressive motility. Coupled with fluid mechanics codes, waveform data enable extraction of experimentally intractable quantities such as energy dissipation, disturbance of the surrounding medium and viscous stresses. We provide a powerful and accessible research tool, enabling connection of the mechanical activity of the sperm to its motility and effect on its environment.
LARGE SCALE DATA: The FAST software package and all documentation can be downloaded from www.flagellarCapture.com.
LIMITATIONS, REASONS FOR CAUTION: The FAST software package has only been tested for use with negative phase contrast microscopy. Other imaging modalities, with bright cells on a dark background, have not been tested but may work. FAST is not designed to analyse raw semen; it is specifically for precise analysis of flagellar kinematics, as that is the promising area for computer use. Flagellar capture will always require that cells are at a dilution where their paths do not frequently cross.
WIDER IMPLICATIONS OF THE FINDINGS: Combining tracked flagella with mathematical modelling has the potential to reveal new mechanistic insight. By providing the capability as a free-to-use software package, we hope that this ability to accurately quantify the flagellar waveform in large populations of motile cells will enable an abundant array of diagnostic, toxicological and therapeutic possibilities, as well as creating new opportunities for assessing and treating male subfertility.
STUDY FUNDING/COMPETING INTEREST(S): M.T.G., G.C., J.C.K-B. and D.J.S. gratefully acknowledge funding from the Engineering and Physical Sciences Research Council, Healthcare Technologies Challenge Award (Rapid Sperm Capture EP/N021096/1). J.C.K-B. is funded by a National Institute of Health Research (NIHR) and Health Education England, Senior Clinical Lectureship Grant: The role of the human sperm in healthy live birth (NIHRDH-HCS SCL-2014-05-001). This article presents independent research funded in part by the NIHR and Health Education England. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health. The data for experimental set (2) were funded through a Wellcome Trust-University of Birmingham Value in People Fellowship Bridging Award (E.H.O.).The authors declare no competing interests.