Rapid Sperm Capture
Lead Research Organisation:
University of Birmingham
Department Name: School of Mathematics
Abstract
Infertility, not being able to conceive after a year of trying for a baby, affects around one in six couples. Problems with sperm - for example low numbers of rapid swimming sperm, or poorly-formed sperm (which may have damaged DNA) contribute in around half of all cases. Therapies such as IVF, or ICSI (injection of sperm into an egg) are used to treat sperm-related problems, however they are ineffective, are very expensive and put physical and emotional strain on the couple, particularly the woman. Worryingly, using sperm with damaged DNA may contribute to miscarriage or health problems in any resulting children. Some patients would be better off continuing to try for a baby naturally, but with some lifestyle changes (stopping smoking, improving diet), or with a less invasive treatment (insemination into the womb). Other patients should be quickly moved to IVF, some will only conceive through ICSI. The difficulty with treatment decisions is that methods to determine the type and severity of sperm problems are imprecise. The main methods are manually 'counting' swimming sperm, and drying them out on a slide to examine their shape. This does not take advantage of the huge leaps in computer and camera technology made in recent years - indeed even 1980s 'Computer-Aided Semen Analysis' methods are not generally used in clinics (partly because of their unsatisfactory accuracy). Think of the technology in a typical smartphone - a high definition (possibly rapid framerate) camera, pattern recognition, and high volume data processing/storage - this is the type of 21st Century technology that needs to be brought into the fertility clinic.
We will develop a new way to examine sperm, using both rapid digital camera imaging, and computer-based pattern recognition. The aim will be to be able to automatically, accurately and repeatably examine a semen sample, collecting simultaneous data on how cells swim, and what their shape is like. The target of this technique will be to look for the 'special' few cells that have the right shape, and can swim well - so that in natural fertilisation they would be able to travel through the cervix, womb and fallopian tubes and fertilise the egg.
There will be a number of practical issues that will need to be solved. For example, do we need to make the cells fluorescent so we can see their shape better, or can we achieve our aims with a 'standard' type of microscopy? Can we work with samples at any concentration, or do we need to dilute them to recognise the cells properly? Should we use a 'micro-fluidic' chamber to separate out the swimming cells first - and should we use a high viscosity ('sticky') fluid that better represents the physical challenge sperm face in the female reproductive tract?
A key question will be how to convert the large volume of information we can measure into information that doctors and patients can make use of. We will apply a type of machine learning based on prototypes, representations of typical types of patients based on the many 'features' we can extract from rapid sperm videos. These prototypes will be progressively modified as more patients come through the system, making the model more accurate. In the long term the possibility of integrating the large volume of data through a model we can train will lead to a very powerful way to bring together clinical information nationally or even internationally.
As the system makes its way into real application, patients will receive the right treatment more quickly, saving resources, patients will have a less difficult experience of fertility treatment and will achieve success more quickly. A longer-term benefit will be by helping clinical research and toxicology - the system will provide researchers with a powerful method to test new advances in fertility treatment, for example drugs, lifestyle changes, and they will also be able to check for unintended sperm-toxic effects of other chemicals.
We will develop a new way to examine sperm, using both rapid digital camera imaging, and computer-based pattern recognition. The aim will be to be able to automatically, accurately and repeatably examine a semen sample, collecting simultaneous data on how cells swim, and what their shape is like. The target of this technique will be to look for the 'special' few cells that have the right shape, and can swim well - so that in natural fertilisation they would be able to travel through the cervix, womb and fallopian tubes and fertilise the egg.
There will be a number of practical issues that will need to be solved. For example, do we need to make the cells fluorescent so we can see their shape better, or can we achieve our aims with a 'standard' type of microscopy? Can we work with samples at any concentration, or do we need to dilute them to recognise the cells properly? Should we use a 'micro-fluidic' chamber to separate out the swimming cells first - and should we use a high viscosity ('sticky') fluid that better represents the physical challenge sperm face in the female reproductive tract?
A key question will be how to convert the large volume of information we can measure into information that doctors and patients can make use of. We will apply a type of machine learning based on prototypes, representations of typical types of patients based on the many 'features' we can extract from rapid sperm videos. These prototypes will be progressively modified as more patients come through the system, making the model more accurate. In the long term the possibility of integrating the large volume of data through a model we can train will lead to a very powerful way to bring together clinical information nationally or even internationally.
