Math. & Phys. Teacher & Nuclear Medical Physicist Lennart Egedal Petersen

Visibility of Physics and Mathematics workability especially in a hospital

1

Examples of cooperation

Viborg Katedralskole&

The Police Force in ViborgDepartment of Clinical Physiology, Region Hospital Viborg

Tallinna Reaalkool D. 11.-12.september 2015

2

Hands on Physics and Mathematics

applied in practice

outside the school

are motivating and awareness-raising

3

Cooperation with The Police Force in Viborg

Physics/mathematical level: 1. year (A/B-level)

Concepts: Linear regression, force, speed,

acceleration, mechanical energy,

laser

Duration: 1½ hour per class

Product: Common group report with all

theoretical considerations and experimental

calculations

Velocity-measurements

LIDAR: LIght Detection And Ranging

Transmitter diode (laser)

(~1000 pulses/sek; λ~800nm)

Receiver diode (photomultiplier)

4

Velocity-measurements

sn: The distance between the LIDAR and the car at time Tn

Tn: Time when pulse n is transmitted

tn: Time the pulse n take to travel the distance 2.sn (LIDAR – CAR – LIDAR)

c: Velocity of light 2,9979258.108 m/s

5

ctsnn

⋅=⋅2

6

Velocity-measurements

sn can be calculated

ctsnn

⋅=⋅2

7

Velocity-measurements

The graph (Tn;sn) shows the distance sn to the car as a function of time Tn

8

Braking distance measurement

The law of Mechcanical Energy gives:

The braking distance (car) and the braking force (bicycle) can be calculated

rceexternalfomek A∆E =

braking

2

bycyclestudent

braking∆s2

v)m(mF

Bicycle

⋅

⋅+=

F2

v)m(m∆s

Car

braking

2

personcar

braking⋅

⋅+=

9

1:Cooperation with The Department of Clinical Physiology (Nuclear Medicine)

Physics/mathematical level: 2. year (A/B-level)

Concepts: Radioactive decays, Absorption of Ionizing Radiation, Dose, Doserate,

Gamma Camera-scintigraphies , 99mTc-99Mo Generator

Student experiment:

Law of Radioactive Decay ( 99mTc 140keV)

Law of Absorption of Gamma-Radiation (137Cs 662keV)

Distance Square Law of Radiation ( 99mTc 140keV)

Duration: 1½-2 hours common lecture by a physician

for all classes at the School:

3 hours visit with Hands On Experiments

at the Department one Class at a time

divided in 3 groups

Product: Common group report with all theoretical and experimental calculations

(~30 pages written guidance)

2

x

x

o

T

t

o

x

1constantD´(x)

)2

1(II(x)

)2

1(AA(t)

½

½

⋅=

⋅=

⋅=

1:Cooperation with The Department of Clinical Physiology (Nuclear Medicine)

Physics/mathematical level: 2. year (A/B-level)

Concepts: Radioactive decays, Absorption of Ionizing Radiation, Dose, Doserate,

Gamma Camera-scintigraphies , 99mTc-99Mo Generator

Student experiment:

Law of Radioactive Decay ( 99mTc 140keV)

Law of Absorption of Gamma-Radiation (137Cs 662keV)

Distance Square Law of Radiation ( 99mTc 140keV)

Duration: 1½-2 hours common lecture by a physician

for all classes at the School:

3 hours visit with Hands On Experiments

at the Department one Class at a time

divided in 3 groups

Product: Common group report with all theoretical and experimental calculations

(~30 pages written guidance)

2

x

x

o

T

t

o

x

1constantD´(x)

)2

1(II(x)

)2

1(AA(t)

½

½

⋅=

⋅=

⋅=

10

2:Cooperation with The Department of Clinical Physiology (Nuclear Medicine)

Physics/mathematical level: 3. year (A-level)

Concepts: 99mTc-99Mo Generators

Filtration rate of the kidney´s (Glomerular Filtration Rate: GFR)

Compartment models, Differential equations, Calculus of integral,

Optimization with least square methods,

Ultrasound, Doppler-Ultrasound,

X-ray

Duration: 14 days to a student task ( approx. 30 pages) over an experimental /

theoretical problem relevant for some equipment or an examination of

data from a real patient at the department

Product: All theoretical and experimental calculations/considerations (~30 pages )

11

Without knowledge of

Mathematics and Physics

a large number of examinations can´t be carried out

http://fas.org/irp/imint/docs/rst/Intro/Part2_26d.html 12

SPECT –CT Camera(Single Photon Emission Computed Tomography & Computer Tomography)

NT

NkA ⋅=⋅=½

)2ln(

13

SPECT-CT Fusion of 2 modalities

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Nuclear Isotopes

Treatment, Examination, Quality test

Mo-Tc Generator

51Cr, 57Co, 75Se, 99Mo, 99mTc, 111In, 125I, 131I, 153Gd, 137Cs

Decay of nuclear isotopes (α, β−,β+, γ; EC)

The Decay Law of Radioactive Isotopes

N(t)kA(t)

)2

1(AeAA(t)

)2

1(NeNN(t)

