1

IN THIS ISSUE: SUPERHYDROPHOBICITY

TSUNAMI DEPOSITS

MAPPING BROWN DWARF STARS

TACKLING CORONARY ARTERY DISEASE

JUST JOURNAL OF UNDERGRADUATE SCIENCE & TECHNOLOGY

VOLUME 2, EDITION 1, SPRING 2014

2

CONTENTS

Acknowledgements 3

About JUST 3

Forewords 4

Bioinspired Superhydrophobicity 5

by L Howes & R Browne

Sediment Transport & Deposition in Tsunamis 16

by T Howell

Brown Dwarf Discs in Upper Scorpius 24

by M. Read, L. Ireland, & N. Mayne

Using Machine Learning to Evaluate Coronary Artery Disease 35

by H Bolt

3

ACKNOWLEDGEMENTS

JUST would like to thank the Exeter

Annual Fund for the generous financial

support given in the production of this

Journal.

ABOUT

The Journal of Undergraduate Science and

Technology (JUST) aims to acknowledge

and showcase undergraduate research being

carried out within the College of

Engineering, Mathematics and Physical

Sciences (CEMPS) at the University of

Exeter. The Journal, as well as providing

undergraduate students with an opportunity

to develop their writing and presentation

skills, also enables them to engage with the

wider ‘STEM’ communities within the

University and beyond, and to exchange

ideas and share intellectual activity.

All undergraduates within CEMPS are

eligible to submit to the Journal for print

and online publication and the editorial

team welcome contributions from students

at any stage of their academic programme.

4

FOREWORDS

JUST is a great opportunity for

undergraduates to showcase some of the

really exciting research activities they are

involved in at the University of Exeter. By

publishing their work in print and online,

they are making a real contribution to

encouraging a national culture of

undergraduate research, and forging what

could be career-long links with their

colleagues in other universities and

academic communities.

Students at the University of Exeter are

immersed in research at the cutting edge of

their chosen fields. JUST demonstrates how

research-informed teaching, along with

opportunities for undergraduates to share

the outcomes of their own research

activities beyond the confines of

assessment, can have a real and lasting

impact on the quality of the student

experience. If you are an academic

colleague reading this edition, I hope that

you will encourage your students to get

involved with JUST, and to submit their

work to our enthusiastic team of student

editors. The next edition of the Journal is

timed to coincide with the College’s

Annual JUST Conference, which, this year,

is taking place on the Streatham Campus on

Wednesday 4th June. All contributors will

be invited to present their work at this

exciting event. If you are a student, do

consider writing for the Journal and

showcasing your work at this year’s

conference, as a presenter or by submitting

an academic poster.

Steve Rose, Academic Adviser to JUST

It is sometimes easy to forget that science

and technology are not obvious things. All

of the great innovations have happened

within 1% of human history, and, in the

modern world, innovation is moving

forward at an astonishing rate.

The foundations of science and technology

are the scientific method – empirical,

measurable, repeatable experiments – and

the process of peer review. The latter lends

papers authority, for those that pass peer

review have demonstrated that they are

well-written, well-researched, and well

worth reading. All researchers need to be

familiar with this process, and it is never too

early to start. This is why JUST exists.

This edition opens with a paper on

superhydrophobes: substances of great

interest to the textiles industry, for they are

virtually self-cleaning. The paper on

sediment deposits from tsunamis is

particularly relevant when one thinks about

the Fukushima incident. This is followed by

a study showing that brown dwarf stars are

typically smaller than previously thought.

Finally, an attempt is made to simulate

atherosclerosis in coronary arteries: a far

too common problem in the worsening

obesity epidemic.

Undergraduates can easily be overlooked

when it comes to research. Thankfully,

universities across the country are starting

to recognise the significant body of

research coming from the talented minds of

students, and finally giving them the

attention they deserve. By the end of this

journal, I am sure that you will agree that

this resource should not be neglected.

Paul Gratrex, Editor

5

ABSTRACT

The aim of this experiment was to explore

natural and artificially produced

superhydrophobic surfaces and investigate

into the physics of self-cleaning surfaces.

These types of surfaces are of great

importance with self-cleaning materials and

fabrics being used in various industries. We

have explored the surface structure and

confirmed the theory that the presence of

micro structures upon a surface increase

contact angles of water droplets with a

decrease in roll off angles. Experimental

data and optical imaging have shown a

difference in inner and outer leaf samples

that have resulted in equally high contact

angle values but differing results for roll

off. Inner samples around the core of the

lotus leaf show an increase in both

hysteresis and roll off values. We speculate

that this is due to surface structure but have

found no current work to compare our

experimental results with.

INTRODUCTION

The production of artificial non-wetting

materials and coatings has been an area of

great industrial interest with popularity

increasing over the turn of the century.

Artificial products are manufactured

attempting to replicate non-wetting

surfaces such as: rose petals; leaves of

numerous flowers; shark skin; and the

backs of beetles. These surfaces all exhibit

water repelling properties, from the beading

up of rain droplets upon leaves, to the

narrow grooves present on shark skin that

reduce drag and allows them to ‘cut’

through the water with ease[1]. In this

investigation we have examined the water

repelling properties of lotus leaves, one of

the most superhydrophobic materials in

nature.

It is commonly accepted that water droplets

should obtain contact angles (CA)

exceeding 150°, with roll off angles no

higher than 10° for a surface to be classed

as superhydrophobic[2]. CA is a quantitative

measure of the wetting of a solid by a liquid.

It is defined geometrically as the angle

formed by a liquid at the three phase

boundary where a liquid, gas and solid

intersect[3], as shown in Figure 1. The angle

that a surface is inclined that results in the

displacement of a droplet is the roll off

angle. These surfaces are very difficult to

wet, with droplets of water simply rolling

off even at low inclinations. This effect is

thought to be created by the surface

(interface) energies of the solid-liquid-gas

boundary and the surface structure and

roughness.

Figure 1: The contact angle between solid,

liquid, and gas.

The lotus leaf surface is often replicated due

to its ability to self-clean. Droplets roll

along the surface of the leaf picking up dirt,

bacteria and other foreign debris and

remove them from the surface. This self-

cleaning effect is known as the ‘Lotus

Effect’, first described by the German

botanist Wilhelm Barthlott and Christoph

Neinhuis in 1997[4]. They emphasise the

BIO-INSPIRED SUPERHYDROPHOBICITY

BY L. HOWES & R. BROWNE

6

importance of surface roughness on the CA,

and that wax coated papillae upon the

surface of leaves contributes to self-

cleaning.

These low wetting and self-cleaning

properties are being exploited in many

industries, from ship hull coatings made to

reduce fuel intake, to fuel cells designed to

vent CO2 through superhydrophobic

membranes, to superhydrophobic clothing.

This led us to a nano-engineered material

known as Nano-Tex. Their website

suggests that the material can repel liquids

and extend the life of fabrics without

effecting breathability[5], something which

superhydrophobic coatings can inhibit. We

obtained a swatch of Nano-Tex from their

head office in California in order for us to

run our investigation.

In our experiment, we have explored the

CA of numerous volumes of water droplets

upon samples of Lotus leaf and Nano-Tex

material. CA hysteresis was investigated

with samples exhibiting differing results.

The surface structure was examined using a

scanning electron microscope (SEM) and

an optical microscope to gain an insight into

what was causing superhydrophobicity on a

micro scale level.

THEORY

When a drop is placed upon a solid surface

you get a three-way boundary between the

solid, liquid and gas described using the

Young equation (1). Young’s model is the

basis of the theory behind how a surface

behaves under wetting and describes the

forces present along the boundary. This

model assumes a flat homogenous

surface[6].

cos 𝜃 =𝛾𝑆𝐺−𝛾𝑆𝐿

𝛾𝐿𝐺 (1)

Here, γSL, γSG and γLG are, respectively, the

surface energies of the solid-liquid, solid-

gas and liquid-air interfaces, and θ is the

static contact angle. The surface energy of a

liquid arises from the force imbalance along

the surface compared to within the bulk of

the fluid[7]. This creates a force known as

surface tension. Water contains one of the

strongest cohesive forces (the hydrogen

bond) because it is a polar fluid, and, to

minimise its surface, droplets will form

spheres[8].

Bulk forces within a surface can categorise

wherever a surface is of high or low energy.

High energy surfaces, such as glass,

ceramics or metals, have strong covalent,

ionic or metallic bonds which would require

large amounts of energy to separate; thus

they are classed as high energy. When in

contact with a high energy surface, a water

droplet will generally wet and achieve θ

values between 0° and 90°[9]. It is

energetically favourable for a liquid to wet

the solid surface rather than be separated

via an air film. For some low energy

materials which are bonded via hydrogen or

Van der Waals forces, it is more

energetically favourable for there to be an

air film separating the solid and liquid.

The CA in (1) is single valued with the

assumption of a flat surface. This

corresponds to the equilibrium position of

the solid-liquid-gas contact line. In reality,

surfaces are not homogenous, and can have

different roughnesses and chemical

compositions. This produces a range of

values for the CA due to adhesive forces

being stronger at certain points upon the

surface. This is more apparent when the

droplet is in motion as surface roughness

plays an important role in the roll off

angles. When placing a droplet upon a

rough surface, you can observe a minimum

and a maximum value for the CA (θrec and

7

θadv respectively) with the difference

between them being the CA hysteresis[10].

Figure 2: Schematic of a droplet upon a tilted

surface showing advancing (θadv) and

receding (θrec) CA. Surfaces that have low

CA hysteresis generally have lower roll

angles. This is dependent on the surface

roughness of the material as discussed on this

page.

To accommodate for the surface roughness,

both the Cassie-Baxter and Wenzel models

were formulated. The Wenzel model

assumes a liquid drop will fill grooves

found upon the surface of the material.

Figure 3: Qualitative representation of

Wenzel’s model with the droplet filling the

grooves that appear on a rough surface[11].

The roughness factor (R) of the surface is a

ratio of the solid surface area (where fluid

fills the grooves) to the area if using the

Young model, assuming a flat surface. For

the Young model, this has a value of one,

but here R>1. This adjusts the contact angle

such that

cos 𝜃 = 𝑅 cos 𝜃0 (2)

where θ is the true contact angle and θ0 is

the angle assumed via the Young model.

