Chapter 9: Signal and Noise in fMRI

 

 

Study Questions

 

 

 

 

1.   Define “signal” and “noise.”

 

Signal is the meaningful changes in some quantity.  In fMRI, an important class of signals includes changes in intensity associated with the BOLD response across a series of T2* images.

      On the other hand, noise is the non-meaningful changes in quantity.  In fMRI, there are many sources of noise and some can be classified as either noise or signal, depending on the study.

 

 

 

 

 

 

 

2.   What are the differences between “raw signal-to-noise-ratio,” “contrast-to-noise-ratio,” and “functional signal-to-noise-ratio”?

Raw signal-to-noise-ratio is the ratio between MR signal intensity and the intensity of the thermal noise that is measured outside the sample. When designing an MR machine, engineers strive to minimize this ratio to create an optimally functioning MR unit. Contrast-to-noise-ration is the magnitude of the intensity difference between different quantities divided by the variability in their measurements. CNR is used to identify differences between tissues. Depending on the resolution of the CNR, the ratio between different tissue samples can be found. When CNR increases, the variability increases, but the difference between tissues is more greater. Functional signal-to-noise-ratio is the ratio between the intensity of a signal associated with changes in brain function and the variability in the data due to all sources of noise. CNR depends upon the intensity difference between voxels, whereas fSNR depends upon the intensity difference with a voxel, or group of voxels over time. fSNR is a main concern in fMRI studies because it shows the difference over time of a given region.

 

 

 

 

 

 

3.   Describe an image with large absolute differences between tissues but small CNR. 

When CNR is reduced, it becomes more difficult to distinguish different tissue types.  The voxels for each tissue types will be harder to distinguish from each other (gray matter can blur itself into white matter).  Furthermore, subcortical nuclei, especially the thalamus can be harder to distinguish when CNR is reduced.  An image with large absolute differences between tissues but small CNR could be one where there is a large difference in intensity values between tissues but also a large amount of noise.

 

 

 

 

 

 

 

4.   What causes thermal noise in a MRI scanner? How does thermal noise vary across the brain?

Thermal noise is the fluctuations in MR signal intensity over space or time that are caused by thermal motion of electrons within the sample or scanner hardware. The excitations of electrons that is the source of the MR signal causes the free electrons to collide with atoms, resulting in an exchange of energy. The higher the temperature of the system, the more frequent the collisions and the greater the distortion of the current signal. The thermal noise also increases linearly with the field strength of the MR magnet. Within voxels in the brain, thermal noise has little effect on the raw SNR (given that signal in such a voxel would be high compared to thermal noise).  The intensity of values of such voxels have a Gaussian (i.e., normal; see http://en.wikipedia.org/wiki/Gaussian_distribution) distribution over time.  Voxels outside or on the edge of the brain which may contain air however have little signal; for these voxels, thermal noise adds to the intensity of the voxels.  The intensity values of such voxels have a Rayleigh (i.e., positively skewed; see  http://en.wikipedia.org/wiki/Rayleigh_distribution) distribution rather than a Gaussian distribution.  Essentially, thermal noise has a more pronounced effect on regions around the edges of the brain (or near areas containing air).

 

 

 

 

 

 

5.   What is the difference between thermal noise and system noise? What are common causes of system noise?

 

 

Thermal and system noise are both fluctuations in the MR signal intensity over space or time.  However, their difference is in their cause: thermal noise is caused by the thermal motion of electrons within the sample or scanner hardware.  System noise is caused by imperfect functioning of the scanner hardware.  System noise is commonly caused by scanner drift, which results in the slow changes in voxel intensity over time.  Moreover, a common cause is change in the resonant frequency of hydrogen protons associated with subtle changes in the strength of the static field.  Problems with the radiofrequency coils can have several effects – inefficiency and intensity variation can happen if the frequency of the excitation pulse does not match the resonant frequency of the sample. 

 

 

 

 

 

 

 

6.   What is actually drifting in “scanner drift”?

Scanner drift is slow changes in voxel intensity over time. It is caused by the change in resonant frequency of hydrogen protons associated with subtle changes in the strength of the magnetic field. The magnet experiences minute drifts over time and these drifts affect the protons therefore creating a “scanner drift.”  What actually drifts is voxel intensity over time.

 

 

 

 

 

 

7.   What are common forms of physiological noise?

 

Physiological noise is commonly attributed to muscles contracting with each breath and heartbeat of the patient.  Also, blood pulses through arteries and veins in the subject.  The metabolic demands on neurons that drive chemical reactions needed to sustain life can create this physiological noise.  Also, the subject shifting position or swallowing can create this.  However, cardiac activity is the main form of physiological noise.

 

 

 

 

 

8.   What are some sources of behavioral or task-related variability in many fMRI experiments?

There are three main kinds of experimental designs: passive viewing, pressing a button in response to an auditory stimuli, and remembering a set of digits over a delay interval. In passive viewing, the arousal of the subject may vary, this variance in arousal causes the MR machine to register varying states of brain activity. In reaction time or response time conditions, there is always a intersubject (within the same subject) or intrasubject (over a group of subject) variability in these times.

