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Contents

1. X-RAYS

1.1 Attenuation of X-rays

1.1.1 Exercise: X-ray transmission of lead

1.1.2 Solution

1.1.3 Exercise: X-ray attenuation of silver bromide

1.1.4 Solution

1.1.5 Exercise: X-ray absorption of film and intensifying screen

1.1.6 Solution

1.1.7 Exercise: X-ray transmission of bone

1.1.8 Solution

1.1.9 Exercise: X-ray contrast of muscle and adipose

1.1.10 Solution

1.1.11 Exercise: K-absorption edge of Calcium

1.1.12 Solution

1.2 X-ray tubes

1.2.1 Exercise: X-ray spectrum of an X-ray tube

1.2.2 Solution

1.2.3 Exercise: Relation of high voltage setting and dose

1.2.4 Solution

1.2.5 Exercise: Relation of distance and exposure time

1.2.6 Solution

1.2.7 Exercise: Characteristic Ka-radiation of molybdenum

1.2.8 Solution

1.2.9 Exercise: Characteristic Ka-radiation radiation of tungsten

1.2.10 Solution

1.3 X-ray scattering

1.3.1 Exercise: Energy of Compton-scattered X-ray radiation

1.3.2 Solution

1.3.3 Exercise: Cross sections of photoelectric absorption and Compton scattering of water

1.3.4 Solution

1.3.5 Exercise: Cross sections of photoelectric absorption and Compton scattering of Calcium

1.3.6 Solution

1.4 X-ray dosimetry

1.4.1 Exercise: Number of X-rays per area in a chest radiograph

1.4.2 Solution

1.4.3 Exercise: Relation of the thickness of X-ray shielding and X-ray energy

1.4.4 Solution

1.5 X-ray statistics

1.5.1 Exercise: Statistical X-ray noise in a chest radiograph

1.5.2 Solution

1.5.3 Exercise: Image noise of an integrating Germanium detector

1.5.4 Solution

1.5.5 Exercise: Relation of the error of the estimated path integral of the attenuation coefficient on the number of irradiated and transmitted X-rays

1.5.6 Solution

1.5.7 Exercise: The path integral of X-ray absorption coefficient µ and the error thereof due to the statistics of irradiated and transmitted X-rays

