Biomedical EngineeringA multidisciplinary Major

Mohamed Bingabr, Ph.D.Associate Professor

Department of Engineering and Physics University of Central Oklahoma

What does make biomedical engineer a good candidate to build and design medical devices?

Biomedical engineer has broad knowledge in math, biology, chemistry, physics, and engineering.

What knowledge do you need to design MRI?

• MRI (Magnetic Resonance Imaging)• Non invasive imaging of cancerous cells and

abnormality in human tissues.

Firs case study: The Design of MRI

Biology in MRI- Cell’s content• Cells are the building blocks of living

systems.• Cell consist of

–70% water (H2O)

–The remaining 30% water-free basis• 50% by weight Carbon• 14% Nitrogen• 4% Phosphorous• Others

Biology in MRI – unhealthy Cells

• Unhealthy cell has either more or less water.

• Cancerous cell in the brain tissue has more than 70% of water.

Idea 1

If we can determine the quantity of water in a cell then we can determine if the cell is healthy or diseased.

Chemistry in MRI

• Water consist of two hydrogen atoms and one oxygen atom (H2O)

• Hydrogen has one electron and one proton

Physics in MRI

• Nucleus with odd protons spin.

• Hydrogen nucleus has 1 proton, so it spins.

• When charge spin in a circular motion it generate magnetic moment µ.

μ

Model proton as a ring of current.

Idea 2

• If we measure the magnetic moments of all hydrogen atoms in a cell, then we can determine the water quantity in the cell (H2O).

• If we know the water quantity, then we can determine if the cell is healthy or not.

Problem 1

Hydrogen atoms in a cell spin at different directions so magnetic moments of different atoms cancel each other and the net magnetic moment is zero.

1μ2μ

3μ 4μ

0M

μμμμM 4321

Solution 1 (from engineering) Place the cell in a strong external magnetic field Bo, so all nucleus of the atoms will spin such that the magnetic moments will be aligned with the external field.

1μ2μ

3μ 4μ

4321 μμμμM

Problem 2Now, it is harder to measure the net magnetic moments M in the presence of the external strong magnetic field Bo

1μ2μ

3μ 4μ

4321 μμμμM

Solution 2 (from engineering)The frequency of spin ω (Larmor frequency) will depend on the magnetic field Bo.

Excitation of the nucleus with external radio-frequency with Larmor frequency will cause the magnetic moments to precess to the xy-plane.

RF excitation

Solution 2 (from engineering)Turning off the external RF excitation will cause the magnetic moments to spin back in the same direction as the external magnetic field.

The magnetic moment will radiate RF magnetic field with Larmor frequency.

RF magnetic field (wave)

Solution 2 (from engineering)• The strength of the radiated wave will depend

on the number of hydrogen atoms.

• We can use Antenna to detect the radiated RF magnetic field.

Problem 3• The measured radio frequency is coming from

all cells located in the external magnetic field.

• How do we differentiate between cells of different organs or of the same organ?

.

.

x

z

y

RF detection coils

(Antenna))(mM x,y,z

Magnetic Field Bo

Bo

RF excitation

Solution 3 (from engineering)

Apply an external magnetic field with gradient in the x direction. M(x).

Now, every location in the human body along the x-axis will be located in a unique magnetic field M(x), and will radiate RF waves with different frequencies.

xBo

Solution 3 (from engineering)Apply an external magnetic field with gradient in the x, y, and z directions. M(x,y,z).

.

.

x

z

y

)(mM x,y,z

Now, every location (cubic pixel) in the human body will be located in a unique magnetic field M(x,y,z).

RF detection coils

(Antenna)

Solution 3 (from engineering)The nucleus of hydrogen atoms located at different magnetic fields (cubic pixel) will have different Larmor frequencies.

.

.

x

z

y

)(mM x,y,z

Apply external RF excitation of different frequencies for a short period of time. Hydrogen atoms in each cubic pixel will radiate RF wave with unique frequency.

RF excitation of many frequencies

RF detection coils

(Antenna)

Solution 3 (from engineering)When the external RF excitation is turned off the hydrogen nucleus will precess to their original position and RF waves would emanate from the hydrogen nucleus.

.

.

x

z

y

)(mM x,y,z

These RF waves will be detected as a decayed sinusoidal voltage with different frequencies and amplitudes in an external antenna.

RF detection coils

(Antenna)

Problem 4How do we display these RF waves of different frequencies and amplitudes in a form that physicians and radiologist can understand?

.

.

x

z

y

)(mM x,y,z

RF detection coils

(Antenna)

Solution 4 (Math in MRI)We use Fourier Transform to determine the frequency components and their amplitudes of the received RF waves by the antenna.

.

.

x

z

y

FourierTransform

$3682 FourierTransform

3 (1000)

6 (100)

8 (10)

2 (1)

Math in MRI - Solution 4

.

.

x

z

y

FourierTransform

We use the frequencies to determine the location of the pixels cube and the amplitude to determine the quantity of the hydrogen atoms in the pixel cube

MRI Image

FourierTransform

Image Resolution

4 pixels/image16 pixels/image

64 pixels/image

Homework (Due Feb. 3)Write a paper (two to three pages ) to answer the following:1. How can you improve the resolution of the

MRI image?2. What parts of the body is MRI not good in

imaging ? And why?3. Include in your paper the following points:

a. Manufacturers of MRI and their prices.b. The different type of MRIs (specifications).c. The common diagnosis of MRI d. MRI limitations.