How a swiss cheese can help us understand eye conditions

Two weeks ago I took part in a workshop on modelling age-related macular degeneration. A group of about 30 mathematicians, scientists and engineers were lucky enough to spend three days in Oxford working on aspects of this condition, including how and why it develops (currently not very well understood) and possible avenues for treatment. Macular degeneration is by far the leading cause of sight loss in this country, with others being glaucoma, cataracts and diabetic retinopathy, and it is worryingly common, with about 600,000 people affected, which is about 1%. Although it can be treated, the current treatments are unpleasant and not always effective so there is good reason for doing research to try to understand what’s going on in the condition.

During the workshop I worked with a group of five others on modelling a layer of tissue at the base of the retina of the eye that might be getting blocked up in patients with macular degeneration. We looked at models of how blockages in this layer could affect the ability of large molecules to pass through it, which is needed for healthy functioning of the eye.

Group 2

The remains of group 2 at the end of the modelling camp: Jennifer Tweedy (Imperial College London), Dave Smith (University of Birmingham), Phil Luthert (University College London), Moussa Zouache (University College London), Helen Byrne (University of Oxford), (photo by Rosemary Dyson)

In our models, we were trying to simplify and idealise the real situation, in order to end up with some equations that we can use to calculate or predict something useful. The problem is that, in simplifying, one can leave out something important… so it’s a tricky business. Our first attempt was the ping pong balls model, in which we modelled the blockage as solid lumps in the layer. We soon decided that this was the wrong model, which meant we needed to try something else.  So next we tried the Swiss cheese model (or at least, that’s what Rich calls it!) in which we modelled the blockage as holes in the layer that gradually close up as stuff is deposited over a lifetime. This produced something that has potential for future development. Meanwhile we were assisted by other group members, who were looking at the problem from alternative angles.

Swiss cheese

How a block of swiss cheese can help solve problems in the eye (a small portion of our whiteboard at the end of the workshop).

We were put up in magnificent rooms in Wadham College, and, even better, there was also time for a bit of sightseeing in the form of a walking tour around the city centre on the first evening.

Visiting the sights

Visiting the sights in Oxford: Krystyna, Rodolfo, Mariia and me with the Bodleian Library in the background

After the conference my long-term collaborator Rodolfo Repetto from Italy and his student Mariia Dvoriashyna from Ukraine came back to Shapwick so that we could make some progress with a paper we are writing. We took them to a pub in Godney, which we discovered to be a village that makes Shapwick look well connected!

Meal at Godney

Enjoying a meal at the Sheppy in Godney: Rich, Rodolfo, Mariia and me

I have attended several mathematical study groups over the years, and even organised one myself in 2009, which was hard work, but rewarding! They are a great way to learn techniques for tackling mathematical modelling problems, as they are one of the few chances we have to work so closely with a range of other people as we develop a new model.

Just an ordinary Saturday in the Polden Wheel… (ahem)

It’s good when great things happen in the parish and the vicar has little to do with them!

This morning started off with the Big Breakfast in Ashcott. It may not be a surprise to some of my readers that an event advertising ‘breakfast’ was going to be a big draw for me! It had been advertised as a charity fundraiser in the village so it was a real pleasure to walk into the hall and find it was effectively being run by the church’s core group! Freda Prime and Margaret Trim’s team cooked over 90 breakfasts between about 9 and 11 – about double what they were expecting!

The Big Breakfast in the Ashcott Village Hall

The Big Breakfast in the Ashcott Village Hall

About a month ago, Nigel Steady told me he’d booked the Christian singer/songwriter Paul Field, and asked whether it would be ok to use Shapwick Church? I was hardly going to say ‘no’ but was a bit worried about his organising a concert in one month flat. I needn’t have worried: this evening’s event was outstanding.

Paul Field in concert at Shapwick church

Paul Field in concert at Shapwick church

Paul Field has been campaigning on slavery and human trafficking issues, such as through the Stolen Lives project.

