Theoretical Basis of Hemodynamic MR Imaging Techniques to Measure Cerebral Blood Volume, Cerebral Blood Flow, and Permeability

Effects of bolus widening (“dispersion”) in the AIF on the tissue-concentration-versus-time curve. A, Residue function, which represents the probability of the tracer remaining in the voxel at time t. Note that this is a monotonically decreasing function, with a value of 1 at time t = 0. The residue function shown here represents a well-mixed single compartment with an MTT of 4 seconds, similar to that seen in brain. For the remainder of the examples, CBF is taken to be 50 mL/100 mL of brain per minute, again typical for brain. The area under the AIF is normalized to 1 arbitrary unit. B, Tissue concentration curve (solid line) for a “perfect bolus” AIF (dotted line), which arrives at t = 0. The tissue concentration curve is just the residue function multiplied by CBF. Note that CBF is equal to the first point of the tissue concentration curve, which is also the peak concentration. C, AIF is a 2-second bolus top hat function corresponding to “plug flow”: note the increase in the arrival time of peak contrast and the decrease in peak concentration, a consequence of the convolution of the AIF and the residue function. No longer is CBF equal to the first time point of the tissue curve or the peak concentration. D, AIF is a gaussian curve with full width at half maximum of 2 seconds, a more realistic model of a bolus that has widened before reaching the tissue. Note that for both C and D, deconvolution techniques are necessary to determine CBF and that the first moment of the tissue concentration curve is not equal to the MTT. Sec indicates seconds.

In ASL, upstream blood protons are either unperturbed (control) or inverted (label) on alternate applications of the pulse sequence, here demonstrated by the up arrows and down arrows, respectively. The signal intensity of the labeled images is approximately 1–2% lower than that of the control images due to the extraction of the negatively magnetized inverted spins into the tissue when they reach the capillary bed. Subtracting label images from control images creates a difference image proportional to CBF. Typically many such image pairs must be subtracted to achieve adequate SNR; the image of CBF in a healthy volunteer shown above was acquired in 5 minutes at 3T.

CBF errors due to prolonged arrival time in ischemic stroke with ASL. A, A contrast-enhanced MR angiogram shows right internal carotid artery occlusion. B, Diffusion-weighted image demonstrates abnormality of the right putamen, caudate, and a small area in the right frontal operculum. C, A PASL image of CBF demonstrates punctate high signal intensity (arrows) surrounding an area of apparent low flow in the right parietal lobe. The high signal intensity is probably due to delayed arrival of the label via collateral flow which is still within large vessels rather than in the parenchyma. The low measured CBF centrally is due to decay of the label before it enters the tissue. Normal flow was seen in this region on Xe-CT (images not shown). D, Follow-up CT 2 days later demonstrates infarction of the right caudate and putamen (arrow) but preserved gray-white contrast in the right parietal region that demonstrates low signal intensity on the ASL CBF map. CBF underestimation in the setting of collateral flow is a fundamental difficulty with the use of standard ASL in this patient population.

A basic model of the imaging voxel for permeability studies. The plasma volume, v_p, is small compared with the EES (shown in gray) and the intracellular space, from which contrast is excluded. Observed relaxivity changes are a weighted average of the plasma and EES contrast concentration. The large black arrows signify isodirectional flux of contrast between these 2 spaces, with a rate constant equal to K_trans. This flux is essentially zero in the presence of an intact BBB but is nonzero in many pathophysiologic conditions.