Neural substrates, experimental evidences and functional hypothesis of acupuncture mechanisms.

OBJECTIVES: Although acupuncture therapy has demonstrated itself to be effective in several clinical areas, the underlying mechanisms of acupuncture in general and the analgesic effect in particular are, however, still not clearly delineated. We, therefore, have studied acupuncture analgesic effect through fMRI and proposed a hypothesis, based on the obtained result, which will enlighten the central role of the brain in acupuncture therapy. METHODS: The proposed model, termed as a broad sense hypothalamus-pituitary-adrenal (BS-HPA) axis, was based on our observed neuroimaging results. The model incorporates the stress-induced HPA axis model together with neuro-immune interaction including the cholinergic anti-inflammatory model. RESULTS: The obtained results coupled with accumulating evidence suggest that the central nervous system is essential for the processing of these effects via its modulation of the autonomic nervous system, neuroimmune system and hormonal regulation. CONCLUSIONS: Based on our fMRI study, it appears that understanding the effects of acupuncture within a neuroscience-based framework is vital. Further, we have proposed the broad sense-HPA axis hypothesis which incorporates the experimental results.

A surprising Radon transform result and its application to motion detection.

An elliptical region of the plane supports a positive-valued function whose Radon transform depends only on the slope of the integrating line. Any two parallel lines that intersect the ellipse generate equal line integrals of the function. We prove that this peculiar property is unique to the ellipse; no other convex, compact region of the plane supports a nonzero-valued function whose Radon transform depends only on slope. We motivate this problem by considering the detection of a constant-velocity moving object in a sequence of images. In the presence of additive, white, Gaussian noise. The intensity distribution of the object is known, but the velocity is only assumed to lie in some known set, for example, an ellipse or a rectangle. The object is to find a space-time linear filter, operating on the image sequence, whose minimum output signal-to-noise ratio (SNR) for any velocity in the set is maximized. For an ellipse (and its special cases, the disk and the line-segment) the special Radon transform property of the ellipse enables us to obtain a closed-form, analytical solution for the minimax filter, which significantly outperforms the conventional three-dimensional (3-D) matched filter. This analytical solution also suggests a constrained minimax filter for other velocity sets, obtainable in closed form, whose SNR can be very close to the minimax SNR.

Limited Angle Reconstruction in Tomography via Squashing.

We give a new algorithm for reconstructing a density f in the plane from its projections along those lines making an angle greater than a fixed delta > 0 with the x axis. Of course, the performance of the algorithm depends on delta and on the smoothness of f, but it appears to give a practical and simple solution to the problem whenever one exists. The basic idea, which seems to be new, is to make an affine (squashing) scale change of f to g for which the projections are then known at n equally spaced angles, so that we know how to find g, and then we obtain f from g by inverting the scale change.

Maximum likelihood reconstruction for emission tomography.

Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknown emission density lambda = lambda(x, y, z) generates, and is to be reconstructed from, the number of counts n(*)(d) in each of D detector units d. Within the model, we give an algorithm for determining an estimate lambdainsertion mark of lambda which maximizes the probability p(n(*)|lambda) of observing the actual detector count data n(*) over all possible densities lambda. Let independent Poisson variables n(b) with unknown means lambda(b), b = 1, ..., B represent the number of unobserved emissions in each of B boxes (pixels) partitioning an object containing an emitter. Suppose each emission in box b is detected in detector unit d with probability p(b, d), d = 1, ..., D with p(b,d) a one-step transition matrix, assumed known. We observe the total number n(*) = n(*)(d) of emissions in each detector unit d and want to estimate the unknown lambda = lambda(b), b = 1, ..., B. For each lambda, the observed data n(*) has probability or likelihood p(n(*)|lambda). The EM algorithm of mathematical statistics starts with an initial estimate lambda(0) and gives the following simple iterative procedure for obtaining a new estimate lambdainsertion mark(new), from an old estimate lambdainsertion mark(old), to obtain lambdainsertion mark(k), k = 1, 2, ..., lambdainsertion mark(new)(b)= lambdainsertion mark(old)(b)Sum of (n(*)p(b,d) from d=1 to D/Sum of lambdainsertion mark()old(b('))p(b('),d) from b(')=1 to B), b=1,...B.

Computerized tomography and nuclear magnetic resonance.

In 1917 Radon gave a simple formula for reconstructing a function (f(x,y,z) from its integrals over all planes in three-dimensions. We give a simple algorithm for numerical quadrature of his formula and suggest its application to imaging the nuclear magnetic resonance spin density of an object.

Two-dimensional remote air-pollution monitoring via tomography.

We propose to apply computerized tomography to measure a two-dimensional pollutant-concentration map over an area that may contain several potential sources of pollution. A tunable-laser source at the center of the area generates secondary or virtual light sources around the perimeter of the area that play the role of x rays in conventional computerized tomography of the human body.