Contents lists available at ScienceDirect Magnetic Resonance Imaging journal homepage: www.elsevier.com/locate/mri Original contribution Estimation of physiological sources of nonlinearity in blood oxygenation level-dependent contrast signals Daehun Kang a,b , Yul-Wan Sung a, ⁎ , Satoshi Shioiri b a Kansei Fukushi Research Institute, Tohoku Fukushi University, Sendai, Japan b Graduate School of Information Sciences and Research Institute of Electrical Communication, Tohoku University, Sendai, Japan ARTICLE INFO Keywords: BOLD signal Multi-echo Gradient-echo Nonlinearity TE-dependence Chemical exchange ABSTRACT Blood oxygenation level-dependent (BOLD) contrast appears through a variation in the transverse relaxation rate of magnetic resonance signals induced by neurovascular coupling and is known to have nonlinear characteristics along echo time (TE) due to the intra-vasculature. However, the physiological causes of this nonlinearity are unclear. We attempted to estimate the physiological information related to the nonlinearity of BOLD signals by using a two-compartment model. For this purpose, we used a multi-echo gradient-echo echo-planar imaging sequence and developed a computational method to estimate the physiological information from the TE-de- pendent BOLD signals. The results showed that the average chemical exchange time in the intra-vasculature varied during stimulation, which might be the essential source of the nonlinearity. 1. Introduction Functional magnetic resonance imaging (fMRI) with blood oxyge- nation level-dependent (BOLD) contrast has been widely used for noninvasive measurement of brain activation [1–4]. Brain activation is measured as a fractional change in image intensity caused by a varia- tion in the transverse relaxation rate of MRI signals. The transverse relaxation rate is affected by the concentration of deoxygenated he- moglobin (deoxy-Hb) in blood that is modulated by physiological fac- tors, such as the cerebral blood volume (CBV), cerebral metabolic rate of oxygen, and cerebral blood flow. The fractional change shown by BOLD signal tends to increase in proportion to echo time (TE). The actual BOLD signals related to brain activation have often shown some nonlinear aspects with change in TE [5–7]. Additionally, it has been reported that the amount of the nonlinearity varies during brain acti- vation [8] or with different types of visual stimuli [9]. The relationship between TE-dependent BOLD signals and a change in the transverse relaxation rate has been investigated by using a model that assumes a single compartment. To estimate the first-order ap- proximation of the change in the transverse relaxation rate, a single- compartment model has been used previously; in this model, the re- lationship with BOLD signals is determined by the equation, ΔS/ S ≅ −ΔR 2 ∙ TE for spin-echo (SE) sequences or ΔS/S ≅ −ΔR 2 * ∙ TE for gradient-echo (GE) sequences, where ΔS/S is the fractional change in image intensity, TE is the echo time, and ΔR 2 (*) is the change in the transverse relaxation rate [10,11]. If the changes in T 1 (longitudinal relaxation rate), inflow, and motion are considered, the relationship is expanded to ΔS/S ≅ ΔS 0 /S 0 −ΔR 2 * ∙ TE where ΔS 0 /S 0 is the fractional change in initial signal intensity when TE = 0 [11]. However, a simple linear approximation based on the single-compartment model with only one transverse relaxation rate cannot accommodate the nonlinearity in TE-dependent BOLD signals. In a two-compartment model, the BOLD signal literally consists of two distinct types of transverse relaxation rates originated from in- travascular (IV) and extravascular (EV) spaces [12]. The two-com- partment model previously has been applied to quantitatively predict the contributions of IV and/or EV to the BOLD signal [7,13]. In the previous experimental studies on the TE-dependence of ΔS/S, a linear dependence on TE was found in brain parenchyma [5,7,14–18]. It has been demonstrated that BOLD signals from the EV space are almost linearly dependent on TE within the commonly used TE ranges [19]. In contrast to the EV space, some studies have shown that the nonlinearity was attributable to an effect of deoxy-Hb in the IV space, where a fast chemical exchange between plasma and deoxy-Hb induced accelerated dephasing of nearby water protons and hence, shortened T 2 and T 2 * [5,20,21]. Thus, the nonlinearity of BOLD signals could possibly be used to separate IV and EV components by estimating values of para- meters based on the model. A phenomenon of chemical exchange is often pH-dependent. Thus, the pH dependence of exchangeable protons at the protein surface has been demonstrated [22], and chemical exchange saturation transfer MRI has been used for pH imaging [23,24]. In recent fMRI studies, https://doi.org/10.1016/j.mri.2017.10.017 Received 9 December 2016; Received in revised form 13 October 2017; Accepted 31 October 2017 ⁎ Corresponding author at: Kansei Fukushi Research Institute, 6-149-1, Kunimigaoka, Aoba-ku, Sendai, Miyagi, Japan. E-mail address: sung@tfu-mail.tfu.ac.jp (Y.-W. Sung). Magnetic Resonance Imaging 46 (2018) 121–129 0730-725X/ © 2017 Elsevier Inc. All rights reserved. T