This indicates that the roughness of a

surface accentuates the water repellency or

the absorbing nature of the surface. The

Nano-Tex is engineered to have nano scale

fibres running along channels upon the

surface of each strand of fabric. When

testing with small volume drops, there is

evidence of wetting similar to that

presented with the Wenzel model, and,

when tilted, it shows high values for CA

hysteresis. It should be stated that Nano-

Tex claim this is a water resistant product

and not a waterproof fabric, so over time

and prolonged exposure water will wet a

surface[12].

The Cassie-Baxter model is the opposite of

the Wenzel and implies that water droplets

sit upon the surface grooves, leaving air

pockets present between the liquid and the

solid surface. This splits the liquid-solid

boundary into a liquid-solid and a liquid-

gas boundary and results in Cassie’s law.

cosθ = Rf fSLcosθ0 + fSL – 1 (3)

Here, θ, θ0 are as described in the Wenzel

model. Rf is now the roughness associated

with the solid surface in contact with the

liquid, and fSL is the fraction of the solid

surface area in contact with the fluid. When

Rf is equal to R and fSL=1, we return to the

Wenzel model.

The Lotus Effect is modelled using the

Cassie-Baxter model, where droplets of

liquid sit upon closely packed micro

structures known as papillae. These are

found upon the upper epidermis of the leaf

and are individually covered in a nanoscale

wax tubular[13].

8

Figure 4: The hierarchical double structure

presented by the lotus leaves consists of

papillae of the order of 10-20 microns in

height, 10-15 microns in width, and covered

in nanoscale wax tubular[13]. It is this wax that

is believed to be the cause of the Lotus Effect

that allows the surfaces of these leaves to

self-clean[14].

With tip diameters of the order of microns,

they provide a small surface contact area

with droplets. These small diameter tips,

paired with a high number density of

papillae (40 can be observed in an area of

100µm2), allow for even large volume

droplets (20µl) to achieve high contact

angles.

Confusion, however, can occur when

looking into literature on the

superhydrophobicity of rose petals. In

general, a high value for CA and a low CA

hysteresis implies low liquid-solid

adhesion. Experiments of water droplets on

roses reveal high values for CA, but such

strong adhesive forces that, even when

tilted to 180°, droplets will stay in contact

with the petal[15]. This is thought to be

produced via higher separation of

microscale structures which allow droplets

to be held by the surface and is known as

the petal effect. This raises questions over

the true meaning of the term

superhydrophobicity, a topic which is still

under discussion.

EXPERIMENTAL METHOD

With the aim of investigating the CA of

various volumes of droplets upon lotus

leaves and Nano-Tex, our samples were

flattened using weights and left for at least

24 hours. Once flat, they were secured on a

substrate at 0° inclination, and drops were

placed upon the surface from a small height

(a few mm). A ruler was secured in front of

the substrate for scaling purposes. A 10µl

pipette with error of ±0.05µl was used

throughout our investigation, as drop

volumes were varied from 2-50µl. This

broad spread of volumes was used to get a

sense of how the CA decreases with

increasing drop volume and to see its effect

on the roll off angle.

A Canon EOS 1000D camera fitted with an

extension tube was used for taking images

throughout our experiment. The images

were processed using the package

dropsnake found in the software ImageJ.

This provided a piecewise polynomial fit

which fits a polynomial between individual

points, even if using non-axisymmetric

drops. To reduce the error of CA

measurements, they were repeated

numerous times, and the half spread of

results obtained for error use. The standard

deviation of results provided errors that we

deemed too small with the human error that

can occur when taking readings and using

the software.

For the CA hysteresis, we used a set up

found in the Appendix. Images were

obtained and analysed using the same

software as before, this time measuring

both θrec and θadv and repeated to reduce

error. Finally, we plotted inclination against

CA hysteresis.

For investigating the surface structure,

samples of leaf and Nano-Tex were

9

investigated using a scanning electron

microscope (SEM). As a further

investigation, we looked at the surface of

the leaves using an optical microscope, as

the gold coating and exposure to a vacuum

within the SEM can affect the papillae of

the leaf.

RESULTS & DISCUSSION

Contact Angle, Volume, & Roll Off

The data in full can be found in the

appendix; only the key findings are

discussed here.

The samples of lotus leaf used in this

experiment have proven to be

superhydrophobic for volumes below 6µl,

achieving CA values above 150° with a

maximum value of 155.9±1.3°. A higher

resolution camera could be used for

increased magnification potentially

resulting in reduction of errors. Better

backlighting to enhance the boundary of the

water droplets allowing for easier CA

measurements could also have been made.

The most surprising result observed is the

difference in roll off angles for samples of

inner leaf (roughly 7.5cm from the core)

compared to the outer (further than 7.5cm).

Inner surfaces show increased roll off (28°

for a 40µl drop) compared to outer samples

(10° for the same volume), with evidence of

being pinned. Values for the CA hysteresis

angle are also increased as a result. This is

a surprising result as it threw open the

investigation into what is stated in literature

to be one of the best examples of

superhydrophobicity in nature. To

strengthen the findings, several inner

samples from numerous leafs were used; all

were found to have increase rolling angles.

This is discussed further later on.

Nano-Tex samples have been shown to

have lower values for CA than for the lotus

leaf, confirming that the presence of

microstructures upon a surface has

increased CA. Similar to what was

observed for the lotus leaves, increasing

drop volume decreases the CA. When it

comes to roll off, small volumes of fluid

(<15µl) did not roll when inclined. One

could speculate that this is due to droplets

being trapped upon the surface with drop

weight not being enough to overcome

adhesive forces with the surface. When

higher volume droplets are used, the weight

of the fluid and the incline appears to be

enough to achieve roll off. Droplets do,

with time, appear to soak into the material,

decreasing CA with time. Unlike the lotus

leaf, Nano-Tex can become wet when

overused, and droplets will soak into the

already wet regions. This decreases CA

even further.

Contact Hysteresis Plots

Figure 5: CA hysteresis against inclination

plot presenting data from all three samples

with: Nano-Tex in blue; outer leaf in red; and

inner leaf in green. Both Nano-Tex and outer

leaf samples show a linear relation between

the two variables. The inner leaf shows

evidence of a linear relation at the point of

inclination and before roll off.

The plot above shows how each sample

behaved under inclination, and the effect of

CA hysteresis to the point of roll off. Outer

and inner leaf samples show roll off values

of 18° and 26° for a 40µl droplet

10

respectively. Outer samples show a linear

relation between roll off and CA hysteresis

value, confirming that droplets roll along

the surface with little resistance, as

explained in the Lotus Effect[5]. The same

can be said for Nano-Tex, which shows

evidence of being pinned even at low

inclinations with eventual roll off at 44°.

The inner leaf appears to show a linear

relation between inclination and CA

hysteresis, both at the start and just before

roll off. This may be due to the droplet

initially rolling (much like the outer

sample) before being abruptly stopped by

the surface roughness. There is then

evidence of the droplet deforming,

increasing CA hysteresis values, before

finally rolling off. As stated earlier, this is

an unexpected result, and further tests

would be required to confirm the reliability

of our results.

Surface Structure

Figure 6: An image at 0° inclination

displaying the stomata (large structures) and

papillae. When taking separate 100µm2 areas,

both researchers counted 38 papillae, with an

average separation of 17.8 microns. This is a

sample of the outer leaf, where stomata

appear more abundant, and papillae

distributed uniformly.

Whilst using the SEM, we confirmed, using

our samples of lotus leaves, some of the

theories over the surface structure causing

the Lotus Effect.

Figure 7: An image of a single papillae on

the same leaf sample. The sample is tilted at

52° with the height calculated to be

approximately 17 microns. The width at the

tips when at a 0° were all on the order of

microns, as predicted[14].

It can clearly be seen in Figure 7 that the

surface and papillae (including the tip) are

covered in the nanoscale wax that is

believed to be the cause of the Lotus Effect.

The stomata scattered around the outer

parts of the leaf are much larger (Figure 12)

and do not show any evidence of wax upon

their surfaces. The underside of the leaf

(Figure 13) is included in the appendix for

comparison. These results confirm with

theory that the surface consists of uniformly

distributed microstructures that are covered

in nanoscale fibres.

Images of the Nano-Tex, in contrast, show

results no different to viewing samples of

cotton. When zooming past 5 microns, the

samples have bubbled up and cracked the

gold coating (Figure 14).

11

Figure 8: The surface of an individual fibre

of Nano-Tex displaying an apparent valley

structure upon the surface. Upon these

valleys, it is believed, are the nano structures

that are the cause of the material’s water

repellency.

When results taken using inner leaf samples

were found to result in greater values for the

roll off, it was predicted that either a higher

number density of stomata would be

present (which may cause pinning) or an

increase in spacing between the

microstructure papillae (like in roses).

Optical images show these findings.

Figure 9: Optical image at 20x zoom for the

outer leaf. Both stomata and papillae can be

made out, with stomata being the larger

brighter structures.

Figure 10: Optical image at 20x zoom for the

inner leaf. There is no evidence of stomata

present and the spacing between papillae is

comparable with that of the outer leaf

samples.

From taking optical images, no distinct

differences have been observed in spacing

between microstructures, although there is

evidence of a decreased number of stomata

upon the inner leaf. No relevant literature

has been found that has observed a

difference between how inner and outer

lotus leaf samples behave under wetting.

This investigation has shown that there is a

clear increase in roll off angle of 40µl drops

upon inner samples of leaf. The results

where volumes are varied have also shown

evidence of increased roll off when

compared to outer leaves, and, for volumes

less than 10µl, complete adhesion.

CONCLUSION

An SEM was used to image the surface of a

natural superhydrophobic source, the lotus

leaf, to confirm the theory for the causes of

such high values for CA. An artificial nano-

engineered fabric has been used for

comparison, with results indicating that

droplets wet upon the surface, which could

be the result of droplets filling between the

nano fibres.

12

The SEM has also been used to show that

closely-packed wax-covered papillae are

present on the surface of the lotus leaf, with

theory suggesting that low roll angles are

due to this wax. High values for CA have

been shown for various volumes of

droplets; however, there is evidence to

suggest that their surfaces are not uniform.

An increased roll off angle has been

observed with higher values for CA

hysteresis than for inner samples around the

core of the leaf. Outer leaves show lower

roll off angles and low CA hysteresis

values, as expected for a self-cleaning

surface. Possible causes of this have been

speculated, but no obvious conclusion as to

why such an effect occurs has been reached.

It is interesting to look back over the

definition of a superhydrophobic surface, as

CA values exceeding 150° for outer leaf

samples and Nano-Tex have been achieved;

however, roll off angles only reach 10° at a

volume of 40µl (for leaves). At this volume,

CA values of around 130° were measured.