 

 

 

 

 

 

9.   What is a “speed–accuracy tradeoff”?

 

 

Speed-accuracy tradeoff is the improvement in the speed of a response at the expense of accuracy.  However, it can be the opposite where the improvement in accuracy of a response is at the expense of speed within an experimental task.

 

 

 

 

 

 

 

10. What is “intersubject variability” in the hemodynamic response? How do researchers account for this variability?

Different brains have different types of responses. The duration, strength, and localization of a brain activation can vary across individuals. In order to make up for this flaw, the researchers have to average the responses of many individuals to come up with a estimate of what the mean hemodynamic response was. However, for some studies this averaging process can destroy some crucial data about the differences between different brain activation. These factors have to be taken into consideration when averaging across individuals.

 

 

 

 

11. What theoretical effect should field strength have upon raw SNR, and why?

 

With increasing field strength, an increasing proportion of spins will align parallel with the static field, and thus net magnetization will increase.  The fundamental rule relating field strength to theoretical signal is simple:  As static field strength increases linearly, raw signal increases quadratically (i.e. with the square of the field strength).  As raw SNR increases, so does the total signal recovered from each voxel.  This allows the image to be parceled into smaller voxels while maintaining sufficient SNR within each, improving spatial resolution.  An improvement in spatial resolution can greatly improve the functional resolution of an experiment.

 

 

 

 

 

 

 

12. What is the effect of field strength upon functional SNR, in practice?

As the field increases in strength, so does the SNR, however the physiological noise and the thermal variability also increase. The increase of fSNR is not linear, so the more the field is increased does not mean a greater fSNR will be elicited. Even though the fSNR may not increase indefinitely, increased field strength does increase the number of activated voxels because the more voxels will reach a threshold value and be registered by the equipment.

 

 

 

 

 

 

13. How do T₁ and T₂^* change with increasing field strength?

 

T1 increases with field strength, which could reduce the effective signal recovery at short TR values.  T2 decreases with field strength, which could reduce the time available to acquire a signal.

 

 

 

 

 

 

 

14. How does the TE needed for BOLD contrast change with field strength?

 

TE or echo time, is the amount of time between an excitation and data acquisition. TR (repetition time) is the amount of time between successive excitation phases. As the magnetic field increases, the amount of time available to detect a signal goes down. The TE, the time between excitation and acquisition, decreases, because this decreases, efficiency of signal recovery goes down.  In short, a higher magnetic field forces one to take readings at faster intervals, thus reducing accuracy.

 

 

 

 

 

 

15. How does the balance between thermal and physiological noise change with increasing field strength? What implications does this have for fMRI?

Thermal noise scales linearly with the field strength, so a 2.0-T scanner measures 2 times as much thermal noise as 1.5-T scanner.  When one divides the quadratic increase in signal by the linear increase in noise, find that the raw SNR only increases linearly with the field strength.  While thermal noise increases linearly with increasing field strength, physiological noise increases quadratically with the field strength.  So, as field strength increases from 1.5-T to 3.0-T, raw signal will quadruple, thermal noise will double, and physiological noise will quadruple.  Physiological noise may become dominant and the improvement of functional SNR with increasing field strength may be considerably less than linear.  This implies that increased functional SNR has an increased spatial extent of activation. 

 

 

 

 

 

 

 

16. At high field, what component of the vascular system would most contribute to the fMRI BOLD signal?

The small-vessel extravascular component increases with field strength faster than large vessel extrascular component. Looking at these differences helps to gauge spatial specificity, which is an effect of changes in the weighting of different vascular components.

 

 

 

 

 

 

 

 

 

17. What is signal averaging? How should functional SNR increase as one averages more and more data (e.g., has a larger sample size)?

 

Signal averaging is the combination of data from multiple instances of the same manipulation in order to improve functional SNR.  The basic assumption of signal averaging is that the signal of interest is identical over repeated stimulus presentations, while the noise is random.  With sufficient numbers of repetitions, the noise will tend to average out while the signal is preserved.  Even a very weak signal is easily detected when averaged over many repetitions.

 

 

 

 

18. How does signal averaging affect the spatial extent of activation? Why does spatial extent change with increased sample size?

The spatial extent is the number of active voxels within a cluster of activity. The spatial extent depends on two factors: statistical value and threshold. The statistical value changes as a function of SNR. fSNR increases with singal averaging, so the spatial extent of activation will also increase with singal averaging. This happens because activity in some of the subthreshold voxels becomes detectable.

 

 

 

19. What are the basic principles of fMRI power analyses? Why are power analyses important?

 

Power analyses estimate the likelihood of detecting a significant effect, if one truly exists, given the expected sizes of the effect and of the sample.  Power analyses are important because their goal is to determine the probability of detecting a real effect.