1.5.8 Solution

1.5.9 Exercise: Signal, signal noise, and signal to noise ratio in a computed tomography system

1.5.10 Solution

1.5.11 Exercise: Signal, noise, signal to noise ratio and DQE of a CCD-based X-ray sensor

1.5.12 Solution

1.5.13 Exercise: Signal to noise ratio of an integrating X-ray detector in the case of a continuous energy spectrum

1.5.14 Solution

1.5.15 Exercise: Signal to noise ratio of the integrated X-ray signal of an X-ray source with continuous X-ray spectrum

1.5.16 Solution

1.5.17 Exercise: Probability to absorb a specific number of X-ray quanta

1.5.18 Solution

1.5.19 Exercise: Probability to absorb a specific number of X-ray quanta for given number of irradiated quanta

1.5.20 Solution

1.5.21 Exercise: Standard deviation of the number of absorbed X-ray quanta

1.5.22 Solution

2. ULTRASOUND

2.1 Ultrasound Waves

2.1.1 Exercise: Wavelength of sinusoidal ultrasound waves

2.1.2 Solution

2.1.3 Exercise: Reflected intensity at an interface

2.1.4 Solution

2.1.5 Exercise: Reflected intensity at an interface of muscle and bone

2.1.6 Solution

2.1.7 Exercise: Change of direction of a sound wave traversing an interface

2.1.8 Solution

2.1.9 Exercise: Transversal deflection of an ultrasound beam

2.1.10 Solution

2.1.11 Exercise: Displayed size of tissues in ultrasound images

2.1.12 Solution

2.1.13 Exercise: Frequency shift in Doppler mode

2.1.14 Solution

2.2 Ultrasound scanners

2.2.1 Exercise: Beam focusing by delaying elements in a linear array

2.2.2 Solution

2.2.3 Exercise: Best size of focus

2.2.4 Solution

2.2.5 Exercise: Depth of focus

2.2.6 Solution

2.2.7 Exercise: Longitudinal resolution of an ultrasound pulse

2.2.8 Solution

3. ELECTROCARDIOGRAPHY (ECG)

3.1 Dipole fields

3.1.1 Exercise: Potential of an electric dipole along the dipole axis

3.1.2 Solution

3.1.3 Exercise: Potential of an electric dipole in the symmetry plane

3.1.4 Solution

3.1.5 Exercise: Component of the electric dipole vector

3.1.6 Solution

3.2 ECG instrumentation

3.2.1 Exercise: Heart rate in an ECG paper print

3.2.2 Solution

3.2.3 Exercise: Angle of the heart electrical axis

3.2.4 Solution

3.2.5 Exercise: Equation to calculate Uiii from Ui and Uii

3.2.6 Solution

3.2.7 Exercise: Angle of the heart electrical axis for given Ui and Uii

3.2.8 Solution

3.2.9 Exercise: The signal lead augmented vector foot aVf

3.2.10 Solution

3.2.11 Exercise: Voltage ratios of Einthoven and Goldberger signal leads

3.2.12 Solution

3.2.13 Exercise: Precordial leads according to Wilson

3.2.14 Solution

4. LASER

4.1 Interaction of laser light with matter

4.1.1 Exercise: Energy density and time range of laser radiation to coagulate soft tissue

4.1.2 Solution

4.1.3 Exercise: Energy density and time range of laser radiation to vaporize soft tissue

4.1.4 Solution

4.1.5 Exercise: Energy density and time range of laser radiation to photoablate soft tissue

4.1.6 Solution

4.1.7 Exercise: Energy density and time range of laser radiation to photodisrupt soft tissue

4.1.8 Solution

4.1.9 Exercise: Power density of a laser diode

4.1.10 Solution

4.1.11 Exercise: Energy density and beam diameter of a pulsed laser

4.1.12 Solution

4.1.13 Exercise: Ablation depth of a laser pulse

4.1.14 Solution

4.1.15 Exercise: Ablation depth versus energy density of laser pulses

4.1.16 Solution

4.1.17 Exercise: Beam diameter and depth of focus of a focused laser

4.1.18 Solution

4.1.19 Exercise: Irradiation time in photodynamic therapy

4.1.20 Solution

4.1.21 Exercise: Therapeutic window

4.1.22 Solution

5. PULSE OXYMETRY

5.1 Interaction of light with blood

5.1.1 Exercise: Optical density of blood

5.1.2 Solution

5.1.3 Exercise: Isobestic point of light absorption in blood

5.1.4 Solution

5.1.5 Exercise: Maximum difference of light absorption in hemoglobin

5.1.6 Solution

