Frequency gradients

In general the velocity is inversely proportional to the phase gradient. For, if there is no frequency gradient, then 

The experiment considered here would be rather difficult to arrange but Winfree (1974c) reports conditions under which phase gradients, in the absence of frequency gradients, naturally arise. 

For example, consider Fig. 2. The period T is a monotonic increasing function of height, z in fact, T(z) = 1+z. At t = 0 the entire cylinder turns blue, that is, phase is initially zero throughout the cylinder. 

At t = 1 a blue band appears at the bottom and moves upward at velocity v = 1 

Simultaneously and independently Theones (1973) published the same explanation of frequency gradient waves. Unfortunately, he erred in claiming to explain trigger waves (target patterns and spirals) in terms of frequency gradients without diffusive coupling between spatially neighboring points. 

---

Fig. 7.2.17 Flow imaging by phase encoding. A bipolar flow-encoding gradient is applied for slice selection to image through-plane flow v (x, y). Both phase and frequency gradients for space encoding are flow compensated.

As for the 2D NOESY data described above, spectra are vulnerable to interference from undesirable zero-quantum contributions between coupled spins this is apparent, for example, in trace (c) of Fig. 8.42 between H4 and H5. This can be especially problematic when shorter mixing times are employed, as in the generation of NOE build-up curves [35], and again the inclusion of the swept-frequency/gradient zero-quantum filter should prove beneficial. The complete selective ID NOESY sequence incorporating this and employing the optimised DPFGSE selection procedure is presented in Fig. 8.43, and an illustration of the improvements provided by the filter may be seen in Fig. 8.44 where the removal of unwelcome anti-phase dispersive contributions between coupled spins is apparent in (b). 

Alvarez and Mahoney [1922] reported the presence of a rhythmic electrical activity (which they called action currents ) in the smooth muscle layers of the stomach, small intestine, and colon. Their data was acquired from cat (stomach and small intestine), dog (stomach, small intestine, and colon), and rabbit (small intestine and colon). They also demonstrated the existence of frequency gradients in excised stomach and bowel. Puestow [1933] confirmed the presence of a rhythmic electrical activity (which he called waves of altered electrical potential ) and a frequency gradient in isolated canine... 

Diamant, N.E. andBortoff, A. 1969a. Nature of the intestinal slow wave frequency gradient. Am. J. Physiol, 216 301 307. 

Fig. 1. Curves of constant phase, 0(z,t) = 2ffn, for a cylinder, 0 < z < 1, with an initial phase gradient but no frequency gradient.

The EGA in stomach, small intestine, and colon behaves like the outputs of a population of coupled nonlinear oscillators. The populations in the stomach and the proximal small intestine are entrained, whereas those in the distal small intestine and colon are not entrained. There are distinct intrinsic frequency gradients in the stomach and small intestine but their profile in the colon is ambiguous. 

Centre field (T) Centre frequency (MHz) Bore (mm) STRAFI (V Fringe frequency Gradient (MHz) (Tm- ) ... 

Parisien, M., and L. Sirois 2003. Distribution and dynamics of tree species across a fire frequency gradient in the James Bay region of Quebec. Can. J. For. Res. 33 243-256. 

---