I am delighted to have been able to attend a Royal Institution ‘Summer School’ workshop on bioengineering this August. The focus in this workshop was on refining drug delivery systems and using mathematics to determine whether a foetus is developing properly.
The first half of the session was lead by Rachel Dorris, a medical physicist, and was centred on how drugs can be better designed for use in inhalers.
Asthma is an autoimmune disease caused by the spontaneous contracting of the smooth muscles that surround the bronchioles in the lungs which results in constricted airways. Inhalers contain a drug (a bronchodilator) that can ‘open up’ the airways.
![bronchiole](https://curiositykilledthecation.wordpress.com/wp-content/uploads/2017/09/bronchiole.jpg?w=720)
(credit: slideplayer)
In order for this treatment to be effective, the drug uptake (the retention of the drug in the necessary organ) must be at its optimum. To measure the drug uptake, a medical imaging technique that suits this purpose must be chosen. After some collaboration, our team decided that a Nuclear Medicine Scan was the ideal technique. It involves giving the patient the bronchodilator with a small amount of a radioactive tracer (Technetium-99m) and then observing the patient with a gamma camera. The image quality is relatively low but provides functional information and can be easily used to observe drug uptake.
![Lung2](https://curiositykilledthecation.wordpress.com/wp-content/uploads/2017/09/lung2.gif?w=400&h=262)
This is an example of a Nuclear Medicine Scan of the lungs. The whitest areas show the highest drug uptake. (credit: slideshare)
From Nuclear Medicine Scans of 4 different drug particle sizes in patients’ lungs, we performed a qualitative analysis of the images- determining which particle size we believed would have the optimum drug uptake in the bronchioles. We then performed a quantitative deposition analysis of the images to confirm our ideas. The conclusion we arrived at is that a bronchodilator with a particle size of 1.5μm was best suited to use in inhalers.
The second half of the workshop was lead by Dr. Stefaan Verbruggen, who is currently researching the effects of kicking in the womb during pregnancy on the development of musculoskeletal diseases, and, in particular, developmental dysplasia of the hip (DDH).
The hip is a type of “ball-and-socket” joint. In a normal hip, the ball at the upper end of the femur fits firmly into its socket in the pelvis. In babies with DDH, this joint is not properly formed and so the ball does not fit well in the socket and is easily dislocated. In all cases of DDH, the socket (acetabulum) is shallow which means that the ball cannot fit inside it comfortably.
![ddh1](https://curiositykilledthecation.wordpress.com/wp-content/uploads/2017/09/ddh1.jpg?w=720)
(Credit: Oxford University Hospitals)
1 in every 1000 babies are born with a form of DDH. There are varying degrees of severity in DDH cases:
- Subluxatable- the ball of joint is simply loose in the socket
- Dislocatable- the ball lies within the socket but can be dislocated easily
- Dislocated- the ball is completely out of the socket.
![ddh](https://curiositykilledthecation.wordpress.com/wp-content/uploads/2017/09/ddh.jpg?w=720)
(Credit: helpmegrowutah.blogspot.co.uk)
DDH is not genetic, but the risk of a baby having DDH greatly increases if there was not enough room in the womb whilst its bones and joints were developing.
A foetus’ bones and muscles, like in adults, react to stress by growing. In adults and children, the main stressor acting on the hip joint is gravity, but this is not the case in foetuses. Instead, the main way that foetuses can ‘exercise’ their hip joints, is by kicking. Considered one of the most endearing interactions between a foetus and the outside world, kicking is vital to its development; if there is not enough room for a foetus to kick, complications with joint development and DDH can arise.
- It is a ‘breech baby’ (the foetus is positioned feet first). In scans, it is revealed that these babies cannot fully extend their legs when kicking.
- There are issues with oligohydramnios (in which there is less amniotic fluid- normally due to a fault in the foetus’ urine production so that it ingests the amniotic fluid but does not pass it out). Notice how, in scans, these babies don’t appear to kick at all.
![MRI](https://curiositykilledthecation.wordpress.com/wp-content/uploads/2017/09/mri.gif?w=720)
Cine-MRI scans of baby kicks
Curiously enough, foetal twins tend to have enough space to kick comfortably, despite having to share the womb. (They also are unable to kick each other due to a membrane wall separating them!)
The progress of a foetus’ joint growth and muscle activity is measured to ensure that the pregnancy is going well and to calculate the risk of DDH. However, when foetuses are in the womb, experimental equipment, naturally, cannot be used and only images can be used. This means that mathematics must be employed in a fascinating manner to calculate strength of a kick from only two MRI scans.
![sok](https://curiositykilledthecation.wordpress.com/wp-content/uploads/2017/09/sok.jpg?w=720)
Start of kick (Frame 76)
![eok](https://curiositykilledthecation.wordpress.com/wp-content/uploads/2017/09/eok.jpg?w=720)
End of kick (Frame 83)
First we must work out the change in angle from the start to the finish of the kick. At the start of the kick, the angle between the hip and the ankle is 87°. At the finish, it is 153°. This means that the change in angle is 66°. Then, this must be converted to radians, making the value 1.15192 radians.
The MRI scan was taken at 3 frames per second and the kick took 8 frames. Using this, we can calculate that the length of the kick in seconds is (to three decimal places) 2.667 seconds.
Speed is found by dividing the distance by time taken to complete the distance. In this case, the distance is the change in angle. Therefore, the speed (or velocity) of the baby’s kick is 1.15192 / 2.667 = 0.432 radians/s.
The length of the lower leg is 58.4 millimetres and it can be considered a radius in this case. Acceleration is found by multiplying the square of the velocity by the radius. So the acceleration of the kick was 0.432² x 58.4 = 10.899 mm/s²
The foetal leg would weigh 0.321 kg. Since force = mass x acceleration, we can now also find the force that the foetus must generate to perform this kick- 3.498 N.
This example demonstrates just how powerful mathematics is; using only 6 relatively simple calculations, we can quickly work out the force of a foetus’ kick from just 2 basic MRI scan frames.
Overall, the workshop was an incredible introduction into the field of bioengineering. Without a doubt, the second half of the workshop was my favourite as I found the exploration of DDH in babies very interesting and I was amazed by how easy a seemingly impossible task was made by using formulae that I had already learnt in school but had never seen being used to solve ‘real-life’ problems.