As the system makes its way into real application, patients will receive the right treatment more quickly, saving resources, patients will have a less difficult experience of fertility treatment and will achieve success more quickly. A longer-term benefit will be by helping clinical research and toxicology - the system will provide researchers with a powerful method to test new advances in fertility treatment, for example drugs, lifestyle changes, and they will also be able to check for unintended sperm-toxic effects of other chemicals.
Planned Impact
Infertility is highly prevalent - around one in six UK couples fail to conceive after a year of trying; birth rates in developed countries are falling. Male factors are present in around 25% of couples undergoing IVF and 70% of couples undergoing ICSI (direct injection of a single sperm into an egg). Assisted reproduction has become a routine treatment in the UK, the number of IVF cycles performed annually increasing steadily over the last 20 years, exceeding 60000/year in 2012 (HFEA data).
Success rates however remain unacceptably low, with the live birth rate per cycle being around 25%. IVF has significant financial cost, limited availability, and takes a physical and emotional toll on the couple, particularly the woman. While ICSI (direct injection of a sperm into the egg) has made treatment possible even with severe sperm motility deficiency, its expense and possible safety risks for the healthy female partner and resulting child continue to cause concern. Despite advances in computer-based motility assays and viscous penetration tests, real-life clinical diagnostics are generally restricted to visual assessments of sperm count, morphology and motility in uncontrolled viscosity microscopy slide environments. While computer-aided methods offer the possibility of rapid and repeatable screening, the counting accuracy of these methods in human patients is unsatisfactory, and moreover morphology cannot be assessed in populations of live cells.
This project will impact infertility treatment by providing a much more accurate and informative way to assess semen samples, 'Rapid Sperm Capture.' This method will combine state of the art high frame rate imaging and analysis with simultaneous motility and morphology assessment, augmented with novel microfluidic techniques to enrich the population of relevant cells under consideration. Data analysis and interpretation will be built around machine learning, which will go beyond simply outputting numbers, and will instead provide a means to progressively carry out differential diagnosis and stratification by comparing new patients to previous patients, hence supporting medical decision making.
These developments will have economic impacts by reducing unnecessary treatment - for example with over 60000 cycles performed per year, each costing several thousand pounds, if even a few percent of couples undergoing IVF could be transferred to a cheaper therapy, the cost savings to the UK would be of the order of millions of pounds per year. Alongside this there will be impact on patient well-being, by reducing the use of invasive treatment methods, directing scarce treatment resources more effectively, and achieving successful fertilisation, pregnancy and live birth in a more timely way. Detecting chromosomal structure and chromatin integrity issues (revealing ploidy problems and elevated DNA damage) through live cell morphology could also provide a means to select sperm for use in treatment - helping to reduce miscarriage and benefiting the health of the resulting child.
Another potential Impact is as a screening tool for new motility-stimulating drugs, assessing lifestyle changes/dietary supplementation, and as a tool for toxicology. At present no fertility drugs exist that directly target sperm motility, however candidate compounds exist, for example 'Omega' being investigated in Birmingham. To design and assess such drugs rationally - and conversely, possible contraceptive substances - it is valuable to have a means to understand and enhance their mechanism of action on motility. These advances would have major economic and societal benefits, saving NHS resources, benefiting the pharmaceutical industry, and assisting toxicologists in protecting the public from fertility-damaging substances.
Computer-aided semen analysis has been most widely-used in domestic animal breeding, therefore there would be significant economic impact beyond healthcare.
Success rates however remain unacceptably low, with the live birth rate per cycle being around 25%. IVF has significant financial cost, limited availability, and takes a physical and emotional toll on the couple, particularly the woman. While ICSI (direct injection of a sperm into the egg) has made treatment possible even with severe sperm motility deficiency, its expense and possible safety risks for the healthy female partner and resulting child continue to cause concern. Despite advances in computer-based motility assays and viscous penetration tests, real-life clinical diagnostics are generally restricted to visual assessments of sperm count, morphology and motility in uncontrolled viscosity microscopy slide environments. While computer-aided methods offer the possibility of rapid and repeatable screening, the counting accuracy of these methods in human patients is unsatisfactory, and moreover morphology cannot be assessed in populations of live cells.