This confusion seems to be replicated in

numerous papers[15][16] that question the

definition of superhydrophobicity. There is

a question as to whether surface roughness

plays a part in the definition.

Superhydrophobicity may only hold if

using the Young model, where there is no

surface roughness. This roughness can

inhibit roll off, even with high CA values,

as shown with inner leaf samples and Nano-

Tex, or even result in no roll off at all when

using low volumes on all samples.

Regardless of any issues with the definition,

this phenomenon is being put to good use in

many industries that attempt to replicate

low wetting and self-cleaning surfaces that

have extensive practical applications.

13

APPENDIX

Setup

Figure 11: Experimental setup for measuring

the CA hysteresis: a simple setup consisting

of a hinged surface that is set at 0°

inclination. A jack is used to slowly raise the

surface, and images were taken side-on. The

angle of inclination was measured using a

protractor secured to the side of the tilting

table.

SEM Images

Figure 12: An image of the tip of the stomata

upon the surface of the leaf. There is no sign

of any wax upon the top of these structures.

As a result, it is not believed they are a factor

in producing low rolling angles.

Figure 13: The underside of the leaf, even at

this magnification, shows no clear

microstructures. There are channels and

valleys that appear to be filled with the

nanoscale wax, and, as predicted[13], are

longer and thicker than the fibres found upon

the upper surface, which are thinner and more

densely packed.

Figure 14: The surface of the Nano-Tex

cracking when attempting to zoom further

into a fibre.

14

TABLES OF RESULTS

Table 1: Table of results for outer samples of leaf.

The angles θrec and θadv and roll off were measured.

A roll off of N/A implies that, when tilted past 90°,

drops have adhered to the surface.

Table 2: Table of results for inner samples of leaf

Table 3: Table of results for samples of Nano-Tex

Volume (µl) θrec (°) θadv (°) Roll off angle (±2°)

2±0.05 149.520±5.7 155.952±1.3 N/A

4±0.05 147.394±1.2 152.319±2.3 70

6±0.05 143.769±0.38 144.847±0.38 30

8±0.05 140.473±1.2 140.663±2.3 13

10±0.05 141.068±3.7 143.776±0.1 24

15±0.10 134.313±0.53 137.680±1.1 18

20±0.10 130.005±1.1 132.682±1.1 14

30±0.15 132.230±2.9 132.363±2.5 12

40±0.20 126.656±2.3 133.317±1.3 10

50±0.25 124.568±2.1 127.331±1.4 23

Volume (µl) θrec (°) θadv (°) Roll off angle (±2°)

2±0.05 149.975±0.44 152.953±3.4 N/A

4±0.05 147.242±0.95 150.310±3.2 N/A

6±0.05 142.515±0.44 142.467±2.6 N/A

8±0.05 136.274±2.3 137.413±2.9 N/A

10±0.05 132.366±1.5 135.420±1.4 85

15±0.10 141.14±0.61 147.254±1.2 67

20±0.10 136.007±2.9 137.939±3.3 65

30±0.15 127.909±1.2 132.752±3.0 22

40±0.20 127.706±1.3 129.298±1.6 28

50±0.25 130.219±1.3 136.068±3.2 19

Volume (µl) θrec (°) θadv (°) Roll off angle (±2°)

2±0.05 149.191±3.2 150.617±1.8 N/A

4±0.05 144.392±2.2 146.490±1.1 N/A

6±0.05 141.071±2.6 145.801±2.6 N/A

8±0.05 134.862±3.3 138.994±3.2 N/A

10±0.05 134.744±3.6 136.100±3.9 N/A

15±0.10 124.998±3.0 126.540±1.3 N/A

20±0.10 124.335±1.3 124.598±2.3 75

30±0.15 115.620±3.2 117.235±2.3 52

40±0.20 116.660±3.0 116.782±2.7 43

50±0.25 112.453±1.8 113.128±2.1 36

15

REFERENCES

[1] http://www.asknature.org/strategy/038caf453c09b3016465cc6a93605#.Uy4UAl63EfI

(accessed 29 Nov. 2013)

[2] http://www.mecheng.osu.edu/nlbb/files/nlbb/Lotus_Effect.pdf (page 3)

(accessed 29 Nov. 2013)

[3] http://attenstion.com/applications/measurements/contact-angle

(accessed 29 Nov. 2013)

[4] Barthlott W, Neinhuis C. 1997. Purity of the Scared Lotus or Escape Biological Surfaces.

Planta. 202(1) pages 1-8

http://www.citeulike.org/user/hendysh/article/2009895

(accessed 29 Nov. 2013)

[5] http://www.nanotex.com/applications/hometextiles_P1.html

(accessed 29 Nov. 2013)

[6] http://web.mit.edu/nnf/education/wettability/wetting.html

(accessed 30 Nov 2013)

[7] http://www.kibron.com/surface-tension

(accessed 30 Nov 2013)

[8] http://hyperphysics.phy-astr.gsu.edu/hbase/surten2.html

(accessed 1 Dec 2013)

[9] http://www.adhesives.org/adhesives-sealants/adhesives-sealants-overview/structural-design/surface-

energy-and-wetting

(accessed 2 Dec 2013)

[10] http://link.springer.com/artcile/10.1007%2Fs00396-012-2796-6

(accessed 2 Dec 2013)

[11] http://www.intechopen.com/source/html/10042/media/image8.jpeg

(accessed 2 Dec 2013)

[12] http://www.nanotex.com/faqs/faqs_spills.html#1

(accessed 2 Dec 2013)

[13] http://www.beilstein-journals.org/bjnano/single/articleFullText.htm?publicId=2190-4286-2-19

(accessed 2 Dec 2013)

[14] http://www.ramehart.com/newsletters/hierarchical_structure.jpg

(accessed 2 Dec 2013)

[15] Petal Effect: A Superhydrophobic State with High Adhesive Force

Feng L, Zhang Y, Xi J, Zhu Y, Wang N, Xia F, Jiang L.

http://www.ncbi.nlm.nih.gov/pubmed/18312016

(accessed 2 Dec 2013)

[16] Green Tribology: Biomimetics, Energy Conservation and Sustainability (page 25)

Michael Nosonovsky, Bharat Bhusan

(accessed 4 Dec 2013)

16

ABSTRACT

Tsunamis have been affecting coastal areas

in significant ways for millions of years, as

sedimentological records and eyewitness

accounts have shown. Research into

tsunami deposits has seemed to raise as

many questions as it has answered, with no

agreed upon definition of a tsunami deposit

currently available.

Sediment transport and deposition studies

cannot only be used in palaeoreconstruction

of past events, but also in the preparation

and harm prevention necessary today.

Important areas of research include

distinguishing storm and tsunami deposits,

characteristics of tsunami deposits in the

geological record, the behaviour of

sediment transport, and deposition and its

long-lasting effects.

The broad range in tsunami deposit

characteristics and areas of available

research is a clear indicator of the

complexity of the topic. By compiling and

reviewing the relevant literature, this report

provides a summary and proposals for

future research regarding the sediment

transport and deposition from tsunamis.

INTRODUCTION

The purpose of this report is to examine the

transportation and deposition of sediments

resulting from tsunamis by providing a

review into recent research surrounding the

topic. The word ‘tsunami’ means ‘harbour

wave’ in Japanese. They may be triggered

by a number of factors, with earthquakes,

land-slides, and bolide impacts considered

to be the main three (Dawson et al.).

Although tsunami events result in

significant alterations to coastal

environments and sediment transport, as

well as loss of life, they are rare in terms of

human history. In terms of the geological

record, however, they are common;

Scheffers et al. estimate that 100

megatsunamis have been recorded

worldwide in the past 2000 years with more

presumably going unrecorded.

In terms of modern science, detailed

tsunami research is in its infancy, and has

displayed increasing prominence within the

last two decades. Catastrophic events such

as the 2004 Indian Ocean tsunami, which

claimed the lives of over 250,000 people, as

well as the more recent 2011 Japanese

tsunami which resulted in contamination of

the Pacific ocean by radioactive waste, have

attracted a great deal of attention.

Excluding the sediment record, past events

have been based on written accounts which

offer little detailed information. It is

thought that the study of sediment transport

and deposition can lead, not only to a

further understanding of the effects of

tsunamis, but also increase the

effectiveness of preparedness and early

warning systems, as well as helping to

reconstruct past tsunamis from the

geological record. Throughout this report,

the term sediment is used to refer to

particles ranging in size from microscopic

foraminifera to large boulders, with grain

size being the main parameter used to

distinguish between tsunami deposits. The

term ‘tsunamiites’ is also used to refer to

sedimentary deposits resulting from a

A TECHNICAL REPORT ON SEDIMENT TRANSPORT &

DEPOSITION FROM TSUNAMIS

BY T. HOWELL

17

tsunami, and covers a range of grain sizes,

sources, transport and depositional

processes.

TSUNAMIS

Tsunamis occur as a series of waves known

as a ‘wave-train’, with significantly

increased wavelengths, which can reach

land within minutes or hours of each other.

Tsunami waves have been recorded as

travelling up to 220m/s (500mph)

(MacInnes et al.), with waves reaching

heights of tens of metres. The first in the

wave-train is not usually the strongest;

indeed, successive waves increase in

strength. These waves can be triggered

through a number of ways, which Dawson

et al. defined as either ‘’bottom-up’

displacement of the sea-bed’, such as

earthquakes, submarine landslides and

volcanic eruptions, or ‘top-down’

displacements such as coastal landslides,

glacier calving and bolide impacts. The

most common trigger for tsunamis is

considered believed to be large, deep-sea

earthquakes originating from tectonic plate

boundaries, such as the 2011 Tohoku

earthquake which registered a magnitude

9.0 and occurred at the Pacific Plate

subduction zone along North-Eastern

Honshu (Nandasena et al.).

Morton et al. stated that the initial tsunami

perturbation could appear as at least one of

three different forms; a continuous surge,

an elevated bore or a recession of the sea.

This perturbation is often influenced by

coastal geography. They also noted that

coastal sites closest to the source region

initially experienced a bore whilst ‘farfield

sites’ initially experienced a surge.

Throughout this report, tsunami sediments

are not distinguished by the origin of the

tsunami but by the sediment type, as no

relationship has yet been discovered

between the cause of the tsunami and any

patterns in transport and deposition.

