Viability Thresholds of Ischemic Penumbra of Hyperacute Stroke Defined by Perfusion-Weighted MRI and Apparent Diffusion Coefficient

Røhl, Lisbeth; Østergaard, Leif; Simonsen, Claus Z; Vestergaard‐Poulsen, Peter; Andersen, Grethe; Sakoh, Masaharu; Bihan, Denis Le; Gyldensted, Carsten

doi:10.1161/01.str.32.5.1140

Cited by 212 publications

(151 citation statements)

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“…[4] and [5]), a value of p ϭ 2 was found to be the best: p ϭ 1 (i.e., "exclude" only one measurement) was not enough to avoid the oversmoothing of the initial part of the solution, while p Ն 3 was found to keep an undesirable level of oscillations. This behavior was observed for a typical (1.0 s), as well as for a much shorter (0.3 s) repetition time (TR), and for various SNR and MTT values (data not shown).…”

Section: Tikhonov Regularizationmentioning

confidence: 99%

“…However, L 1 was found to be inappropriate to regularize the dispersed R(t) models (Eqs. [4] and [5]): the initial part of these residue functions is considered as "unwanted" oscillations by L 1 , and the regularization tends to oversmooth this part of the curve, distorting the true shape (see Fig. 2, bottom graph).…”

Section: Tikhonov Regularizationmentioning

confidence: 99%

“…[2] and [3]) using the L 1 matrix, and the middle and bottom graphs display the results for the dispersed models (Eqs. [4] and [5]) using the L 1,mod matrix. Figure 5 shows the corresponding results using the conventional TSVD method.…”

Section: L-curvementioning

confidence: 99%

“…After an initial comparison between the solutions obtained with different-order difference operators (L i ) for the R lor (t) model (note that since the derivatives of an exponential function are proportional to the function, all of the L i matrices give similar results for the R exp (t) model), the first-order difference operator L 1 was chosen because it produced the closest solution to the simulated model (data not shown). However, L 1 was found to be inappropriate to regularize the dispersed R(t) models (Eqs.[4] and [5]): the initial part of these residue functions is considered as "unwanted" oscillations by L 1 , and the regularization tends to oversmooth this part of the curve, distorting the true shape (see Fig. 2, bottom graph).…”

mentioning

confidence: 99%

“…Although an alternative option might have been to replace I p by 0 p؋p (the p ϫ p matrix of zeros), this was found to lead to a wrong solution: the initial part of the solution would have no regularization at all and the large oscillations due to the smaller singular values would remain in this region. From a preliminary investigation of the effect of various values of p on the regularization of the dispersed residue models (Eqs.[4] and [5]), a value of p ϭ 2 was found to be the best: p ϭ 1 (i.e., "exclude" only one measurement) was not enough to avoid the oversmoothing of the initial part of the solution, while p Ն 3 was found to keep an undesirable level of oscillations. This behavior was observed for a typical (1.0 s), as well as for a much shorter (0.3 s) repetition time (TR), and for various SNR and MTT values (data not shown).…”

mentioning

confidence: 99%

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Quantification of bolus‐tracking MRI: Improved characterization of the tissue residue function using Tikhonov regularization

Calamante

Gadian

Connelly

2003

Magnetic Resonance in Med

122

129

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Quantification of cerebral blood flow (CBF) and the tissue residue function (R) using bolus-tracking MRI requires deconvolution of the arterial input function (AIF). Currently, the most commonly used deconvolution method is singular value decomposition (SVD), which has been shown to produce accurate estimations of CBF. However, this method introduces unwanted oscillations in the time course of R, and there are situations in which the actual shape is of interest (e.g., in calculating flow heterogeneity and assessing bolus dispersion). In such cases, the conventional SVD method may no longer be suitable, and an alternative approach may be required. This work describes the implementation of Tikhonov regularization with the L-curve criterion to quantify CBF and obtain a better characterization of R. The methodology is tested on simulated and patient data, and the results are compared to those found using the conventional SVD approach. Although both methods produce similar CBF values, the deconvolved R shape obtained using SVD is dominated by oscillations and fails to characterize the shape in the presence of dispersion. On the other hand, the use of the proposed regularization method improves the char- Key words: perfusion; dynamic susceptibility contrast MRI; deconvolution; singular value decomposition; arterial input function Bolus-tracking MRI, also known as dynamic susceptibility contrast MRI, is becoming a well-established technique for measuring cerebral blood flow (CBF) (1). The most important clinical application by far is in the investigation of cerebral ischemia. Although some limitations have been reported (2,3), this technique is playing an increasingly important role in the diagnosis, assessment, and management of acute stroke patients (4 -7).The fundamental equation for CBF quantification is (8):where C(t) is the tissue concentration time curve, C a (t) is the arterial input function (AIF; i.e., the concentration of contrast entering the tissue of interest at time t), R(t) is the tissue residue function (i.e., the fraction of contrast agent concentration at time t for the case of an ideal instantaneous bolus injected at t ϭ 0), and the symbol V indicates the convolution operation (1). Bolus-tracking MRI relies on the deconvolution of the AIF to obtain the product function CBF ⅐ R(t), and the calculation of CBF from the initial (or maximum) value of this function (8). Currently, the most common deconvolution method is singular value decomposition (SVD), which has been shown to produce fairly accurate estimations of CBF (8). However, this method introduces unwanted oscillations 1 in the shape of R(t) (9,10), and there are situations in which the actual shape of R(t)-not just its initial value-is of interest. For example, the determination of flow heterogeneity and oxygen delivery relies on characterization of the whole residue function (11). In addition, the presence of bolus dispersion has been shown to be a significant source of error in CBF quantification (11,12), and accurate determination of the sha...

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Section: Tikhonov Regularizationmentioning

confidence: 99%

Section: Tikhonov Regularizationmentioning

confidence: 99%