This project will impact infertility treatment by providing a much more accurate and informative way to assess semen samples, 'Rapid Sperm Capture.' This method will combine state of the art high frame rate imaging and analysis with simultaneous motility and morphology assessment, augmented with novel microfluidic techniques to enrich the population of relevant cells under consideration. Data analysis and interpretation will be built around machine learning, which will go beyond simply outputting numbers, and will instead provide a means to progressively carry out differential diagnosis and stratification by comparing new patients to previous patients, hence supporting medical decision making.
These developments will have economic impacts by reducing unnecessary treatment - for example with over 60000 cycles performed per year, each costing several thousand pounds, if even a few percent of couples undergoing IVF could be transferred to a cheaper therapy, the cost savings to the UK would be of the order of millions of pounds per year. Alongside this there will be impact on patient well-being, by reducing the use of invasive treatment methods, directing scarce treatment resources more effectively, and achieving successful fertilisation, pregnancy and live birth in a more timely way. Detecting chromosomal structure and chromatin integrity issues (revealing ploidy problems and elevated DNA damage) through live cell morphology could also provide a means to select sperm for use in treatment - helping to reduce miscarriage and benefiting the health of the resulting child.
Another potential Impact is as a screening tool for new motility-stimulating drugs, assessing lifestyle changes/dietary supplementation, and as a tool for toxicology. At present no fertility drugs exist that directly target sperm motility, however candidate compounds exist, for example 'Omega' being investigated in Birmingham. To design and assess such drugs rationally - and conversely, possible contraceptive substances - it is valuable to have a means to understand and enhance their mechanism of action on motility. These advances would have major economic and societal benefits, saving NHS resources, benefiting the pharmaceutical industry, and assisting toxicologists in protecting the public from fertility-damaging substances.
Computer-aided semen analysis has been most widely-used in domestic animal breeding, therefore there would be significant economic impact beyond healthcare.
Publications
Bunte K
(2018)
Learning pharmacokinetic models for in vivo glucocorticoid activation.
in Journal of theoretical biology
Cupples G
(2019)
Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy
in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Cupples G
(2021)
XIIIth International Symposium on Spermatology
Gallagher M
(2018)
Meshfree and efficient modeling of swimming cells
in Physical Review Fluids
Gallagher M
(2018)
Meshfree and efficient modelling of swimming cells
| Description | We have developed the first automated, highthroughput method for capturing the flagellar movement of human spermatozoa. Alongside this, we developed highly efficient algorithms to calculate flow fields and forces associated with flagellar movement and other microscale flow systems. |
| Exploitation Route | Deployment of the method in clinical, pharmacological and toxicological studies. |
| Sectors | Environment Healthcare Pharmaceuticals and Medical Biotechnology |
| URL | http://flagellarCapture.com |
| Description | FAST is currently being used in South Africa, Australia, France, Brazil, Argentina, India, and the United States of America. In the UK FAST is being employed within a sub-study of the UNiTY Clinical trial (The UNITY Trial: The UNexplained InfertiliTY treatment Trial - NIHR Funding and Awards) to assess the sperm flagellar parameters of men in couples with unexplained infertility who are attending clinics for treatment. The University of Birmingham are currently exploring options to spin-out a company that will include applications underpinned by FAST. FAST has also formed a key part of a £750k Gates Foundation project led by a former team member which will commence in 2025 "Determining sperm in vitro-assay thresholds for male infertility". |
| First Year Of Impact | 2020 |
| Sector | Healthcare |
| Impact Types | Societal |
| Title | FAST: Automated flagellar capture software |
| Description | The tool comprises software (in the Matlab language) for the automated capture of the motion of the human sperm flagellum to analyse motility and mechanical metabolic requirements. |
| Type Of Material | Physiological assessment or outcome measure |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| Impact | Only released February 2019. |
| URL | http://www.flagellarcapture.com/ |
| Title | NEAREST: fluid dynamics code for microscale biological systems |
| Description | Customisable suite of routines written in the Matlab language to simulate cell motility via flagellar motion and other biological fluid dynamic systems. |
| Type Of Material | Physiological assessment or outcome measure |
| Year Produced | 2017 |
| Provided To Others? | Yes |
| Impact | The code is being actively taken up by several other groups internationally and has formed the basis for one publication and one submitted manuscript. |