SEDIMENT TRANSPORT

Tsunamis are capable of transporting a

large amount of material, ranging in grain

size from fine sand and mud to coarse

boulders and clasts, through suspension,

saltation and creep. The amount of

sediment is inferred from several

eyewitness reports from the 2004 Indian

Ocean tsunami, which describe the waves

as ‘being black before breaking on land’

(Lavigne et al.). This grain size range

reflects the sheer size of the source region

for the sediment, and is influenced by

sediment availability and ‘magnitude of the

hydraulic source of the tsunami’

(Nandasena et al.). It is possible to split

sediment transport into two principal flows,

named ‘run-up’ and ‘backwash’. The

former consists of the tsunamigenic waves

reaching inland up to the maximum point of

inundation, where velocity decreases to

zero; thereafter, the wave recedes, and

backwash begins.

Figure 1 (on the following page)

demonstrates the principal pathways of

tsunami sediment transport and deposition.

Inundation can range from tens of metres up

to a kilometre inland, as was nearly seen in

the 2004 Indian Ocean tsunami which Paris

et al. reported as having a maximum

inundation of 763m. As the diagram

demonstrates, the effect on the land surface

consists of a very small part of the passage

of a tsunami.

18

Figure 1: Schematic diagram illustrating the

principal pathways of tsunami sediment

transport and deposition (Sugawara et al.).

RUN-UP

As a tsunami nears land and travels into

shallower waters, its individual waves

decrease in velocity, whilst their amplitude

increases (Dawson et al.). This transition

zone from ocean basin into a shallower

environment is where the coastal

morphology and nature of the nearshore

environment affects the tsunami, and its

potential for sediment transport. As a

tsunami approaches the coast, the

increasing amplitude results in increased

seabed sediment suspension, leaving a

basal erosion surface which is cut.

The amount of sediment available for

transportation at this point in the process

has a significant impact upon the tsunami

deposit, as a nearshore zone which is barren

may result in only a minor trace of the

tsunami’s passage being left (Coleman

1978). For example, there would be a

greater volume of sediment transport from

the accumulation of unlithified sediment

found on a continental shelf compared to

volcanic flanks, resulting in a larger

deposit. The method of arrival of the

tsunami also influences sediment transport.

As mentioned earlier, Morton et al.

identified three forms of initial perturbation

which will each affect transport differently.

For example, a recession and drawdown of

the sea surface and will likely result in

increased erosion and onshore

transportation during run-up in comparison

to a continuous surge, due to the exposure

of nearshore sediment during recession.

Once the decrease in water depth and

velocity has occurred, and the flow has

become turbulent, the movement of water

and sediment in a landward direction slows

to around 10-20m/s, which Nanayama et al.

found to be the average run-up velocity

onto the coast. This is a considerable

reduction from the 220m/s recorded in the

past (MacInnes et al.). Even at such reduced

velocities, Ye et al. established it is possible

for tsunamis to transport a full range of

sediments from fine clays to large boulders.

As the tsunami flow moves landward its

velocity reduces further to around 5m/s as

it appears to resemble a ‘tide-like flood’

(Nanayama et al.). As velocity displays a

negative correlation with distance inland,

the capacity of the water to transport coarse

sediment also decreases, resulting in

deposition of larger sediments nearer the

shoreline, with only the finer sediments

transported further inland.

It is possible for sediments to be transported

over distances greater than a kilometre, and

have even been recorded up to 30km inland

at sites located along the west coast of

19

Australia (Dawson et al.). Figure 2

demonstrates this relationship in tsunami

deposits from the September 2009 tsunami

which struck the U.S. territory of American

Samoa. Sediment thickness is greatest near

the shoreline, where velocity decreases and

larger sediments are unable to be

transported, leading to deposition. The finer

sediments carried in suspension, however,

are able to be transported around 250m

inland before velocity decreases enough for

deposition to occur.

Figure 2: Cross-shore distribution of

sediment thickness plotted against distance

from shoreline for the American Samoa,

September 2009 South Pacific Tsunami

(Apotsos et al.)

Dawson et al. also found that run-up often

caused widespread deposition of large

boulders; the 1992 Flores tsunami led to the

deposition of numerous coral boulders in

the backshore environment, which caused

significant destruction. Evidence from Paris

et al. supports this, as it was found that

more than 80% of transported boulders

were found more than 100m inland after the

2004 Indian Ocean tsunami. It was also

found that the boulders transported from

offshore and deposited inland represent

only 7% of the boulders moved during the

tsunami, demonstrating the sheer force of

tsunami run-up.

BACKWASH

After the tsunami has reached its maximum

point of inundation, the subsequent

backwash flow occurs. Although little is

known about the hydraulics of the

backwash flow, eyewitness reports from the

2004 Indian Ocean tsunami suggest

‘exceptionally high flow velocities’

(Dawson & Stewart) and Nanayama et al.

estimate the outflow velocity of the 1993

Hokkaido tsunami at around 2.3 m/s. The

erosive and carrying capacity of these flows

is unknown, with the only indicators being

the possible imbrication of clasts as well as

any terrestrial debris found seaward of its

source. Aalto et al. found that that coastal

topography and bathymetry often

concentrates backwash into channelized

flows increasing erosive and carrying

capacity, and even possibly ‘inducing

corrosion and cavitation of bedrock

platforms’. This was also strengthened by

Kon’no et al., who found that backwater

converging on topographic depressions led

to further erosion and deposition of

reworked sediments. Sediment previously

agitated by the run-up flow is also

considerably easier to be transported by the

channelised backwash flows, as they have

only just been deposited, leading to seaward

transport and deposition of these sediments

in nearshore zones (Sugawara et al.).

Sugawara et al. attempted to quantify the

characteristics of the 2004 Indian Ocean

Tsunami backwash through a review of

previous studies of submarine

sedimentation by tsunamis. It is possible for

a backwash flow to transport a considerable

amount of terrestrial coastal material

seawards, and, therefore, the accumulation

of allochthonous sediments offshore gives

evidence for the effect of backwash flows.

The specific proxy studied was the change

in benthic foraminiferal assemblages,

which were found to have migrated

seaward alongside plant debris and other

terrestrial materials. They found that the

extent of sediment transport from backwash

did not reach as far as deeper water regions,

but remained constrained to nearshore and

offshore zones.

20

Figure 3: Schematic diagram showing the

interpreted mode of sedimentation by

backwash (Sugarara et al.).

Figure 3 displays the interpreted mode of

sedimentation by a tsunami backwash. The

primary rolling and suspension of sediment

results in bottom surface erosion as any

agitated sediment from run-up is also

transported into the nearshore to offshore

zones. An example of the large volumes of

sediment which these outflows are capable

of moving was seen in the 1983 Sea of

Japan tsunami, which was triggered by a 7.8

magnitude earthquake. Minoura and

Nakaya noted that the mass transport of

sediment occurred predominantly through

suspension and rolling, which led to the

accumulation of allochthonous materials in

nearshore to offshore zones, including the

bodies of some victims. Although large

amounts of sediment are able to be

transported seaward, the volume does not

correspond to the amount previously eroded

and transported elsewhere. Paris et al.

estimated that in Lhok Nga, Indonesia, less

than 10% of the eroded sediments were

deposited inland, meaning very little can

become entrained within the backwash.

Little is known concerning the deposition

location of such eroded sediments, as

nearshore and offshore zones do not display

significant sea level rises, and sampling

deeper regions has not been possible.

GLOBAL DEPOSITION PATTERNS

As mentioned earlier, previous research has

encountered problems with identifying and

classifying tsunami deposits in the

geological record. Deposition occurs on

such a large scale, in terms of grain size and

locality, that researchers such as Scheffers

et al. have taken an inductive approach in

their endeavours to identify deposition

processes and relationships. The world map

in Figure 4 (following page) demonstrates

this approach through ‘considering a

tsunamigenic origin of unusual depositions

21

or geomorphological features in coastal

areas’, as inductive fieldwork is the most

reliable source for data in recent studies.

The main Atlantic tsunami deposits within

sedimentary records can be found in

Scotland, west Norway, the Caribbean, and

the southern coast of Portugal. In the

Mediterranean, deposits are located in

southern Italy, Cyprus, and the Aegean Sea,

whilst evidence in the Indian Ocean is so far

restricted to north-western Australia. The

Pacific Ocean displays the highest

frequency of onshore tsunamigenic

deposits, and is where approximately 80%

of tsunamis and 90% of earthquakes occur.

It is the most geologically active area of the

globe – hence its name, the ‘Pacific Ring of

Fire’ – due to the surrounding active plate

boundaries, resulting in the high abundance

of tsunami deposits.

It is possible for tsunamigenic sediments to

have been deposited during the run-up or

backwash processes. A study from Java

established that this sediment deposition

was frequently associated with ‘sediment

sheets that rise in altitude inland as tapering

sediment wedges’ (Paris et al.). Whether or

not such sediment was a result of run-up or

backwash is dependent upon characteristics

such as imbrications and sediment sources.

Dawson et al. established, whilst studying

the 1992 Flores tsunami, that tsunami run-

up may often cause widespread deposition

of large boulders. With this pattern of

deposition identified as having a

tsunamigenic source, they identified several

former tsunamis which have also been

associated with widespread boulder

deposition. For example, the coral reef at

Rangiroa, Tuamoto archipelago, in the

south-east Pacific, displays a boulder field

in which there is a progressive decrease in

size landwards. This characteristic deposit

can be seen to continue with run-up

inundation, as shown in Figure 5 (following

page).

Figure 4: World map displaying the

distribution of tsunamigenic deposits

according to an inductive approach (Scheffers

et al.).

22

Figure 5 demonstrates the decreasing

sediment thickness in a landward direction

the farther the inundation reaches, as was

seen on American Samoa from the 2009

South Pacific tsunami. After breaching the

shoreline, the sediment deposits begin to

decrease immediately from around 10 cm to

less than 1 cm in thickness at the farthest

point of deposition. Gelfenbaum et al.

studied the 1998 Papua New Guinea

tsunami, and found that, on average, the

farthest deposition was 40 m short of the

inundation point, accounting for 70% of the

inundation distance. This supports the

general theory that MacInnes et al. aimed to

prove, by calculating average run-up and

deposition height of tsunamis. Their

research yielded a figure which states

average deposition distance is 90% of the

inundation distance.

Due to the physical constraints of deep sea

sediment sampling, it has not been possible

to obtain a thorough model for the

deposition of sediments in the offshore and

deep sea zones. However, Sugawara et al.

were able to conclude, through the study of

benthic foraminifer redistribution after the

2004 Indian Ocean tsunami, that a large-

scale redistribution of sediments on the sea

floor akin to related terrestrial deposits did

not occur. Overall, their results found only

a slight landward migration within offshore

zones, suggesting that the main sediment

transport and deposition occurs on land

rather than in nearshore to deep sea areas.

