# Role of Physics in Medicine

Physics plays a significant role in medicine, encompassing a range of applications that allow for better diagnosis, treatment, and understanding of human physiology. It is at the heart of medical imaging, radiation therapy, and the development of various diagnostic and therapeutic equipment. The intersection of physics with medicine has given rise to the field of medical physics, which focuses on applying the concepts of physics to medicine in a practical manner.

## Medical Imaging

One of the most prominent applications of physics in medicine is medical imaging. Techniques such as X-rays, computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, and positron emission tomography (PET) rely on physical principles to visualize the interior of the human body.

– **X-rays** are a form of electromagnetic radiation that can pass through the body and are used to create images of bones and certain body tissues.

– **CT scans** combine X-ray measurements from different angles to create cross-sectional images of the body.

– **MRI** uses strong magnetic fields and radio waves to generate images of organs and structures inside the body.

– **Ultrasound** imaging utilizes high-frequency sound waves to produce images of the inside of the body.

– **PET scans** detect gamma rays emitted by a radioactive tracer injected into the body to produce three-dimensional images.

## Radiation Therapy

Physics is also fundamental in the treatment of diseases such as cancer. Radiation therapy utilizes ionizing radiation to target and destroy cancerous cells. Precise calculations of dosage and the physical interactions of radiation with tissue are critical to minimizing damage to healthy cells while effectively treating the tumor.

## Biophysics

The field of biophysics applies physical principles to understand biological systems. This includes the study of the mechanics of the human body, the electrical properties of cells and tissues, and the fluid dynamics of blood. Understanding these processes is crucial for the development of medical devices such as pacemakers, artificial joints, and stents.

## Diagnostic and Therapeutic Equipment

A vast array of medical equipment is designed using principles of physics. Examples include:

– **Defibrillators** which deliver a dose of electric current to the heart.

– **Laser surgery devices** that use light to cut or destroy tissue.

– **Ventilators** which apply principles of fluid dynamics and gas laws to assist or replace spontaneous breathing.

## Problems and Solutions in Physics in Medicine

Here are 20 problems and solutions that you might encounter in the field of medical physics:

1. **Problem**: Calculate the energy (in keV) of an X-ray photon with a wavelength of 0.10 nm.

**Solution**: Using the formula \( E = \frac{hc}{\lambda} \), where \( h \) is Planck’s constant (\( 4.135667696 \times 10^{-15} \) eV·s), \( c \) is the speed of light (\( 3 \times 10^8 \) m/s), and \( \lambda \) is the wavelength. \( E = \frac{(4.135667696 \times 10^{-15})(3 \times 10^8)}{0.10 \times 10^{-9}} = 12.407 \) keV.

2. **Problem**: Determine the intensity of an ultrasound wave after it has passed through a tissue with an attenuation coefficient of 1 dB/cm when its initial intensity is 0.5 W/cm² and the thickness of the tissue is 2 cm.

**Solution**: The intensity can be calculated using the formula \( I = I_0 \cdot 10^{-\alpha x} \), where \( I_0 \) is the initial intensity, \( \alpha \) is the attenuation coefficient (in dB/cm), and \( x \) is the thickness of the tissue. \( I = 0.5 \cdot 10^{-(1)(2)} = 0.5 \cdot 10^{-2} = 0.005 \) W/cm².

3. **Problem**: How does the energy of a PET scan photon compare with that of a visible light photon?

**Solution**: PET scans use gamma rays with energies typically around 511 keV (electron mass energy equivalent), whereas visible light photons have energies between approximately 1.65 to 3.1 eV. The energy of PET scan photons is therefore orders of magnitude higher than that of visible light photons.

4. **Problem**: What is the resonant frequency of hydrogen in an MRI machine with a magnetic field strength of 1.5 T?

**Solution**: The Larmor equation gives the resonant frequency \( f \) as \( f = \gamma B_0 / (2\pi) \), where \( \gamma \) is the gyromagnetic ratio for hydrogen (\( 42.58 \) MHz/T) and \( B_0 \) is the magnetic field strength. \( f = (42.58)(1.5) = 63.87 \) MHz.

5. **Problem**: If sound travels at 1,540 m/s in soft tissue, how long will it take for an ultrasound pulse to travel to an organ 10 cm away and back?

**Solution**: The total distance traveled is \( 2 \times 0.10 \) m, and the speed of sound is \( 1,540 \) m/s. Time \( t = \text{distance/speed} = (2 \times 0.10 \text{ m}) / (1,540 \text{ m/s}) = 0.000130 \) s, or 130 µs.

6. **Problem**: A CT scanner uses an X-ray tube current of 400 mA and a tube potential of 120 kV. Calculate the power of the X-ray tube.

**Solution**: The power \( P \) of an X-ray tube is given by the product of the current \( I \) and the tube potential \( V \). \( P = IV = (400 \text{ mA})(120 \text{ kV}) = 48 \text{ kW} \).