| URL | https://gitlab.com/meuriggallagher/NEAREST |
| Title | Data from: Mathematical modelling of the vitamin C clock reaction |
| Description | Chemical clock reactions are characterised by a relatively long induction period followed by a rapid `switchover' during which the concentration of a \emph{clock chemical} rises rapidly. In addition to their interest in chemistry education, these reactions are relevant to industrial and biochemical applications. A substrate-depletive, non-autocatalytic clock reaction involving household chemicals (vitamin C, iodine, hydrogen peroxide and starch) is modelled mathematically via a system of nonlinear ordinary differential equations. Following dimensional analysis the model is analysed in the phase plane and via matched asymptotic expansions. Asymptotic approximations are found to agree closely with numerical solutions in the appropriate time regions. Asymptotic analysis also yields an approximate formula for the dependence of switchover time on initial concentrations and the rate of the slow reaction. This formula is tested via `kitchen sink chemistry' experiments, and is found to enable a good fit to experimental series varying in initial concentrations of both iodine and vitamin C. The vitamin C clock reaction provides an accessible model system for mathematical chemistry. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| URL | https://datadryad.org/stash/dataset/doi:10.5061/dryad.68q4hf7 |
| Title | List of calculated orientation parameter averages for steady flow from Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy |
| Description | Flow linear dichroism is a biophysical spectroscopic technique that exploits the shear-induced alignment of elongated particles in suspension. Motivated by the broad aim of optimizing the sensitivity of this technique, and more specifically by a hand-held synthetic biotechnology prototype for waterborne-pathogen detection, a model of steady and oscillating pressure-driven channel flow and orientation dynamics of a suspension of slender microscopic fibres is developed. The model couples the Fokker-Planck equation for Brownian suspensions with the narrow channel flow equations, the latter modified to incorporate mechanical anisotropy induced by the particles. The linear dichroism signal is estimated through integrating the perpendicular components of the distribution function via an appropriate formula which takes the bi-axial nature of the orientation into account. For the specific application of pathogen detection via binding of M13 bacteriophage, it is found that increases in the channel depth are more significant in improving the linear dichroism signal than increases in the channel width. Increasing the channel depth to 2 mm and pressure gradient to 5 × 104 Pa m-1 essentially maximizes the alignment. Oscillating flow can produce nearly equal alignment to steady flow at appropriate frequencies, which has significant potential practical value in the analysis of small sample volumes. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/List_of_calculated_orientation_parameter_averages_for_stead... |
| Title | List of calculated orientation parameter averages for steady flow from Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy. |
| Description | Flow linear dichroism is a biophysical spectroscopic technique that exploits the shear-induced alignment of elongated particles in suspension. Motivated by the broad aim of optimizing the sensitivity of this technique, and more specifically by a hand-held synthetic biotechnology prototype for waterborne-pathogen detection, a model of steady and oscillating pressure-driven channel flow and orientation dynamics of a suspension of slender microscopic fibres is developed. The model couples the Fokker-Planck equation for Brownian suspensions with the narrow channel flow equations, the latter modified to incorporate mechanical anisotropy induced by the particles. The linear dichroism signal is estimated through integrating the perpendicular components of the distribution function via an appropriate formula which takes the biaxial nature of the orientation into account. For the specific application of pathogen detection via binding of M13 bacteriophage, it is found that increases in the channel depth are more significant in improving the linear dichroism signal than increases in the channel width. Increasing the channel depth to 2 mm and pressure gradient to 5 × 104 Pa m-1 essentially maximizes the alignment. Oscillating flow can produce nearly equal alignment to steady flow at appropriate frequencies, which has significant potential practical value in the analysis of small sample volumes. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/List_of_calculated_orientation_parameter_averages_for_stead... |
| Title | List of calculated orientation parameter averages for steady flow from Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy. |
