Central projections and connections of lumbar primary afferent fibers in adult rats:effectively revealed using Texas red-dextran amine tracing

Signals from lumbar primary afferent fibers are important for modulating locomotion of the hind-limbs.However,silver impregnation techniques,autoradiography,wheat germ agglutinin-horseradish peroxidase and cholera toxin B subunit-horseradish peroxidase cannot image the central projections and connections of the dorsal root in detail.Thus,we injected 3-k Da Texas red-dextran amine into the proximal trunks of L4 dorsal roots in adult rats.Confocal microscopy results revealed that numerous labeled arborizations and varicosities extended to the dorsal horn from T12–S4,to Clarke＇s column from T10–L2,and to the ventral horn from L1–5.The labeled varicosities at the L4 cord level were very dense,particularly in laminae I–Ⅲ,and the density decreased gradually in more rostral and caudal segments.In addition,they were predominately distributed in laminae I–IV,moderately in laminae V–VⅡ and sparsely in laminae VⅢ–X.Furthermore,direct contacts of lumbar afferent fibers with propriospinal neurons were widespread in gray matter.In conclusion,the projection and connection patterns of L4 afferents were illustrated in detail by Texas red-dextran amine-dorsal root tracing.

New Constructions in Axonometric System Fundamentals

In this communication we start both from a trirectangular trihedral defined by the three coordinate planes and a fourth plane, called the chart or projection, which contains the vertex of the trihedral above. Later we define the main related views or trihedral views as those produced by the tilt of the three coordinate planes to the outside of their trihedral on the chart plane. For each projection plane there are some unique main related views, regardless of the projection direction. In turn, from the trihedral views we can obtain the axonometric perspective from which they come. These properties can simplify some graphic constructions of the axonometric system, for example, determine the projections of the axes from the main related views or determine the axonometric scales from the axes. It is considered that this new definition of related views allows a simplification as to the understanding of the representation systems and it is intended to be suitable for teaching purposes and programming.

The Closed Orbits of a Class of Cubic Vector Fields in R^(3)

In this paper,we investigate the isolated closed orbits of two types of cubic vector fields in R^3 by using the idea of central projection transformation,which sets up a bridge connecting the vector field X(x)in R^3 with the planar vector fields.We have proved that the cubic vector field in R^3 can have two isolated closed orbits or one closed orbit on the invariant cone.As an application of this result,we have shown that a class of 3-dimensional cubic system has at least 10 isolated closed orbits located on 5 invariant cones,and another type of 3-dimensional cubic system has at least 26 isolated closed orbits located on 13 invariant cones or 26 invariant cones.