The time-to-maximum of the tissue residue function (T(max)) perfusion index has proven very predictive of infarct growth in large clinical trials, yet its dependency on simple tracer delays remains unknown. Here, we determine the dependency of computed tomography (CT) perfusion (CTP) T(max) estimates on tracer delay using a range of deconvolution techniques and digital phantoms. Digital phantom data sets simulating the tracer delay were created from CTP data of six healthy individuals, in which time frames of the left cerebral hemisphere were shifted forward and backward by up to ±5 seconds. These phantoms were postprocessed with three common singular value decomposition (SVD) deconvolution algorithms-standard SVD (sSVD), block-circulant SVD (bSVD), and delay-corrected SVD (dSVD)-with an arterial input function (AIF) obtained from the right middle cerebral artery (MCA). The T(max) values of the left hemisphere were compared among different tracer delays and algorithms by a region of interest-based analysis. The T(max) values by sSVD were positively correlated with 'positive shifts' but unchanged with 'negative shifts,' those by bSVD had an excellent positive linear correlation with both positive and negative shifts, and those by dSVD were relatively constant, although slightly increased with the positive shifts. The T(max) is a parameter highly dependent on tracer delays and deconvolution algorithm.