5.1.7 Exercise: Optical densities of oxy- and deoxygenated hemoglobin

5.1.8 Solution

5.2 Analysis of oxygen saturation

5.2.1 Exercise: Variation of the optical path length

5.2.2 Solution

5.2.3 Exercise: Ratio of optical density differences during a heartbeat

5.2.4 Solution

5.2.5 Exercise: Ratio of optical density differences at specific oxygen saturation

5.2.6 Solution

6. HIGH-FREQUENCY SURGERY

6.1.1 Exercise: Current densities around a spherical electrode

6.1.2 Solution

6.1.3 Exercise: Electrical potentials around a spherical electrode

6.1.4 Solution

6.1.5 Exercise: Current between a spherical and a large neutral electrode

6.1.6 Solution

6.1.7 Exercise: Current between a spherical and a large neutral electrode for a given set of parameter values

6.1.8 Solution

6.1.9 Exercise: Power density caused by current flow

6.1.10 Solution

6.1.11 Exercise: Supplied heat energy and rise of temperature

6.1.12 Solution

6.1.13 Exercise: Ratio of peak and average power

6.1.14 Solution

6.1.15 Exercise: Dissipated power versus specific resistance

6.1.16 Solution

6.1.17 Exercise: Dissipated power at different orientations of tissues

6.1.18 Solution

6.1.19 Exercise: Dissipated power at different orientations of tissues with specific resistances

6.1.20 Solution

7. COMPUTED RADIOGRAPHY (CR)

7.1 Storage phosphors

7.1.1 Exercise: Number of generated photostimulable storage centers per X-ray quantum

7.1.2 Solution

7.1.3 Exercise: Wavelength of maximum photostimulability

7.1.4 Solution

7.1.5 Exercise: Crosstalk of subsequently scanned pixel

7.1.6 Solution

7.1.7 Exercise: Probability of F-center electrons to escape to the conduction band

7.1.8 Solution

7.1.9 Exercise: Schottky defect pair concentration in NaCl

7.1.10 Solution

7.2 CR scanner

7.2.1 Exercise: Diffraction limited spot size of a CR scanner

7.2.2 Solution

7.2.3 Exercise: Maximum scan speed at specific pixel size and crosstalk

7.2.4 Solution

7.2.5 Exercise: Rotational speed of a mirror and scan speed of laser beam

7.2.6 Solution

7.2.7 Exercise: Bearing play and projected beam positioning

7.2.8 Solution

7.2.9 Exercise: Readout time and efficiency of information readout

7.2.10 Solution

7.2.11 Exercise: DQE of a CR-system

7.2.12 Solution

8. COMPUTED TOMOGRAPHY (CT)

8.1 Tomographic Reconstruction

8.1.1 Exercise: Number of X-ray projections and number of voxels

8.1.2 Solution

8.1.3 Exercise: Point spread function using unfiltered backprojection

8.1.4 Solution

8.1.5 Exercise: Ideal filter function in filtered backprojection

8.1.6 Solution

8.1.7 Exercise: Transmitted dose signals in real and in Fourier space

8.1.8 Solution

8.1.9 Exercise: Grid pattern of Fourier transformed absorption data

8.1.10 Solution

8.2 Instrumentation

8.2.1 Exercise: Acceleration of a rotated X-ray tube

8.2.2 Solution

8.2.3 Exercise: Data rate of a CT scanner

8.2.4 Solution

8.2.5 Exercise: Decay time of luminescence and crosstalk

8.2.6 Solution

8.2.7 Exercise: Number of angular positions of X-ray exposures and number of pixel elements in a sectional image

8.2.8 Solution

8.2.9 Exercise: Acquisition time of a tomogram and pixel rate of a CT scanner

8.2.10 Solution

8.2.11 Exercise: CT number of adipose tissue

8.2.12 Solution

8.2.13 Exercise: CT numbers of cortical bone

8.2.14 Solution

8.2.15 Exercise: CT numbers in dual Energy CT

8.2.16 Solution

8.2.17 Exercise: CT artefacts of a metal sphere

8.2.18 Solution

8.2.19 Exercise: Number of photons and electrons per absorbed X-ray

8.2.20 Solution

8.2.21 Exercise: Photodiode current in a detector element of a CT scanner

8.2.22 Solution

8.3 X-ray Dose

8.3.1 Exercise: Error of measured absorption coefficients and X-ray dose

8.3.2 Solution

9. NUCLEAR MAGNETIC RESONANCE IMAGING

9.1 Nuclear magnetic resonance

9.1.1 Exercise: Energy levels of hydrogen nuclei in a magnetic field

9.1.2 Solution