7. **Problem**: For a linear accelerator used in radiation therapy, determine the kinetic energy in MeV of an electron beam accelerated through a potential difference of 25 MV.

**Solution**: The kinetic energy \( KE \) of an electron accelerated through a potential difference \( V \) is equal to the charge \( e \) of the electron times the potential difference. \( KE = eV = (1 \text{ e})(25 \times 10^6 \text{ V}) = 25 \text{ MeV} \).

8. **Problem**: Estimate the electrical power required by a defibrillator to deliver a 200 J shock in 5 ms.

**Solution**: Power \( P \) is the rate of energy delivery over time \( t \). \( P = \frac{E}{t} = \frac{200 \text{ J}}{0.005 \text{ s}} = 40,000 \text{ W} \), or 40 kW.

9. **Problem**: In MR imaging, if the field gradient is 10 mT/m, what is the difference in resonance frequency between two points 10 cm apart?

**Solution**: The frequency shift \( \Delta f \) can be calculated by \( \Delta f = \gamma \Delta B \), where \( \Delta B \) is the change in magnetic field over the distance \( \Delta x \). \( \Delta f = (42.58 \text{ MHz/T})(0.10 \text{ T/m})(0.10 \text{ m}) = 0.4258 \text{ MHz} \).

10. **Problem**: Determine the pressure exerted on the chest wall by an ultrasound transducer if the force applied is 5 N and the area of the transducer head is 10 cm².

**Solution**: Pressure \( P \) is the force \( F \) per unit area \( A \). \( P = \frac{F}{A} = \frac{5 \text{ N}}{0.0010 \text{ m²}} = 5,000 \text{ Pa} \), or 5 kPa.

11. **Problem**: Calculate the stopping power of a particular tissue for a 1 MeV proton if it loses 2 keV of energy per millimeter.

**Solution**: Stopping power \( S \) is the energy loss \( dE \) per unit length \( dx \). \( S = \frac{dE}{dx} = \frac{2 \text{ keV}}{1 \text{ mm}} = 2 \text{ keV/mm} \).

12. **Problem**: A gamma ray of 0.5 MeV is scattered at an angle of 60 degrees during a Compton scattering event. Find the final energy of the photon.

**Solution**: The Compton shift formula is \( \Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta) \), where \( \Delta \lambda \) is the change in wavelength, \( h \) is Planck’s constant, \( m_ec \) is the electron rest mass energy, and \( \theta \) is the scattering angle. Convert the initial energy to wavelength using \( E = \frac{hc}{\lambda} \), then calculate the change in wavelength and convert back to energy.

13. **Problem**: How much time is required for a heart pacemaker with a battery life of 5 years if it uses a charge of 0.8 Coulombs per beat and the patient’s heart rate is 70 beats per minute?

**Solution**: The total charge used per year \( Q \) can be calculated by multiplying the charge per beat by the number of beats per year. Then divide the battery capacity by \( Q \) to find the number of years the battery will last.

14. **Problem**: If a laser surgery device operates at a wavelength of 532 nm with a power of 2 W, how many photons per second does it emit?

**Solution**: First, find the energy \( E \) of one photon at the given wavelength, then divide the power by the energy per photon to find the number of photons per second.

15. **Problem**: A ventilator delivers a volume of 500 mL of air (measured at standard temperature and pressure) to the patient’s lungs with each breath. If the ventilator operates at 12 breaths per minute, what is the flow rate in liters per minute?

**Solution**: Multiply the volume per breath by the number of breaths per minute.

16. **Problem**: For an eye surgery correcting myopia using a laser, if the cornea’s refractive power needs to be reduced by 2 diopters and the ablation removes 15 µm of corneal tissue per diopter, calculate the total depth of tissue that needs to be removed.

**Solution**: Multiply the correction required in diopters by the tissue removal rate per diopter.

17. **Problem**: If the sound intensity level at the operator’s station of an ultrasound machine is 85 dB and the threshold of pain is 120 dB, how many times more intense is the pain threshold compared to the operating level?

**Solution**: Using the formula for intensity levels, calculate the ratio of intensities.

18. **Problem**: A Glucose PET tracer has a half-life of 110 minutes. If you start with 20 mCi of the tracer, how much will be left after 3 hours?

**Solution**: Use the half-life formula to calculate the remaining activity.

19. **Problem**: A bone densitometer uses a dual-energy X-ray source with energies of 80 keV and 100 keV. If the lower energy beam has twice the intensity of the higher one after passing through the body, estimate the effective density difference that caused this.

**Solution**: Apply the Beer-Lambert law to model the attenuation differences and solve for density.

20. **Problem**: In laser photocoagulation used for treating retinal disorders, what is the intensity of a 0.2 W laser with a spot size diameter of 2 mm on the retina?

**Solution**: Use the formula for intensity with the given power and area of the spot size.

These problems represent only a handful of the vast array of potential issues physicists might address in the field of medicine. Solving these requires a solid understanding of both the theoretical and practical aspects of physics as it applies to medical technology and treatment modalities.