Over a career spanning forty years, Paul has worked with secular artists like Gloria Gaynor, Katie Melua and Rick Wakeman, as well as Christian singers like Cliff Richard, Natalie Grant and Rebecca St James. More recently he’s been involved with social issues like modern-day slavery and human trafficking. His concert included some powerful and challenging videos and songs that brought out the reality of slavery in the world today. For example, there are currently believed to be 21 million people enslaved worldwide, 13,000 of whom are in the UK [eg Free the Slaves stats]. This has led to his doing work for the Stolen Lives project, which featured in this concert.

This all contributed to a high-quality and very thought-provoking evening. For me personally it all contributed to a great weekend – not least in realising the gifts and talents of those in the parish!

Mist, sun and reflections in the Lake District

Jen and I could hardly have picked a better week to be in the Lake District last week! Although we had to contend with mist and cloud on occasions, the weather was stunning for much of it the time. I’m going to let the photos tell most of the story this time.

Our first full day was the one where the clouds never fully left the scene. We did the Dale Head round, which is one of my favourites in the Lake District, but Jen never quite got the views that I’d promised!

Dramatic clouds from the top of Dale Head towards Maiden Moor (Newlands Valley just visible on the left)

Dramatic clouds from the top of Dale Head towards Maiden Moor (Newlands Valley just visible on the left)

Late on the following morning around Buttermere, we had the most spectacular scenery of the entire week – and this view of the reflections from High Crag scarcely does it justice.

Reflections on Buttermere: High Stile is the mountain

Reflections on Buttermere: High Stile is the mountain

Our walk that day started late. Further up, a light mist had settled across the landscape, and I haven’t yet worked out to compensate for this photographically – but the mountains still looked magnificent.

Jen on Stile looking towards Great Gable

Jen on Stile looking towards Great Gable

I’m sure I’ve done Red Pike before but I’d certainly forgotten how amazing the views are, despite the mist. Nevertheless the entire descent from top to bottom was dreadful – it’ll have to be another route down next time!

Getting clear views was difficult because there was a light mist all day, but Crummock Water and Grasmoor still looked stunning from Red Pike.

Getting clear views was difficult because there was a light mist all day, but Crummock Water and Grasmoor still looked stunning from Red Pike.

We were based at the Black Sail youth hostel for Thursday and Friday nights, and our best day’s walking was on the Friday. We did some peaks neither of us had done before: Pillar, Scoat Fell, Steeple and Haycock. The clouds prevented obtaining great photos – but it was a most rewarding walk.

Jen crossing Scoat Fell, with Steeple in the background on the right

Jen crossing Scoat Fell, with Steeple in the background on the right

Our final walk, on the Saturday, was on Grasmoor – just out of the main tourist area but a very rewarding climb. I particularly enjoyed this view of Dale Head and the Newlands Valley.

The evening Sun gave some nice textures in the view towards Dale Head and the Newlands Valley

The evening Sun gave some nice textures in the view towards Dale Head and the Newlands Valley

Cuthbert and the otters

There’s a story about the Celtic hermit-monk, St Cuthbert, and a pair of otters, which is very endearing – but whose truth, until recently, I doubted. It’s told by Bede, his biographer and near-contemporary.

An icon of Cuthbert praying - with otters in attendance

An icon of Cuthbert praying – with otters in attendance (from Aidan Hart Sacred Icons)

Cuthbert lived as a monk on Lindisfarne in the 7th century, and soon acquired a reputation of great holiness. While visiting another monastic community he was known to slip outside in the middle of the night and return in the morning. A fellow monk wanted to find out what he did, so one night he followed him from a distance. He discovered that Cuthbert waded into the sea up to his neck. When morning came he returned, knelt on the beach, and prayed. While he did so, “two otters bounded out of the water, stretched themselves out before him, warmed his feet with their breath, and tried to dry him with their fur. They finished, received his blessing, and slipped back to their watery home”.

It’s hardly surprising that Cuthbert had a reputation for closeness to nature! But when I frist read the story my thoughts were, “I wish this were true, but really, it’s too far-fetched; it must be pious legend.”

I thought the same about another story of Cuthbert – his association with crows – but that changed because of evidence from an unexpected source.