Sugawara et al. therefore highlighted the

important factor that, although backwash

plays an important role, the main deposit

occurs terrestrially, and is deposited by run-

up; ‘deposition by tsunami run-ups is

prominent in coastal lowlands, and

deposition by tsunami backwashes is

evident in nearshore to offshore zones’

(Sugawara 2009).

CONCLUSIONS

Although rare in human history, within the

geological record catastrophic tsunamis

occur frequently. The three main methods

of triggering a tsunami are landslides,

bolide impacts and earthquakes.

Sediment transport can be divided into two

principal flows: run-up and backwash. The

former has an average velocity of

approximately 10-20 m/s, deposits the

majority of sediment, and is what most

people associate with a tsunami; the latter

has an average velocity of around 2-3 m/s

and transports significantly less sediment

seaward.

Future research should attempt to sample

offshore to deep sea tsunamigenic

sediments in an attempt to understand the

processes which occur in such areas. In

locations at the greatest risk, such as the

Indonesian and Japanese archipelagos,

continuous pressure, seismicity,

temperature and other proxy indicators

should be used to improve the accuracy of

Figure 5: ‘C’ shows

the Tsunami run-up

height in relation to

average topographic

height (black line).

‘D’ shows the sediment

thickness against

distance inland for the

same transect (Apotsos

et al.).

23

prediction. This will also help in

understanding the sedimentary processes

involved. Given the high variability in the

nature of tsunami sediments, Dawson states

that ‘solving this particular problem is a

priority for future research’.

REFERENCES

CHENG, W., WEISS, R. 2013. On sediment extent and runup of tsunami waves. Earth and Planetary Science

Letters, 362, 305-309.

DAWSON, A., SHI, S. 2000. Tsunami Deposits. Pure and Applied Geophysics, 157, 875-897.

DAWSON, A., STEWART. Tsunami Deposits in the Geological Record. Sedimentary Geology, 200, 166-183.

GELFENBAUM, G., JAFFE., B. Erosion and Sedimentation from the 17 July, 1998

Papua New Guinea Tsunami’. 2003. Pure and Applied Geophysics, 160, 1969-1999.

GOODMAN-TCHERNOV et al. 2009. Tsunami Waves Generated By The Santorini Eruption Reached

Mediterranean Shores. Geology Society of America-Geology Journal, 37. 943-946.

MACINNES et al. 2009. Tsunami Geomorphology: Erosion and Deposition From 15 Nov ’06 Kuril Island

Tsunami. Geology Society of America-Geology Journal, 37, 1043-1046.

MORTON, R., GELFENBAUM, G., JAFFE, B. ‘Physical criteria for distinguishing sandy tsunami and storm

deposits using modern examples’. 2007. Sedimentary Geology, 200, 184-207.

NANDASENA, N., TANAKA, N., SASAKI, Y., OSADA, M. 2003. Boulder transport by the 2011 Great East

Japan tsunami: Comprehensive field observations and whither model predictions?. Marine Geology, 346, 292-

309.

PARIS, R., FOURNIER, J., POIZOT, E., ETIENNE, S., MORIN, J., LAVIGNE, F., WASSMER, F. 2009.

Boulder and fine sediment transport and deposition by the 2004 tsunami in Lhok Nga (western Banda Aceh,

Sumatra, Indonesia): A coupled offshore–onshore model. Marine Geology, 268, 43-54.

PHANTUWONGRAJ, S., CHOOWONG, M., NANAYAMA, F., HISADA, K., CHARUSIRI, P.,

CHUTAKOSITKANON, V., PAILOPLEE, S., CHABANGBON, A. Coastal geomorphic conditions and styles

of storm surge washover deposits from Southern Thailand. Geomorphology, 192, 43-58.

SCHEFFERS, A., KELLETAT, D. 2003. Sedimentologic and geomorphologic tsunami imprints worldwide—a

review. Earth Science Reviews, 63, 83-92.

SUGAWARA, D., MINOURA, K., NEMOTO, N., TSUKAWAKI, S., GOTO, K., IMAMURA, F. 2009.

Foraminiferal evidence of submarine sediment transport and deposition by backwash during the 2004 Indian

Ocean tsunami. Kanazawa University Repository for Academic Recources Island Arc, 18, 513-525.

IMAMURA, F., GOTO, K., OHKUBO, S. 2008. A numerical model for the transport of a boulder by tsunami.

Journal of Geophysical Research, 113, 1-12.

24

ABSTRACT

We present parameters derived through

fitting of literature fluxes, covering a large

wavelength range, to simulated spectra for

brown dwarfs with and without discs in

Upper Scorpius. Our models include the

contribution of accretion flux to the

photospheric (surface) emission.

Comparisons of our results with previous

studies neglecting accretion flux show they

have systematically overestimated the mass

of the brown dwarf, as photospheric

emission must be increased to account for

the contribution of the accretion flux. Our

non-disc models derived a distance and age

to Upper Scorpius of 138±7pc and

5.5±1.0Myr respectively, agreeing with

previously derived values of 140±20pc and

5±2Myr. Thus we conclude treatment of

accretion flux is vital when modelling the

spectra of brown dwarf objects with discs.

INTRODUCTION

Several studies in recent years have used

radiative transfer models to fit observations

of young brown dwarfs (BDs) with

circumstellar discs[1][2]. BDs correspond to

stars not large enough to ignite fusion in the

core, relying instead on convection currents

for energy transport. Evidence is mounting

that these objects have significant

similarities with higher mass classical T

Tauri star, where matter is accreted onto the

star along magnetic field lines from the

truncated inner edge of a dusty

circumstellar disc[3][4]. The observations,

and resulting fits to the spectral energy

distributions (SEDs), which measure flux

as a function of wavelength, show that

dusty circumstellar discs can exist around

these young pre-main sequence

stars[5][6][7][8]. However, these discs are

challenging to observe and disentangle

from the stellar emission. Mayne et al.[2]

investigated BD discs in the Taurus region,

highlighting the necessity for fluxes to

cover a broad wavelength range to begin

deriving robust disc and stellar parameters.

Additionally, Mayne et al.[2] highlighted the

importance of consistently accounting for

the flux emitted by accreting (infalling)

matter, which has been shown to

significantly alter photometric observations

of young low-mass stars9.

BDs in the Upper Scorpius (UpSco) region,

at 145 ±20pc in distance and an age of

∼5Myr, have recently been surveyed and

the data presented in a number of

publications[5][6][7][8]. The youth and lack of

intermediate dust between the observer and

the region (also called extinction, Av) to

UpSco means the BD population is easier to

observe than older regions with larger

extinctions.

In this paper, we gathered and input

existing literature data into a sophisticated

SED fitting tool[2]. With a large wavelength

coverage of many BD disc candidates, the

data was applied to an associated grid of

theoretical BD models. The derived

parameters could then be compared to those

of external authors.

FITTING SPECTRAL ENERGY DISTRIBUTIONS FOR

BROWN DWARF DISCS IN UPPER SCORPIUS

BY M. READ, L. IRELAND, & N. MAYNE

25

The associated grid of models and

photometry is freely available online1.

DATA

Upper Scorpius (UpSco) is one of three

subgroups belonging to the Scorpius

Centaurus region[10]. At a distance of

∼145pc[10], UpSco shows evidence of

recent or ongoing star formation. It is

relatively free of extinction, AV ≤2[11], and

is a young region at ∼5±2Myr[12]: ideal

conditions for the possible detection of

post-formation BDs associated disc

structures.

UpSco has been extensively probed in the

search for BDs and other very low mass

candidates (≤0.35M⊙ i.e. ≤0.35 solar masses)[6][7][8][13][14][15][16], with

observations covering the near to far

infrared, allowing the separation of

photospheric (surface) and disc emission

components in a given spectrum.

Photometry & Uncertainties

We selected 86 objects from UpSco,

covering a population of BDs and very low

mass stars in the mass range of

∼0.01−0.35M⊙. Photometric magnitudes

(or fluxes) for these objects were sourced

from multiple samples and divided into four

sub-samples according to the source author,

each with their own combination of filter

systems. For the sake of brevity, we refer to

each sub-sample according to the lead

author of the data source. Therefore,

Slesnick et al. (2006)[6], Slesnick et al.

(2008)[13] and Riaz et al. (2009)[14] are

referred to by SL2006, Scholz et al.

(2007)[8] by SC2007, Carpenter et al.

1 http://bd- server.astro.ex.ac.uk/

(2006)[15] and Carpenter et al. (2009)[16] by

CA2006, and Lodieu et al. (2006)[7] by

LO2006.

To investigate disc structure in our sample,

we use a wide spectral coverage of

photometric fluxes from ∼1−70μm, taken

from the UKIDSS, DENIS, SDSS, WISE

and 2MASS mission surveys, and using the

IRAC, IRS and MIPS instruments (the

acronyms of surveys/instruments are

unimportant). We adopt an uncertainty of

0.2mag for all instruments apart from

0.3mag for MIPS. This will account for any

temporal variability in the

observations[6][7][8][13][14][15][16].

Uncertainties correspond to ~1-5% of the

original data points[6][7][8][13][14][15][16] .

Parameters & Constraints

Assuming that the UpSco association has

an approximately spherical shape, the

intrinsic spread of distances is ±20pc[5]

about the mean distance 145pc[10], therefore

we adopt 145±20pc as our distance range.

We use an extinction range 0−2mag[7].

Slesnick et al. (2008)[13] and Scholz et al.

(2007)[8] included their own derived stellar

parameters for each object in their samples.

We use these derived parameters to inform

our fitting process, essentially adopting

them as weak constraints.

THEORY

Flux Components

The need for wide spectral coverage of

fluxes in BD/very low mass star

observations is vital in the separation of the

26

photosphere from any potential infrared

excess, indicating a disk. A majority of

SED fittings for BD and very low mass

objects have previously been akin to

higher-mass main sequence objects, with

parameters arbitrarily modified to produce

a best-fit model, i.e. stellar mass, radius,

etc[8]. This has the disadvantage of lacking

any physical coupling between parameters,

with derived results being entirely

statistical. This technique has been widely

successful in deriving stellar parameters for

naked objects[1]. When fitting objects with

discs it is also common, in order to reduce

the number of free parameters, to assume

accretion to be negligible[8].

