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Basic Plane Mathematics of MRI
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:
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.

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.

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.



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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