½

½

t/T

o

kt

o

t/T

o

kt

o

⋅=

==

==

−

−

Mo-Tc generator. Model

15

Mo-Tc generator. Model

99Mo

1

99mTc

2

99Tc

3

16

111 Nk

dt

dN⋅−=

0,876f

NkNkfdt

dN2211

2

=

⋅−⋅⋅=

17

Mo-Tc generator. Activities for Mo and Tc

k

ln2T

Mo)( 65,94h T

2

1A(t)A

1

½1

99

½1

T

t

Mo,0Mo

½1

=

=

⋅=

½1T

t

Mo,0Mo2

1N(t)N

⋅= ½2½2½1 T

t

Tc,0

T

t

T

t

½2½1

½2Mo,0Tc )

2

1(N)

2

1()

2

1(

TT

TNf(t)N ⋅+

−⋅

−⋅⋅=

½2½2½1 T

t

Tc,0

T

t

T

t

½2½1

½1Mo,0Tc )

2

1(A)

2

1()

2

1(

TT

TAf(t)A ⋅+

−⋅

−⋅⋅=

2

½2

99m

½2

k

ln2T

Tc)( 6,02h T

=

=

18

Mo-Tc generator. Activities for Mo and Tc

Blue: 99Mo activity

Red: 99mTc activity

f=0,876

19

Mo-Tc generator. Optimal elute time

Blue: 99Mo activity

Red: 99mTc activity

f=0,876

t*

22,9ht*

Tc)( 6,02h T

Mo)( 65,94h T

)T(Tln2

TT)T

Tln(

t*

99m

½2

99

½1

½2½1

½2½1

½2

½1

=

=

=

−⋅

⋅⋅

=

20

Mo-Tc generator. Elute schedule

Activity of 99Mo and 99mTc as a function of time for a week

21

Thyroid- scintigraphy

http://www.thyroiduk.org.uk/tuk/about_the_thyroid/thyroid_overview.html

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Bone-scintigraphy

Is it multiple bone metastases?

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Bone-scintigraphy

Is it multiple bone metastases?

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Kidney- Renograhpy

Sentinel node /Lymphoscintigraphy

25

26

Leucocyt-scintigraphy (111In)

X-ray: DEXA (Dual Energy X-ray Absorptiometry)

X-ray; Absorption of ionizing radiation

27

X-ray: DEXA (Dual Energy X-ray Absorptiometry)

Bone mineral density

Body contribution (Fat, muscle, bone)

28

Ultra-sound

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Medium Velocity of

sound v (m/s)

Air 330

Water (20oC) 1480

Fat 1450

Blood 1570

Muscle 1580

Bone 3500

Soft tissue (middle) 1540

fλ v ⋅=

Time/Distance

Intensity

http://www.ni.com/white-paper/3368/en/

Ultra-sound: Reflection and Refraction

vFat=1450m/s > vMuscle=1580m/s

Refraction artifacts

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b

i

v

v

sin(b)

sin(i)r i ==

Diagnostic Ultrasound. Peter Hoskins, Kevin Martin & Abigail Thrush, Cambridge University Press 2010Basics of Ultrasound Imaging. Vincent & Anahi Perlas. Springer 2011

Ultra-sound: Acoustic impedance

Z =ρ.v Acoustic Impedance of a media

ρ: Density of a media

v: Velocity of sound in a media

Why is gel used on the skin when we are scanning with ultrasound?

It feels good…. or is there a physical explanation?

31

212

12

12

12

)(

42 )(

thenb0i If

ZZ

ZZ

i

t

IZZ

ZZ

i

r

I

I

IT

I

IR

++

−====

==

Diagnostic Ultrasound. Peter Hoskins, Kevin Martin & Abigail Thrush, Cambridge University Press 2010

Ultra-sound. Acoustic impedance

Z =ρ.v Acoustic Impedance of a media

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Medium Acoustic impedance Z

(kg/(m2s))

Liver 1,66.106

Kidney 1,64.106

Blood 1,67.106

Fat 1,33.106

Water 1,48.106

Air 430

Bone 6,47.106

Medium / Medium RI TI

Kidney/Blood 0,00008 0,99992

Bone/Kidney 0,355 0,645

Fat/Liver 0,012 0,988

Water/Air 0,999 0,0012

Fat/Bone 0,434 0,566

Blood/Air 0,999 0,0010

Diagnostic Ultrasound. Peter Hoskins, Kevin Martin & Abigail Thrush, Cambridge University Press 2010

Ultra-sound: Doppler-Ultrasound

Doppler-effect for ultrasound is used to detect the movement of blood (erytrocytes)

and tissue (example: the heart)

Total change in frequency for transmitted and received

ultrasound waves at the ultrasound transducer

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fv

cosθ2vf

Ultrasound

bloodDoppler

⋅=∆

fv

cosθ2vf

Ultrasound

bloodDoppler

⋅−=∆

https://sites.google.com/site/wwwgooglecomkrystynabywalec/doppler

Ultra-sound: Doppler-Ultrasound.

Flow velocity of blood in artery

Calcification of artery

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Beamline for ultrasound signal

Angel correction-cursor

Sample Volume

Colour Box

Velocity spectrum for

bloodflow in Sample Volume

Law of Ideal Gas: Lungs Capacity

Changes in volume in the lungs = Changes in volume in the box

Changes in the pressure in the lungs can be measured as changes in the pressure

in the mouth

35

P∆P

∆PfV Mouth

Mouth

boxcal volumeGas Thoracal ⋅

⋅=

Blood-Pressure in toes and fingers

Wheatstone Bridge with a Mercury tube and a Strain Gauge

36

l

∆l2

R

∆R

A

lρR

=

⋅=

l

A

Thank You for Your Attention

37

Visibility of Physics and Mathematics workability especially in a hospital