Accretion flux is produced in BD disc

systems as material flows from the inner

disc along truncated magnetic field lines to

hot spots on the surface of the photosphere.

Hot spots can provide the primary source of

flux from an object[17][18]. Hence, a

treatment of accretion flux is necessary to

obtain a more realistic SED.

For example, one may overestimate the

mass of an object if accretion is not

considered, as flux contributions from the

photosphere with and without accretion

may be misinterpreted as the intrinsic

stellar luminosity.

We make use of a wide range of wavelength

observations and fit to the models described

in Mayne & Harries (2010)[9], which

include detailed disc physics such as

accretion, dust sublimation, disc flaring,

and vertical hydrostatic equilibrium, using

the fitting techniques and tools of Mayne et

al. (2012)[2]. We summarise the modelling

and fitting procedure below, with a detailed

description given by Mayne & Harries

(2010)[9] and Mayne et al. (2012)[2],

respectively.

Disc Structure/Model

We use a combination of DUSTY00 stellar

interior models and AMES-Dusty

atmospheric models[19], with photospheric

fluxes calculated for many mass or age

contributions through interpolation over

surface gravity, temperature, radius, and

surface luminosity[9].

We model accretion flux as blackbody

emission:

𝐿𝑎𝑐𝑐 = 𝐺𝑀∗�̇�

𝑅(1 −

𝑅∗

𝑅𝑖𝑛𝑛𝑒𝑟)

where 𝐿𝑎𝑐𝑐 is the accretion luminosity, 𝑀∗ is the stellar mass, �̇� is the mass accretion

rate, 𝑅∗ is the stellar radius and Rinner is the

inner radius disc boundary. We

subsequently constrain this flux to a hotspot

area 𝐴 and assume an effective hotspot

temperature:

𝑇𝑎𝑐𝑐 =𝐿𝑎𝑐𝑐

4𝜋𝑅∗2𝜎𝐴

This temperature is used to construct the

accretion flux as a blackbody, and

combined with the modelled photosphere to

produce a final flux distribution of the

object.

Sublimation of material at the inner disc

occurs at temperatures ∼1500K due to

photospheric heating[20], causing the

geometry of the inner disc to become

curved as opposed to a vertical wall[21]. This

can majorly affect the observed infrared

excess, with curved geometries showing

reduced inclination dependence[22]. We

include treatment for dust sublimation

using TORUS, a radiative transfer and

radiation-hydrodynamics code[23], detailed

in Simulating SED. We do not include

models of any other disc clearing

mechanisms, for instance clearing by

planets, or ablation due to flux from nearby

stars.

27

Simulating SED

Radiative transfer models using TORUS[23]

have been run to represent various

combinations of parameters, producing a

grid of models where the corresponding

SED can be derived2.

Simulating Fluxes & Magnitudes

To derive photometric magnitudes and

colours, an SED at a given inclination is

folded through the different filter responses

of the required photometric system[2]. The

models were calibrated using Vega or using

the associated instrument handbook, then

distance and extinction diluted.

RESULTS & ANALYSIS

We present SED models for a sample of 80

objects, excluding six objects for which the

best fits were unsatisfactory. These were fit

with a distance range 145±20pc and an

extinction range 0−2mag. First, we fit our

entire sample using a model grid including

detailed treatment of disc physics[2] (dust

sublimation, accretion flux, etc., section

3.2), with a mass range of 0.01−0.08M⊙

(∆0.01M⊙) and ages between 1Myr and

10Myr. If evidence for a disc was sparse,

i.e. zero disc mass or a lack of infrared

excess, it was identified as a naked object,

and subsequently fit using semi-empirical

modelling[2]. This includes an extended

range for photospheric specific parameters

such as mass and age (see Naked Objects).

The graphs are displayed at the end of this

paper. Figures 1 and 2 respectively show

our best fitting models for naked and disc

systems, with Figure 3 and Figure 4

respectively showing the best fits for our

2 See Mayne & Harries (2010)[9], for the full range

of parameters

least satisfactory cases, for stars with and

without discs. Our naked objects produce a

mean age of 5.5±1.0Myr with a mean

distance of 138±7pc. Disc objects were

omitted from these calculations, because

the grid for actively accreting systems has

just two available age parameters (1Myr

and 10Myr).

Below, we split our analysis into the

modelling of naked and disc objects.

Naked Objects

Our sample contains 41 naked objects.

Assumed to have negligible accretion flux,

these were fitted using a model with an

extended mass and age range of

0.01−1.40M⊙ (∆0.01M⊙) and 1−10Myr

(∆1Myr) respectively. This modelling

technique consists of a static vertical

structure and inner edge location, placing

the inner disc edge at a set semi-empirically

derived dust sublimation radius[2]. Naked

candidates were found in the SL2006 and

LO2006 sub-samples, with a selection of

the best and worst fits shown in Figure 1

and Figure 3 respectively.

Out of 25 objects in SL2006, 19 were found

to be naked systems. These have previously

derived masses, ages and extinctions[13].

Literature masses agree with 14 objects,

with the remaining four objects falling

outside the range of our uncertainty limits

by 0.01M⊙. Previously derived age

estimates were unavailable for two of our

21 objects, with a further six disagreeing

with Slesnick et al. (2008)[13]. We speculate

that this could be a result of Slesnick et al.

(2008)[13] fitting for age and mass using the

region as a whole, compared with using

object specific models, although further

investigations would need to be made to

28

confirm this. Our calculated extinctions

show strong correlation to those from

Slesnick et al. (2006)[6], with just four

objects showing disagreement within

uncertainties. However, these lie within a

range AV≤2mag, assumed by Lodieu et al.

(2006)[7].

The LO2006 sub-sample of 32 contained 21

naked objects. Unlike the SL2006 sub-

sample, these objects do not have

previously derived parameters. Masses

were constrained during the fitting process

at an upper mass limit of 0.4M⊙, indicating

that all our objects do indeed lie within or

close to the 0.01−0.35M⊙ range as defined

by Lodieu et al. (2006)[7]. Our best-fit

extinctions, however, show that four

objects have an extinction unbound by our

upper limit of AV=2mag. Due to the

inherent degeneracy of multiple

parameters, we are unable to prove that one

parameter is responsible (i.e. a possible

systematic age underestimate). However,

one could argue that it is plausible for

extinctions ≥2mag to exist in this region;

Slesnick et al. (2006)[6] showed them to be

∼3mag in some cases. In the future, objects

will be fit using an extended extinction

range.

Disc Objects

Disc candidates were found in all four sub-

samples, totalling 39 objects, with SC2007

and CA2006 entirely consisting of objects

with infrared excess. We note that

satisfactory fits could not be achieved for

the following: SL2006: SCH16093018-

20595409, SCH16224384-19510575,

CA2006: [PBB2002] Usco J161115.3-

175721, [PBB2002] Usco J160827.5-

194904 and LO2006: J163919.07-

253406.8. These objects were removed

from the sample; justifications for this will

be given as they arise. All disc fits are

present in Figure 2, with two unsuitable fits

seen in Figure 4.

Out of the entire SL2006 sub-sample, we fit

four disc systems. A disc fraction for

objects in this region was reported to be

10.7%−3.3%8.7% [14], agreeing with our fraction

for the whole sample of 16%. Due to the age

constraints of the model treating accretion

flux, age comparisons with available

literature values was not possible. We

instead compare derived masses and

extinctions from Slesnick et al. (2006,

2008)[6][13]. Literature masses correlate well

with our data, excluding SCH16263026-

23365552, where a difference of 0.01M⊙ outside the uncertainty range was

calculated. We suggest that this could be

due to disadvantages in fitting masses using

region specific fitting[24], as

SCH16263026-23365552 (Figure 2(a))

represented one of our best-fitting models.

As stated earlier, we could not find

satisfactory fits for SL2006:

SCH16093018-20595409 and

SCH16224384- 19510575. SCH16093018-

20595409 was found to have excess

emission in MIPs 24μm, with emission at

shorter wavelengths originating from the

photosphere[14]. A possible explanation is

that this is a transition disc system, with an

inner hole in the disc too large for our fitting

techniques to model. Slesnick et al.

(2006)[6] postulates that SCH16224384-

19510575 could be an unresolved binary,

being overly luminous and younger. This

agrees with our analysis, as, although a

satisfactory fit could not be achieved when

compared with other objects, the best fit

calculated was one where the mass was

significantly higher than any surrounding

system in this sub-sample (0.2M⊙).

Objects in the SC2007 sub-sample were

chosen if they had infrared excess in

29

literature[8]. Our models support these

observations, with 13 systems found to

include a disc. Direct comparisons were

made with parameters derived by Scholz et

al. (2007)[8], as they also use SED

modelling. However, this fitting technique

neglected accretion rate, unlike our models.

We show differences between derived

masses, photospheric temperatures and

stellar radii. Out of 13 objects, 11 have

photospheric temperatures significantly

reduced when compared with values from

Scholz et al. (2007)[8]. However, we find

that changes in other parameters

compensate for this loss in apparent

photospheric luminosity, either through a

decrease in mass or, most noticeably, a high

accretion temperature, for six of our 11

objects. This suggests that accretion

luminosity has a significant contribution to

the overall flux distribution of our objects.

Therefore, Scholz et al. (2007)[8] may have

overestimated masses due to the lack of

treatment of accretion flux.

Similar to the SC2007 sub-sample, all

objects in CA2006 were chosen due to

showing infrared excess. Again we show

this in our models, with discs present for all

objects. The majority of fits in this sub-

sample have an extinction of zero.

However, our sub-samples all differ in

location within UpSco, thus variations in

extinctions within 0−2mag are expected.

We found 10 objects out of 31 in LO2006

to be disc systems. Comparisons with

previous measurements were limited, due

to the lack of derived parameters in

literature. We note, however, that our

models favour larger disc radii with smaller

masses, demonstrating how UpSco is a

potential region to feature systems with

evolved diffuse disc structure, as outlined in

the Data section.

SUMMARY & CONCLUSIONS

We use sophisticated models, including

thorough dust physics involving the

treatment of accretion, dust sublimation,

disc flaring and vertical hydrostatic

equilibrium, to fit SEDs to 80 members of

the UpSco region. We fit 41 naked and 39

disc objects, producing a mean distance of

138±7pc and a mean age of 5.5±1.0Myr

from the naked objects, agreeing with the

previously derived distance of 145±20pc

and 5±2Myr. We highlight the importance

of treating non-negligible accretion flux in

SED models for disc objects, as this was

found to significantly reduce derived

masses when compared with models that

concentrated on fitting systems without

accretion contributions.