| Description | Flow linear dichroism is a biophysical spectroscopic technique that exploits the shear-induced alignment of elongated particles in suspension. Motivated by the broad aim of optimizing the sensitivity of this technique, and more specifically by a hand-held synthetic biotechnology prototype for waterborne-pathogen detection, a model of steady and oscillating pressure-driven channel flow and orientation dynamics of a suspension of slender microscopic fibres is developed. The model couples the Fokker-Planck equation for Brownian suspensions with the narrow channel flow equations, the latter modified to incorporate mechanical anisotropy induced by the particles. The linear dichroism signal is estimated through integrating the perpendicular components of the distribution function via an appropriate formula which takes the biaxial nature of the orientation into account. For the specific application of pathogen detection via binding of M13 bacteriophage, it is found that increases in the channel depth are more significant in improving the linear dichroism signal than increases in the channel width. Increasing the channel depth to 2 mm and pressure gradient to 5 × 104 Pa m-1 essentially maximizes the alignment. Oscillating flow can produce nearly equal alignment to steady flow at appropriate frequencies, which has significant potential practical value in the analysis of small sample volumes. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/List_of_calculated_orientation_parameter_averages_for_stead... |
| Title | List of calculated velocity and orientation parameter averages for oscillating flow from Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy |
| Description | Flow linear dichroism is a biophysical spectroscopic technique that exploits the shear-induced alignment of elongated particles in suspension. Motivated by the broad aim of optimizing the sensitivity of this technique, and more specifically by a hand-held synthetic biotechnology prototype for waterborne-pathogen detection, a model of steady and oscillating pressure-driven channel flow and orientation dynamics of a suspension of slender microscopic fibres is developed. The model couples the Fokker-Planck equation for Brownian suspensions with the narrow channel flow equations, the latter modified to incorporate mechanical anisotropy induced by the particles. The linear dichroism signal is estimated through integrating the perpendicular components of the distribution function via an appropriate formula which takes the bi-axial nature of the orientation into account. For the specific application of pathogen detection via binding of M13 bacteriophage, it is found that increases in the channel depth are more significant in improving the linear dichroism signal than increases in the channel width. Increasing the channel depth to 2 mm and pressure gradient to 5 × 104 Pa m-1 essentially maximizes the alignment. Oscillating flow can produce nearly equal alignment to steady flow at appropriate frequencies, which has significant potential practical value in the analysis of small sample volumes. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/List_of_calculated_velocity_and_orientation_parameter_avera... |
| Title | List of calculated velocity and orientation parameter averages for oscillating flow from Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy. |
| Description | Flow linear dichroism is a biophysical spectroscopic technique that exploits the shear-induced alignment of elongated particles in suspension. Motivated by the broad aim of optimizing the sensitivity of this technique, and more specifically by a hand-held synthetic biotechnology prototype for waterborne-pathogen detection, a model of steady and oscillating pressure-driven channel flow and orientation dynamics of a suspension of slender microscopic fibres is developed. The model couples the Fokker-Planck equation for Brownian suspensions with the narrow channel flow equations, the latter modified to incorporate mechanical anisotropy induced by the particles. The linear dichroism signal is estimated through integrating the perpendicular components of the distribution function via an appropriate formula which takes the biaxial nature of the orientation into account. For the specific application of pathogen detection via binding of M13 bacteriophage, it is found that increases in the channel depth are more significant in improving the linear dichroism signal than increases in the channel width. Increasing the channel depth to 2 mm and pressure gradient to 5 × 104 Pa m-1 essentially maximizes the alignment. Oscillating flow can produce nearly equal alignment to steady flow at appropriate frequencies, which has significant potential practical value in the analysis of small sample volumes. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/List_of_calculated_velocity_and_orientation_parameter_avera... |
| Title | List of calculated velocity and orientation parameter averages for oscillating flow from Oriented suspension mechanics with application to improving flow linear dichroism spectroscopy. |
