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Basic Plane Mathematics of MRI
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Magnetic resonance imaging (MRI) is partially defined by the plane or direction
of the image that is taken. The most important model coordinate system for medical
imaging is the anatomical coordinate system (also called patient coordinate system).
MRI is viewed as if it were a picture, so left is shown on the right. With this being
said, when viewing images, the sides are switched but the top/bottom and front/back
positions remain the same.
This coordinate system consists of three planes to describe the standard anatomical
position of a human. The basic orientation terms for a MRI of the body taken:
From the side would be a sagittal plane;
from the front, would be a coronal plane;
and from the top down, would be a transverse plane.
In the anatomical position, and with an x-y-z coordinate system, the x-axis
would go from front to back, the y-axis would go from left to right, and the
z-axis would go from up to down. The x-axis axis is always forward (Tait-Bryan
angles) and the right-hand rule applies. The diagrams below should help clear
any confusion up.
The three dimensional Cartesian coordinate system provides the three physical
dimensions of space — depth, width, and height. The 3-Dimensional figure
directly below and to the right shows a common way of representing it.
The x, y, and z-coordinates of a point can also be taken as the distances from
the yz-plane, xz-plane, and xy-plane respectively. The xy, yz, and xz-planes
divide the three-dimensional space into eight subdivisions known as octants,
similar to the quadrants of 2-D space. While conventions have been established
for the labeling of the four quadrants of the x-y plane, only the first octant
of three dimensional space is labeled. It contains all of the points whose x, y,
and z-coordinates are positive. The z-coordinate is also called applicate.
MRI is also a tomographic imaging modality, in that it produces two-dimensional
images that consist of individual slices of the brain. Images in MRI need not
be acquired transaxially, and the table or scanner doesn't move to cover
different slices in the brain. Rather, images can be obtained in any plane
through the head by electronically "steering" the plane of the scan. Precise
spatial localization is achieved through a process termed gradient encoding.
The switching on and off of these magnetic field gradients are the source of
the loud clicking and whirring noises that are heard during an MRI scan. While
this process requires more time than CT scanning, imaging can be performed
relatively rapidly using modern gradient systems.
It's important to realize that the MR scanner actually can only measure
signal in the xy plane. That is, you can't measure the Mz component of net
magnetization. You have to flip M into the xy plane in order to measure its
z-component.
2 Dimensional Coordinates (x & y axis)
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3 Dimensional Coordinates (x, y & z axis)
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| The Three Basic Anatomical Planes: |
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A sagittal plane, (also known as
median plane) is an y-z plane,
perpendicular to the ground, which separates left from right.
The mid-sagittal plane is the specific sagittal plane that is
exactly in the middle of the body. |
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A coronal plane, (also known as
frontal plane) is an x-z plane,
perpendicular to the ground, which (in humans) separates the
anterior from the posterior, the front from the back, the
ventral from the dorsal. |
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A transverse plane, (also known as
axial or
horizontal plane) is an x-y-z plane, parallel to the ground,
which (in humans) separates the superior from the inferior, or
put another way, the head from the feet. |
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The Three Basic Anatomical Planes
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Cerebral Sagittal Axis
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Coronal Image Spacing
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Transverse Image Spacing
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