30

GRAPHS

Figure 1: Best-fit

spectra for eight of our

naked objects. Black

crosses represent

external observational

magnitudes, with red

circles as the

corresponding model

value according to our

fitting tool. The

triangle for

J162725.52-213804.0

represents an upper

limit.

31

Figure 2: Best-fit spectra

for eight disc objects.

Objects shown are those

producing the best fitting

statistical values, with

black crosses showing

observation fluxes and red

circles showing the

corresponding model flux.

32

Figure 3: Best-fit

spectra for two examples

where satisfactory fits

could not be obtained.

Slight excess in WISE 4

indicates the possibility

of disc structure;

however, our model is

currently not sensitive

enough to represent it.

Figure 4: Best-fit spectra

for two disc objects,

where satisfactory fits

could not be obtained.

High photospheric flux

and mid/far-IR excess in

observational data

indicates the possibility

of transition discs[14],

which our fitting

technique is currently

unable to model.

33

REFERENCES

[1] Guieu S., Pinte C., Monin J.-L., Ménard F., Fukagawa M., Padgett D. L., Noriega-Crespo A., Carey

S. J., Rebull L. M., Huard T., Guedel M., 2007, A&A, 465, 855

[2] Mayne N. J., Harries T. J., Rowe J., Acreman D. M., 2012, MNRAS, 423, 1775

[3] Jayawardhana R., Ardila D. R., Stelzer B., Haisch Jr. K. E., 2003, AJ, 126, 1515

[4] Mohanty S., Jayawardhana R., Natta A., Fujiyoshi T., Tamura M., Barrado y Navascués D., 2004,

ApJL, 609, L33

[5] Preibisch T., Brown A. G. A., Bridges T., Guenther E., Zinnecker H., 2002, AJ, 124, 404

[6] Slesnick C. L., Carpenter J. M., Hillenbrand L. A., 2006, AJ, 131, 3016

[7] Lodieu N., Hambly N. C., Jameson R. F., 2006, MNRAS, 373, 95

[8] Scholz A., Jayawardhana R., Wood K., Meeus G., Stelzer B., Walker C., O’Sullivan M., 2007, ApJ,

660, 1517

[9] Mayne N. J., Harries T. J., 2010, MNRAS, 409, 1307

[10] de Zeeuw P. T., Hoogerwerf R., de Bruijne J. H. J., Brown A. G. A., Blaauw A., 1999, AJ, 117, 354

[11] Walter F. M., Vrba F. J., Mathieu R. D., Brown A., Myers P. C., 1994, AJ, 107, 692

[12] Preibisch T., Zinnecker H., 1999, AJ, 117, 2381

[13] Slesnick C. L., 2008, PhD thesis, California Institute of Technology

[14] Riaz B., Lodieu N., Gizis J. E., 2009, ApJ, 705, 1173

[15] Carpenter J. M., Mamajek E. E., Hillenbrand L. A., Meyer M. R., 2006, ApJL, 651, L49

[16] Carpenter J. M., Mamajek E. E., Hillenbrand L. A., Meyer M. R., 2009, ApJ, 705, 1646

[17] Bouvier J., Covino E., Kovo O., Martin E. L., Matthews J. M., Terranegra L., Beck S. C., 1995, A&A,

299, 89

[18] Herbst W., Eislöffel J., Mundt R., Scholz A., 2007, Proto-stars and Planets V, pp 297–311

[19] Chabrier G., Baraffe I., Allard F., Hauschildt P., 2000, ApJ, 542, 464

[20] Kobayashi H., Kimura H., Watanabe S.-i., Yamamoto T., Müller S., 2011, Earth, Planets, and Space,

63, 1067

[21] Dullemond C. P., Monnier J. D., 2010, ARA&A, 48, 205

[22] Tannirkulam A., Harries T. J., Monnier J. D., 2007, ApJ, 661, 374

[23] Harries T. J., 2000, MNRAS, 315, 722

[24] Mayne N. J., Naylor T., 2008, MNRAS, 386, 261

34

ABSTRACT

Coronary heart disease is where

atherosclerosis occurs in the coronary

arteries. The aim of this project was to

investigate the possibility of using

Computational Fluid Dynamics (CFD) to

train an Artificial Neural Network (ANN)

to predict the pressure drop across an

idealised stenosis in a coronary artery. A

CFD model was created to represent an

idealised stenosis and the model creation

and analysis were automated to provide

data to train an ANN. Initially a Radial

Basis Function (RBF) network was trained

on the generated data, however this was

unsuccessful and so a Multilayer

Perceptron (MLP) network was tried

instead. The MLP network was more

successful than the RBF network, and was

able to learn the training data with an

average test error of 5% (when using 5-10

hidden units and a weight-decay coefficient

of 0.3). There were signs of instability with

the MLP network however, which was most

likely caused by a lack of training data.

Further work would be needed in order to

fully automate the data creation; this would

enable the significant increase in training

data that would almost certainly improve

the performance of the MLP network.

Heather Bolt would like to thank Dr. Gavin

Tabor for supervising her project. She

would also like to acknowledge Prof.

Richard Everson for his assistance, and to

thank Shenan Grossberg, Matt Berry, and

David Tranter for their help. Her work was

funded by the Education and Physical

Sciences Research Council.

INTRODUCTION

Coronary Heart Disease

Atherosclerosis is a condition where fatty

deposits (such as cholesterol) accumulate

inside arteries. This narrows the arteries and

consequently impedes the blood flow.

Coronary heart disease is where

atherosclerosis occurs in the coronary

arteries (see Figure 1[1]). Coronary heart

disease is the most common cause of

myocardial ischemia, which occurs when

there is a decreased supply of oxygen to the

heart muscle caused by a decrease in blood

flow to the heart. Myocardial ischemia can

lead to a number of complications including

chest pain, irregular heart rhythm, heart

failure, and heart attack.

Figure 1: A coronary artery affected by

atherosclerosis[1].

A STUDY INTO THE FEASIBILITY OF USING MACHINE

LEARNING TO EVALUATE THE SEVERITY OF

CORONARY ARTERY DISEASE

BY H. BOLT

35

Fractional Flow Reserve (FFR)

The fractional flow reserve is a

dimensionless quantity used to measure the

severity of myocardial ischemia in a

patient. It is a measure of the pressure drop

across the stenosis in the coronary artery

and is given as:

𝐹𝐹𝑅 =𝑃𝑏

𝑃𝑎 (1)

where Pb is the pressure after lesion and Pa

is the pressure before lesion. In general, if

the value of FFR is less than 0.8, then the

obstruction is severe enough to cause

myocardial ischemia, and medical

intervention is required. Currently, the FFR

is determined experimentally; a catheter

with a transducer pressure sensor at the tip

is inserted into an artery in the groin and

then fed to the heart to measure the pressure

before and after the stenosis (blockage) in

the coronary artery. This procedure is

unpleasant for the patient and not without

risk; hence, there is currently research into

alternative ways of determining the FFR for

a coronary artery.

One non-invasive method of measuring the

FFR involves using Computational Fluid

Dynamics (CFD). CFD uses a computer to

solve the equations that govern fluid flow in

order to model the behaviour of fluids. In

this process, the geometry for the CFD

model is taken from an MRI scan, the blood

flow through the diseased artery is

simulated, and the pressure drop is

calculated. However, a certain level of skill

is required to carry out a CFD analysis, and

it can be computationally expensive.

Machine Learning

Due to the high cost of CFD (in terms of

both time and money), it is necessary to

investigate quicker and cheaper non-

invasive ways of measuring the FFR. One

possible method is to train a machine

learning system to predict the FFR value

across a stenosis when given a set of input

parameters. Machine learning is a branch of

computer science which involves training a

computer to perform a task (i.e. filter spam

emails, predict the weather, recognise

handwriting) without being explicitly

programmed. One type of machine

learning system is an Artificial Neural

Network (see Figure 2[2]).

Figure 2: Schematic diagram of a feed-

forward artificial neural network[3].

An artificial neural network (ANN) is a

system of interconnected neurons (or

nodes) that imitates a biological neural

network. These nodes ‘can be seen as

computational units that receive inputs and

process them to obtain an output’[4]; the

connections between these nodes are

weighted and determine how the

information is fed through the network. The

ANN is trained by providing a set of inputs

and outputs to the network, called the

training data. The error between the

computed output and the actual output is

then minimised. Once the network has

learned the data, it can be used to predict the

outputs for inputs that were not in the

original training data. One way of

improving the accuracy of the network is to

increase the number of nodes in the hidden

layer (called hidden units). However, if

there are too many hidden units then the

network will learn each point individually

instead of learning the general trend of the

36

data. This is known as over fitting and is

shown in Figure 3[5].

Figure 3: Graphs demonstrating too few

hidden units (left), the correct amount of

hidden units (centre), and too many hidden

units (right)[5].

The aim of this project is to investigate the

possibility of using CFD to train an

Artificial Neural Network to predict the

pressure drop across an idealised stenosis in

a coronary artery.

METHODOLOGY

This project involved three main phases.

The first phase was to create a CFD model

to represent an idealised stenosis. The

second was to automate the CFD model

creation and analysis to provide data to train

the ANN, and the third was to set-up and

train an ANN.

The CFD Model

A CFD model was created to replicate an

idealised stenosis. The CFD software used

in this project was ANSYS FLUENT[6].

Several different geometries for the CFD

model were tried. The final geometry was

chosen by comparing the FFR values given

by FLUENT with experimental FFR

values. The experimental data consisted of

MRI scans and corresponding FFR values

for different stenoses. This annonimised

data was taken from patients at Derriford

Hospital. The final geometry of the

FLUENT model gave FFR predictions that

were 20–40% above the experimental

values. However, an over-simplistic CFD

model was required in order to run multiple

simulations within the timeframe of this

project. The chosen FLUENT geometry

was deemed to be a suitable compromise

between accuracy and computational cost.

The chosen geometry for the CFD model is

shown in Figure 4 and Figure 5 (following

page). This model has: six variable

parameters; a fixed inlet and outlet length

of 80mm and 100mm respectively; and a

fixed outlet diameter of 1.3mm. Figure 5

shows the different variable parameters. D1

is the initial diameter of the artery, D2 is the

smallest diameter of the artery (at the point

of maximum constriction) and D3 is the

recovery diameter. L1 is the length from the

onset of the stenosis to the worst point in

the stenosis, L2 is the length of maximum

constriction of the stenosis and L3 is the

length from maximum restriction to the

recovery diameter. The inlet length to the

stenosis is fixed at 80mm to ensure fully

developed flow at the stenosis. The outlet

length is 100mm to make sure the outlet is

at a sufficient distance from the stenosis so

it does not affect the pressure drop across

the stenosis. The outlet diameter of the

model is 1.3mm, this is a typical diameter

of the distal tip of the Left Anterior

Descending Artery.