9.1.3 Exercise: Frequency of a nuclear spin flip in a magnetic field

9.1.4 Solution

9.1.5 Exercise: Relative occupation difference of energy levels in a magnetic field

9.1.6 Solution

9.1.7 Exercise: Required field direction to induce spin flips

9.1.8 Solution

9.1.9 Exercise: Nuclear spin quantum numbers in the ground state

9.1.10 Solution

9.1.11 Exercise: Number of energy levels of nuclei in a magnetic field

9.1.12 Solution

9.1.13 Exercise: Influence of the electron shell on nuclear energy levels

9.1.14 Solution

9.1.15 Exercise: Types of nuclear spin relaxations and relaxation times

9.1.16 Solution

9.1.17 Exercise: Mechanism of contrast agents in NMR

9.1.18 Solution

9.1.19 Exercise: Decay of the transversal magnetizations after a pulse sequence

9.1.20 Solution

9.1.21 Exercise: Transversal magnetizations after different pulse sequences

9.1.22 Solution

9.1.23 Exercise: Time interval between 180° and 90° pulses to get transversal magnetization down to zero

9.1.24 Solution

9.1.25 Exercise: Spin echo signals of different tissues at a specific pulse sequence

9.1.26 Solution

9.1.27 Exercise: TR and TE values in proton density weighted MRI

9.1.28 Solution

9.2 Magnetic resonance imaging instrumentation

9.2.1 Exercise: Number of gradient coils in an MRI scanner

9.2.2 Solution

9.2.3 Exercise: Magnetic flux of MRI scanners using normally conducting electro magnets

9.2.4 Solution

9.2.5 Exercise: Waveform of the high frequency pulse to excite spins in a plane

9.2.6 Solution

9.3 Image reconstruction

9.3.1 Exercise: Relation between spin signals in real and Fourier space

9.3.2 Solution

9.3.3 Exercise: Location of the Fourier transforms of nuclear resonance signals in Fourier space

9.3.4 Solution

10. NUCLEAR MEDICAL IMAGING

10.1 Radionuclides

10.1.1 Exercise: Half-life and decrease of activity

10.1.2 Solution

10.1.3 Exercise: Amount of decays within a time period after incorporation of the radionuclide

10.1.4 Solution

10.2 Instrumentation

10.2.1 Exercise: Radius of field of a circular collimator

10.2.2 Solution

10.2.3 Exercise: Efficiencies of circular collimators

10.2.4 Solution

10.2.5 Exercise: Amount of γ-absorption within a body using ^99mTc as radioactive emitter

10.2.6 Solution

10.2.7 Exercise: Amount of γ-absorption within a body in PET

10.2.8 Solution

10.2.9 Exercise: Probability of coincident photoabsorption of two γ quanta in PET

10.2.10 Solution

10.2.11 Exercise: Energy resolutions of scintillation detectors

10.2.12 Solution

10.2.13 Exercise: Compton scattering angles of counted γ quanta for a given energy window in PET

10.2.14 Solution

11. RECEIVER OPERATOR CHARACTERISTIC (ROC)

11.1 Binary classification

11.1.1 Exercise: Tables of confusion for different threshold values

11.1.2 Solution

11.1.3 Exercise: Sensitivity and specificity for different threshold values

11.1.4 Solution

11.2 ROC curves

11.2.1 Exercise: ROC curve for different threshold values

11.2.2 Solution

12. MODULATION TRANSFER FUNCTION (MTF)

12.1.1 Exercise: Evaluation of the MTF using a sinusoidal test pattern

12.1.2 Solution

12.1.3 Exercise: Relation between two MTFs corresponding to PSFs of different width

12.1.4 Solution

12.1.5 Exercise: Standard deviation of the PSF of a CR scanner comprising two processes of spatial broadening of information

12.1.6 Solution

12.1.7 Exercise: Spatial frequency at a specific value of the MTF of an X-ray detector having a PSF with Gaussian profile

12.1.8 Solution

12.1.9 Exercise: Calculation of the MTF at a specific spatial frequency for a PSF with Gaussian profile

12.1.10 Solution

12.1.11 Exercise: MTF of a second process that broadens the PSF

12.1.12 Solution

12.1.13 Exercise: Fourier expansion of a rectangular grid pattern

12.1.14 Solution

13. LIST OF ABBREVIATIONS

14. LIST OF IMPORTANT SYMBOLS

15. SUBJECT INDEX