| Description | Flow linear dichroism is a biophysical spectroscopic technique that exploits the shear-induced alignment of elongated particles in suspension. Motivated by the broad aim of optimizing the sensitivity of this technique, and more specifically by a hand-held synthetic biotechnology prototype for waterborne-pathogen detection, a model of steady and oscillating pressure-driven channel flow and orientation dynamics of a suspension of slender microscopic fibres is developed. The model couples the Fokker-Planck equation for Brownian suspensions with the narrow channel flow equations, the latter modified to incorporate mechanical anisotropy induced by the particles. The linear dichroism signal is estimated through integrating the perpendicular components of the distribution function via an appropriate formula which takes the biaxial nature of the orientation into account. For the specific application of pathogen detection via binding of M13 bacteriophage, it is found that increases in the channel depth are more significant in improving the linear dichroism signal than increases in the channel width. Increasing the channel depth to 2 mm and pressure gradient to 5 × 104 Pa m-1 essentially maximizes the alignment. Oscillating flow can produce nearly equal alignment to steady flow at appropriate frequencies, which has significant potential practical value in the analysis of small sample volumes. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/List_of_calculated_velocity_and_orientation_parameter_avera... |
| Description | Clinical assessment of FAST software |
| Organisation | Birmingham Women's and Children's NHS Foundation Trust |
| Country | United Kingdom |
| Sector | Public |
| PI Contribution | Provision of FAST software for clinical assessment of sperm flagellar movement |
| Collaborator Contribution | Carrying out FAST assessment on 75 IVF samples alongside provision of IVF outcome data |
| Impact | Dataset still in development. Multidisciplinary (clinical science and mathematics). |
| Start Year | 2019 |
| Title | Flagellar Analysis and Sperm Tracking (FAST) |
| Description | Software for automated detection and extraction of sperm flagellar motion |
| Type Of Technology | Software |
| Year Produced | 2019 |
| Impact | Software currently in use for routine assessment of semen samples at Birmingham Women's Fertility Centre |
| URL | http://flagellarcapture.com/ |
| Title | The art of coarse Stokes: Code for manuscript - Gallagher and Smith 2021, Roy. Soc. Open. Sci. |
| Description | The method of regularised stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly- varying regularised stokeslet kernel. Here we show how Richardson extrapolation with coarse values of the regularisation parameter is ideally-suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency. This Zenodo repository contains all the MATLAB code for the manuscript: Gallagher and Smith 2021, The art of coarse Stokes: Richardson extrapolation improves the accuracy and efficiency of the method of regularized stokeslets. This work was supported by Engineering and Physical Sciences Research Council (EPSRC) Award No. EP/N021096/1. MTG acknowledges support from EPSRC Centre Grant EP/N014391/2. |
| Type Of Technology | Software |
| Year Produced | 2021 |
| Open Source License? | Yes |
| URL | https://zenodo.org/record/4632956 |
| Title | The art of coarse Stokes: Code for manuscript - Gallagher and Smith 2021, Roy. Soc. Open. Sci. |
| Description | The method of regularised stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly- varying regularised stokeslet kernel. Here we show how Richardson extrapolation with coarse values of the regularisation parameter is ideally-suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency. This Zenodo repository contains all the MATLAB code for the manuscript: Gallagher and Smith 2021, The art of coarse Stokes: Richardson extrapolation improves the accuracy and efficiency of the method of regularized stokeslets. This work was supported by Engineering and Physical Sciences Research Council (EPSRC) Award No. EP/N021096/1. MTG acknowledges support from EPSRC Centre Grant EP/N014391/2. |
| Type Of Technology | Software |
| Year Produced | 2021 |
| Open Source License? | Yes |
| URL | https://zenodo.org/record/4632955 |
| Description | Birmingham Popular Maths Lecture |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Schools |
| Results and Impact | About 60 school pupils and members of the public attended for a talk at the research organisation and discussion after the talk. |
| Year(s) Of Engagement Activity | 2020 |
| URL | https://www.birmingham.ac.uk/schools/mathematics/news-and-events/events/2019/bpml-dr-meurig-gallaghe... |
| Description | Pint of Science: How do sperm get to the egg? |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Public/other audiences |
| Results and Impact | About 50 people attended a talk in a pub followed by questions and debate |
| Year(s) Of Engagement Activity | 2018 |
| URL | https://pintofscience.co.uk/events/birmingham |
| Description | School visit (King Edwards VI Five Ways) |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Schools |
| Results and Impact | About 80 pupils attended a talk about my EPSRC funded research. There were a number of requests for additional information and slides, the school reported that the talk was enjoyable. |
| Year(s) Of Engagement Activity | 2016 |
| Description | thinktank Futures Gallery Exhibit 'Microbots' |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Public/other audiences |
| Results and Impact | Research team members created an interactive exhibit for Birmingham Science Museum 'thinktank' futures Gallery engaging members of the public with microscale fluid dynamics, image analysis and medical applications. Over 2500 visitors interacted with the exhibit in the first 30 months (October-December 2019). |
| Year(s) Of Engagement Activity | 2019,2020 |
| URL | https://artsandsciencefestival.co.uk/festival-event/microbots/ |