Figure 4: CFD model of artery with idealised

stenosis.

37

Figure 5: Variable parameters for CFD

model of idealised stenosis.

Boundary Conditions & Assumptions

For this project, the fluid was defined as

blood with a density of 1050kg/m3 and a

viscosity of 0.004kg/ms. The boundary

conditions were defined as a velocity inlet

and pressure outlet, with values of 0.2m/s

and 0Pa respectively. The walls of the

model were rigid with no slip, as the effects

of vessel elasticity on the model were

assumed to be negligible. The flow was

steady state for simplicity, as accurately

modelling the pulsatile motion of blood

flow would be very difficult and

unachievable within the time frame of this

project. It was assumed that no heat transfer

was taking place between the vessel walls

and the blood flow. The Reynolds number

for the flow was much less than the

laminar/turbulent boundary value of 2,300

so the flow was set as laminar. A mesh

convergence study on the model indicated

that a mesh of around 100,000 cells would

be sufficient.

Automating the Process

The process of creating the geometry for the

model and running the analysis was

automated using the parametric analysis

function in FLUENT. It was decided to use

100 data sets to train the machine learning

system. Each data set consisted of the six

parameter values (D1, D2, D3, L1, L2, L3)

and a corresponding FFR value. The range

of the parameter values are shown in the

table below. These ranges were chosen

from assessing the typical sizes of stenoses

in the experimental data.

2mm ≤ D1

≤ 5mm

0.3 D1 ≤

D2 ≤ 0.9

D1

D2 ≤ D3

≤ D1

1.5mm ≤

L1, L2, L3

≤ 30mm

Table 1: Range of parameter values

Using the parametric analysis function in

ANSYS Workbench, 100 different models

were created, meshed, and analysed. This

formed the data sets for the machine

learning. The FFR value from FLUENT

was found by looking at the pressure graph

for each stenosis. Figure 6 shows where the

values for Pa and Pb are taken from the

pressure vs. distance graph and then

Equation 1 was used to calculate the FFR

value. The pressure data for each stenosis

model was manually exported as a .csv file

from FLUENT (as a way to automate this

part of the process was not found). The .csv

file was then imported into Matlab[7] where

the FFR value was found using a Matlab

function written by Richard Everson.

Training the ANN

The Netlab[8] toolkit in Matlab was used to

select and train two Artificial Neural

Networks on the CFD generated data: a

Gaussian based Radial Basis Function

(RBF) and a Multilayer Perceptron (MLP).

In order to determine the correct amount of

hidden units to use, the number of hidden

units was increased incrementally from 1,

and the training and test error was recorded.

The training error (the average error over

the training data) was found using the

commands rbftrain and mlptrain for the

RBF network and the MLP network

respectively. The test error (the average

prediction error over the independent test

38

data) was found using a technique known as

‘leave one out cross validation’. This

involves removing one point from the data

set and using the remaining points as the

training data. The ANN is trained on the n-

1 data points and the point that has been left

out is used to test the accuracy of the

network. This process is then repeated so

that each point in the data is used once.

RESULTS & DISCUSSION

As mentioned in Methodology, 100 data

sets were created to train the ANN. Initially

a Gaussian-based RBF network was trained

on the data from one to 11 hidden units (the

training of the network failed when using

more than 11 hidden units). Figure 6 is a

graph of the training error and test error

versus the number of hidden units for the

RBF. The test and training error is around

0.04; this is the squared error, and so

corresponds to a percentage error of around

20%. This, together with the failure to run

at more than 11 hidden units, suggested that

there were serious problems with the initial

RBF.

Figure 6: Graph of test error and training

error vs. no. of hidden units for the initial

RBF.

To try and alleviate the problems with the

RBF, the individual error for each data set

was found, and five outliers were identified

and removed from the data. Next, the ‘best

error’ was found by initialising the network

several times, (‘it is common practice to

train the same network many times’[9]) and

the smallest error was taken. However,

neither removing the outliers nor finding

the best error has made any notable

improvement to the RBF.

As it was evident that there were serious

errors with the RBF, an alternative ANN (a

Multilayer Perceptron) was tried. The MLP

was trained on the generated data minus the

five outlying data sets. The coefficient of

weight decay (α) was fixed at 0.01 and the

MLP was trained using 1 to 80 hidden units

(see Figure 7 for the graph of results).

Figure 7: Graph of Test error and training

error vs. no. of hidden units for the initial

MLP.

Figure 7 shows that the error for the MLP is

lower than the RBF at the optimum number

of hidden units (around 10). However, at 10

0

0.01

0.02

0.03

0.04

0.05

0 5 10 15

Err

or

No. of hidden units

RBF1 Test RBF1 Train

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Err

or

No. of hidden units

MLP Test MLP Train

39

hidden units the test error is still quite high

at around 0.01 (10%).

To try to reduce the error of the MLP, the

test error was plotted against the FFR value

to see if there was any correlation between

the error and the FFR value (see Figure 8).

Figure 8 shows that the data sets with the

highest error also have very low FFR

values. This is most likely because there is

a lack of data around the lower FFR values,

and so the network has difficulty learning

these data sets.

The range of FFR values from the

experimental data given by Derriford

hospital was 0.67-0.98. Thus the FFR range

of interest is approximately 0.6–1.

Consequently, it was decided to remove the

15 data sets that had an FFR of less than 0.6

and replace them with data sets that had an

FFR of 0.6 or greater and rerun the MLP

training. This reduced the test error of the

MLP (when trained with 10 hidden units

and an alpha value of 0.01) to 7%.

For the MLP the value of alpha (0.01) was

chosen arbitrarily. In order to further

improve the MLP the number of hidden

units was fixed at 10 (the optimum

suggested by Figure 7) and the value of

alpha was varied logarithmically from 10-5

to 10. Figure 8 is a graph of test error versus

alpha for the MLP. From this graph it is

apparent that the optimum value for alpha

is around 0.3.

The MLP was retrained with the improved

data (all points with an FFR value between

0.6 and 1), with the optimum alpha value of

0.3 and with the best of four random

initialisations. This network was trained

with 1-25 hidden units (see Figure 9). This

graph suggests that between 5-10 hidden

units is the optimum number for the MLP.

This graph also shows that increasing the

value of alpha from 0.01-0.30 has caused

greater instability within the training error.

Figure 9: Graph of test error and training

error vs. no. of hidden units for MLP network

with α=0.3.

Training an MLP network with around 5-10

hidden units and an alpha value of 0.3 gave

an average test error of approximately

0.003 or 5%. Figure 9 indicates that there

are some issues with the training of the data,

especially at larger number of hidden units.

The instability displayed in the training

error of the MLP network demonstrates that

the network is having difficulty

determining the correct weights to use. The

MLP network used in this project has six

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.0001 0.001 0.01 0.1 1 10

Err

or

Alpha

Figure 8: Graph of test error vs.

coefficient of weight decay for

the initial MLP network with 10

hidden units.

0

0.005

0.01

0.015

0.02

0.025

0 10 20

Err

or

No. of hidden units

MLP2 Test

40

input nodes and one output node; thus using

ten hidden units results in 70 network

weights. However, the data only contain

100 data sets, and this is probably not

enough to determine the network weights at

higher number of hidden units. It is

therefore most likely that there is not

enough data to train the MLP, which is

causing the instability within the network.

Another indication that there might not be

enough data sets is the failure of the RBF to

learn the data. One study by P. Crowder et

al. into Radial Basis Functions, found that

‘an MLP network appears to outperform an

RBF network when there are fewer data

points’[10]. The fact that the MLP network

has been far more successful in learning the

data than the RBF network also indicates

that there is not enough training data.

CONCLUSIONS

This project has used a MLP network (with

5-10 hidden units and an alpha value of 0.3)

to predict the FFR value of an idealised

stenosis with an average error of 5%.

However, this MLP network displayed

signs of instability, which was most likely

caused by a lack of training data. Although

the majority of the process of creating the

data sets for the ANN was automated, there

were still several steps that had to be done

manually. These steps were: exporting the

pressure data from ANSYS FLUENT as a

.csv file; importing the .csv file into Matlab;

and recording the FFR value. Whilst

individually these steps are not particularly

laborious, when repeated numerous times it

becomes very time-consuming. This was

the primary reason why only 100 data sets

were created. Further work could be done

on this project to fully automate the process

of CFD model creation, analysis and FFR

calculation. It would be useful to have

1,000 or even 10,000 data sets to train the

MLP, which would almost certainly

improve its performance.

41

REFERENCES

[1] Bupa Health Information, 2010. Coronary Heart Disease.

http://www.bupa.co.uk/individuals/health-information/directory/c/coronary-heart-disease

(accessed 28/03/2013)

[2] Versteed, HK, & Malalalsekera, W, 2006.

An Introduction to Computation Fluid Dynamics: The Finite Volume Method

2nd Ed Harlow: Prentic Hall

[3] Kalogirou, SA, 2001.

Artificial Neural Networks in Renewable Energy Systems Applications: A Review.

Renewable and Sustainable Energy Reviews 5(4): 373-401.

[4] Gershenson, C, 2013

Artificial Neural Networks for Beginners

http://arxiv.org/ftp/cs/papers/0308/0308031.pdf

(accessed 28/03/2013)

[5] 2013, The Shape of Data: General Regression and Over Fitting

http://shapeofdata.wordpress.com/2013/03/26/general-regression-and-over-fitting/

(accessed 28/03/2013)

[6] ANSYS, Inc, ANSYS FLUENT (Version 14.5)

[7] Mathworks, Matblab (R2012a)

[8] Nabney, I, Bishop, C, Netlab

[9] Berthold, M, Hand, D (Eds) 2007

Intelligent Data Analysis: An Introduction

2nd Ed. Chapter 8: Neural Networks. New York: Springer

[10] Crowder, P, Cox, R, Dharmendra, S, 2004

A Study of the Radial Basis Function Neural Network Classifiers using Known Data of Varying

Accuracy and Complexity.

Knowledge-Based Intelligent Information and Engineering Systems, 8th International Conference

Wellington, New Zealand. September 2004. New York: Springer