Cuthbert had sought greater solitude in later life and ended up on Inner Farne, a small, bleak island in the North Sea off the Northumbrian coast. Some ravens that shared the island decided that straw on the visitors’ house would make great nesting material. Cuthbert rebuked them – but they ignored him. So Cuthbert resorted to more drastic words: “In the name of Jesus Christ, depart forthwith!”. At this, the ravens departed.

Bede records what happened next: “Three days later, one of a pair of them returned, and finding Cuthbert digging, stood before him, with feathers outspread and head bowed low to its feet in a sign of grief. Using whatever signs it could to express contrition it very humbly asked pardon. When Cuthbert realised what it meant, he gave permission for them all to return. Back they came with a fitting gift – a lump of pig’s lard. Cuthbert would often show this to his visitors, inviting them to grease their shoes with it”.

Again a lovely story – but again one that my sceptical mind doubted severely.

Until I read a couple of articles on the BBC News website about crows bringing gifts. The one that really struck me was about a crow called Sheryl (geddit?!): “Sheryl brings me gifts. My first was presented to me with her wings splayed open and head bowed. I was very ceremoniously handed a yellow foam dart from a toy gun! She refused to take the dart back as she does when we play games. I felt truly honoured.”

What really struck me about the story is not just the fact that it brought the gift, but the gesture while doing so which evoked Bede’s description of Cuthbert’s raven. I suddenly realised that story had a ring of truth to it: he was accurately describing the bird’s behaviour. Whether the ravens were “repentant” in the way that Bede described is a little less clear- but perhaps the event itself is described accurately.

I wonder whether the same might be said of Cuthbert and the otters? Perhaps they did indeed play around his feet as described – but perhaps with less intention to warm him with their breath and dry him with their fur as the monk described? I’m realising that I may have underestimated the veracity of Bede’s ‘Life of Cuthbert’, which the story of the ravens unexpectedly reveals.

An otter sighting

I may have otters on the brain at the moment. I went for a birding trip last week to the new hide at Catcott Lows which overlooks a small, reed-lined lake. There was hardly a bird in sight, apart from a little egret on the far side and three little grebes in the middle. Then I became aware that there was a form in the water to my left – “What have we here?” I thought, as I saw the unmistakable shape of an otter swimming through. It cruised along, diving gracefully, emerging to swim further on and dive again. I watched it doing this for about five minutes before it disappeared. It was a stunning sighting!

The stories about Cuthbert are from “The Age of Bede”, Penguin (2004), p54 and p71

Gill and Ian’s wedding

A couple of weeks ago, Rich and I had the privilege of attending the wedding of my good friend Gillian Overend to Ian Jones. I met Gill as a fellow leader on Basecamp in 2009, which is a Christian summer camp whose aim is to encourage young christians in godliness and leadership skills. It takes place every year in a National Trust centre at High Wray in the Lake District just to the west of Lake Windermere, and there are around ten leaders and 16 young people aged 16-20. On alternate days we work for the National Trust on things like building footpaths through bogs, or chopping down and burning rhododendron trees . On the intermediate days we do activities like walking and kayaking. There are small Bible study groups and a big meeting every evening with a Bible talk. I went back to Basecamp in 2011 and 2013, in which years Gill acted as an excellent overall leader of the camp!

Gill looking useful

Gill looking useful at Basecamp in 2011 – path building at the Kirkstone Pass. Photo by unknown Basecamp member

Ian and Gill

Walking out of the church! Photo by Rich

Ian and Gill got married in the church where Gill’s father is vicar, although another vicar took the service so that Gill’s dad could focus on his father-of-the-bride job. The church is in Billinge, which is in historic Lancashire, but is now part of modern day Merseyside. Although we set off really early (for us), there had been a major accident on the M6 causing long delays, and we ended up trailing in behind the bride!

The service itself was really joyful, and Rich and I appreciated the sense of God’s presence within it. We were impressed by the address on Ecclesiastes 4:9-12, which was given by the comedian Ian Macdonald, as it was thoughtful and highlighted some of the priorities that are relevant to marriages in the 21st century.

