DWI b-Value

What is meant by the b-value? 
How do I pick it?   

The b-value is a factor that reflects the strength and timing of the gradients used to generate diffusion-weighted images. The higher the b-value, the stronger the diffusion effects. Specifically, if So is the MR signal at baseline and D is the diffusion coefficient, the signal (S) after the diffusion gradients have been applied is given by

S = S_oe^−bD

The term e^−bD thus behaves very much like the T2-weighting term e^−TE/T2 found in many other pulse sequences. The value of b is selected by the operator prior to imaging. This choice controls the degree of observed diffusion-weighting similar to the way choosing TE affects T2-weighting. Diffusion may thus be thought of as another relaxation mechanism in addition to T1 and T2. In pulse sequences without extra diffusion gradients, this relaxation mechanism is relatively unimportant, affecting the final signal by no more than 5%. When diffusion gradients are applied, however, the effects of diffusion are significantly amplified and become the dominant mechanism of tissue contrast.

In a prior Q&A we showed that because diffusion is the flux of particles across a surface in a period of time, the units of D are of the form [area/time]. So that exp(−bD) will be dimensionless, the units for b should be the inverse of D. In other words, b should be expressed as [time/area]. Typical b-values available on modern MRI scanners range from 0 to about 4000 s/mm².

The term "b-value" derives from the landmark 1965 paper by Stejskal and Tanner in which they described their pulsed gradient diffusion method. This technique still forms the basis for most modern DWI pulse sequences and consists of two strong gradient pulses of magnitude (G) and duration (δ), separated by time interval (Δ). The formula for b, specific to this particular implementation only, is shown in the diagram right. 

Stejskal-Tanner pulsed gradient diffusion method.

b = γ² G² δ² (Δ−δ/3)

The b-value depends on the strength, duration, and spacing of these pulsed gradients.  A larger b-value is achieved with increasing the gradient amplitude and duration and by widening the interval between gradient pulses.

The "optimal" choice of b-value is not clearly defined and depends upon field strength, number of signals averaged, anatomical features, and predicted pathology. Three brain images using b-values of 0, 1000, and 3000 s/mm² below show progressively more diffusion weighting (as evidenced by the brighter corticospinal tracts) but also more noise. Mechanical vibration artifacts may also be a problem as b-values are increased.  As a practical matter, most routine clinical DWI currently use b-values between 0 and 1000, with slightly lower values being used outside the central nervous system. 

Brain DWI images using 3 different b-values (0, 1000, and 3000 s/mm²)

The brains of neonates and young infants have much higher water content than adults with T2- and ADC-values 25-40% longer. In these patients the b-value is often made shorter, in the range of 600-700 s/mm².  A useful rule of thumb is to pick the b-value so that (b × ADC) ≈ 1.

Advanced Discussion (show/hide)»

Although the historical Stejskal-Tanner equation for b is given above and found in most textbooks, this particular implementation is seldom used in modern clinical or experimental systems. Rather than pure rectangular pulses, either sinusoidal or trapezoidal pulses are more frequently employed. For sinusoidal pulses the equation becomes b = 4γ²G²δ²(Δ−δ/4)/π². If trapezoidal pulses with rise times ξ are used, then b = γ²G²[δ²(Δ−δ/3) + ξ³/30 −δξ²/6].

Diffusion schemes other than the pulsed gradient method have also been studied, with the calculation of the b-value depending on the details of the gradient scheme used. For example, if a single long diffusion gradient G is applied during the time TE, then b = γ²G²TE³/12. If a fast spin echo technique with n echoes is used, then b = γ²G²TE³/12n².

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References
     Burdette JH, Durden DD, Elster AD, Yen YF. High b-value diffusion-weighted MRI of normal brain. J Comput Assist Tomogr 2001; 25:515-519.
     Kingsley PB, Monahan WG. Selection of the optimum b factor for diffusion-weighted 
magnetic resonance imaging assessment of ischemic stroke. Mag Reson Med 2004; 51:996-1001.
     Stejskal EO, Tanner JE. Spin diffusion measurements: spin echoes in the presence of
time-dependent field gradient. J Chem Phys 1965; 42(1):288-292

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Related Questions
     How do you make a DW image?
     In body imaging a starting b-value of 50 (s/mm²) instead of b=0 is often used. Why is this? 

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