A simple intuitive method for seeking intersections of hyperbolas for acoustic positioning biotelemetry.

We proposed a simple hyperbolic positioning method that does not require solving simultaneous quadratic equations. Moreover, we introduced the mathematical concept of a "pencil" into analytical calculations in the hyperbolic positioning method for a better understanding. In many recent studies using positioning biotelemetry, the specific procedure for intersection calculation of hyperbolas has rarely been described. This might be one of two major obstacles, with the other being clock synchronisation among receivers, for positioning biotelemetry users, including potential users. We focus only on the intersection calculation in this paper. Therefore, we propose a novel method and introduce the mathematical concept into analytical calculations. The computing performances of the novel method, an analytical method applying the concept of a pencil, and an approximating method using the Newton-Raphson method were compared regarding positioning correctness, accuracy, and calculation speed. In the novel method, hyperbolas were represented using the parameter θ, which was treated as a discrete variant. The finer the tick-width of the parameter θ, the more accurate was its positioning, but it took slightly longer to calculate. By setting the tick-width to 0.01°, a simulated trajectory was correctly and accurately localised, as in the analytical method which always correctly returned the accurate solution. The approximating method has a major limitation concerning correctness. It returns a single solution regardless of two intersections of hyperbolas; however, the positioning is accurate when the hyperbolas intersect at a single point. This study approached one major difficulty in positioning biotelemetry and will help biotelemetry users overcome this drawback with a simple and intuitive understanding of hyperbolic positioning.

Tubular cell loss in early inv/nphp2 mutant kidneys represents a possible homeostatic mechanism in cortical tubular formation.

Inversion of embryonic turning (inv) cystic mice develop multiple renal cysts and are a model for type II nephronophthisis (NPHP2). The defect of planar cell polarity (PCP) by oriented cell division was proposed as the underlying cellular phenotype, while abnormal cell proliferation and apoptosis occur in some polycystic kidney disease models. However, how these cystogenic phenotypes are linked and what is most critical for cystogenesis remain largely unknown. In particular, in early cortical cytogenesis in the inv mutant cystic model, it remains uncertain whether the increased proliferation index results from changes in cell cycle length or cell fate determination. To address tubular cell kinetics, doubling time and total number of tubular cells, as well as amount of genomic DNA (gDNA), were measured in mutant and normal control kidneys. Despite a significantly higher bromodeoxyuridine (BrdU)-proliferation index in the mutant, total tubular cell number and doubling time were unaffected. Unexpectedly, the mutant had tubular cell loss, characterized by a temporal decrease in tubular cells incorporating 5-ethynyl-2´-deoxyuridine (EdU) and significantly increased nuclear debris. Based on current data we established a new multi-population shift model in postnatal renal development, indicating that a few restricted tubular cell populations contribute to cortical tubular formation. As in the inv mutant phenotype, the model simulation revealed a large population of tubular cells with rapid cell cycling and tubular cell loss. The proposed cellular kinetics suggest not only the underlying mechanism of the inv mutant phenotype but also a possible renal homeostatic mechanism for tubule formation.