Rich and Jen

Rich and Jen at the reception. Photo by John Southcombe

The day also provided a chance to catch up with some other old friends: Nicola Morris, much revered cook at Basecamp, John and Dawn Southcombe and Hilary Gardner who were all a lot of fun to be around and have inspirational stories of their own faith journeys.

Gill’s attention to detail meant that at the reception we were put on the same table as a family who live in Kenilworth, which is where I grew up. Tim is the churchwarden of St John’s Church in Kenilworth, and it was exciting to hear about the major building project they are currently undertaking. Tim and Fiona’s twin daughters Rhian and Sian were also there celebrating – one day after their own 21st birthdays! I also particularly enjoyed the beautiful piano music at the service and reception, which was played by two of Ian’s friends.

Our table at the reception

Our table at the reception: Ian, Rhian, Sian, Fiona, Hilary, Dawn, John, Nicola, Jen. Photo by Rich

We left before the dancing, much to Rich’s relief, and headed back down to Somerset. Lots of people had reassured us that, at that hour of the evening, the journey back would be much easier than our long journey up. Four-and-a-half hours later and several sets of roadworks later we weren’t so convinced about that, but as we finally got to bed at 1.30am, we agreed that it had been a most excellent day and we were so pleased to have been invited.

The majestic kingfisher

One of the lesser-known hides here – Canada Lake – is brilliant for kingfishers. Having decided to visit more of the reserves in the area, I’d gone to see what was there, and after a while noticed a couple of them zipping around the near side of the lake. A branch next to the hide had been deliberately placed as a perch for them, but they seemed to be using one closer to the water’s edge, and on the wrong side of the reeds from where I was sat; but then, just before I was about to leave, one landed on the branch. Watching and photographing it made me realise, yet again, what magnificent birds they are.

Kingfisher at the Canada Lake hide

Kingfisher from the Canada Lake hide

Kingfisher at the Canada Lake hide: I was lucky that the lighting was just right for the photos - as long as she looked in the right direction!

Kingfisher from the Canada Lake hide: I was lucky that the lighting was just right for the photos – as long as she looked in the right direction!

Kingfisher at the Canada Lake hide: magificent he may be, but you wouldn't want to be on the wrong end of that bill...

Kingfisher from the Canada Lake hide: magificent she may be, but you wouldn’t want to be on the wrong end of that bill…

And then she was off...

And then she was off…

Seeing a little bittern – really well!

Three years ago, little knowing I would end up living here, I travelled from Worcestershire to Ham Wall in order to see a little bittern. I stayed at a local campsite in order to be on site in the early morning. Earlier this summer, rumours began to circulate that a little bittern was being heard and seen again – so, living less than ten minutes from Ham Wall, I was eager for another sighting of this notoriously elusive bird.

Thus it was that, one evening in early July, I headed along the main track towards the eastern end of the reserve, keeping my ears open. Eventually I heard the muffled barking: huf… huf… huf…. With monotonous regularity, there were ten barks every 23 seconds. I waited for well over half an hour, every so often straining over the reeds to see whether I could at least glimpse it – but despite its audibility, it remained out of sight.

Then without warning it suddenly flew up from just below where I was stood, across in front of me – it can’t have been more than ten feet away at one point – before cruising into the middle of the reedbed on the opposite side of the path. I was able to take in the black wings with large white elliptical patches and the bright orangey-yellow bill as it passed by. I’d have been thoroughly content with that – but a few minutes later it returned, albeit a bit further away. Then, shortly after, it flew along the reedbed. Three sightings in about ten minutes – each one far better than the glimpses three years ago.

Little bittern - photo by local wildlife photographer James Packer.

Little bittern – photo by local wildlife photographer James Packer.

A few days later I was chatting with a neighbour who is also a birding enthusiast. I was bemoaning the fact that I’d missed the collared pratincole that had been seen at Ham Wall while Jen and I were in the Scillies. I then mentioned this little bittern sighting, which he thought was more notable: “Some people would kill you for that!” he said.