Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces

This paper deals with the existence of ω-periodic solutions for nth-order ordinary differential equation involving fixed delay in Banach space E. Lnu(t)=f(t,u(t),u(t−τ)),t∈R, where Lnu(t):=u(n)(t)+∑i=0n−1aiu(i)(t), ai∈R, i=0,1,⋯,n−1, are constants, f(t,x,y):R×E×E⟶E is continuous and ω-periodic with respect to t, τ>0. By applying the approach of upper and lower solutions and the monotone iterative technique, some existence and uniqueness theorems are proved under essential conditions.

The feasibility of low iodine dynamic CT angiography with test bolus for evaluation of lower extremity peripheral artery disease

Objective This study aims to determine if low iodine dynamic computed tomography angiography performed after a fixed delay or test bolus acquisition demonstrates high concordance with clinical computed tomography angiography (using a routine amount of iodinated contrast) to display lower extremity peripheral arterial disease. Methods After informed consent, low iodine dynamic computed tomography angiography examination (using either a fixed delay or test bolus) using 50 ml of iodine contrast media was performed. A subsequent clinical computed tomography angiography using standard iodine dose (115 or 145 ml) served as the reference standard. A vascular radiologist reviewed dynamic and clinical computed tomography angiography images to categorize the lumen into “not opacified”, “<50% stenosis”, “ 50 ̶70% stenosis”, “>70% stenosis”, and “occluded” for seven arterial segments in each lower extremity. Concordance between low iodine dynamic computed tomography angiography and the routine iodine reference standard was calculated. The clinical utility of 4D volume-rendered images was also evaluated. Results Sixty-eight patients (average age 66.1 ± 12.3 years, male; female = 49: 19) were enrolled, with 34 patients each undergoing low iodine dynamic computed tomography angiography using fixed delay and test bolus techniques, respectively. One patient assigned to the test bolus group did not undergo low iodine computed tomography angiography due to unavailable delayed time. The fixed delay was 13 s, with test bolus acquisition resulting in a mean variable delay prior to image acquisition of 19.5 s (range; 8–32 s). Run-off to the ankle was observed using low iodine dynamic computed tomography angiography following fixed delay and test bolus acquisition in 76.4% (26/34) and 100% (33/33) of patients, respectively ( p = 0.005). Considering extremities with run-off to the ankle and without severe artifact, the concordance rate between low iodine dynamic computed tomography angiography and the routine iodine reference standard was 86.8% (310/357) using fixed delay and 97.9% (425/434) using test bolus ( p < 0.001). 4D volume-rendered images using fixed delay and test bolus demonstrated asymmetric flow in 57.7% (15/26) and 58.1% (18/31) ( p = 0.978) of patients, and collateral blood flow in 11.5% (3/26) and 22.6% (7/31) of patients ( p = 0.319), respectively. Conclusion Low iodine dynamic computed tomography angiography with test bolus acquisition has a high concordance with routine peripheral computed tomography angiography performed with standard iodine dose, resulting in improved run-off to the ankle compared to dynamic computed tomography angiography performed after a fixed delay. This method is useful for minimizing iodine dose in patients at risk for contrast-induced nephropathy. 4D volume-rendered computed tomography angiography images provide useful dynamic information.

Dynamically changing neuronal activity supporting working memory for predictable and unpredictable durations

Diverse neural processes have been proposed as the neural basis of working memory. To investigate whether the medial prefrontal cortex (mPFC) relies on different neural processes to mediate working memory depending on the predictability of delay duration, we examined mPFC neural activity in mice performing a delayed response task with fixed (4 s) or random (between 1–7 s) delay durations. mPFC neural activity was strongly influenced by the predictability of delay duration. Nevertheless, mPFC neurons seldom showed persistent activity spanning the entire delay period and instead showed dynamically-changing delay-period activity under both the fixed-delay and random-delay conditions. mPFC neurons conveyed higher working memory information under the random-delay than fixed-delay conditions, possibly due to a higher demand for stable working memory maintenance. Our results suggest that the rodent mPFC may rely on dynamically-changing neuronal activity to maintain working memory regardless of the predictability of delay duration.

Reward timing and its expression by inhibitory interneurons in the mouse primary visual cortex

Primary sensory cortex has historically been studied as a low-level feature detector, but has more recently been implicated in many higher-level cognitive functions. For instance, after an animal learns that a light predicts water at a fixed delay, neurons in primary visual cortex (V1) can produce “reward timing activity” (i.e., spike modulation of various forms that relate the interval between the visual stimulus and expected reward). The manner by which V1 produces these representations is unknown. Here, we combine behavior, in vivo electrophysiology, and optogenetics to investigate the characteristics of and circuit mechanisms underlying V1 reward timing in the head-fixed mouse. We find that reward timing activity is present in mouse V1, that inhibitory interneurons participate in reward timing, and that these representations are consistent with a theorized network architecture. Together, these results deepen our understanding of V1 reward timing and the manner by which it is produced.