Acoustic radiation and scattering from cylindrical bodies and analysis of transducer arrays

New mathematical methods to analytically investigate linear acoustic radiation and scattering from cylindrical bodies and transducer arrays are presented. Three problems of interest involving cylinders in an infinite fluid are studied. In all the three problems, the Helmholtz equation is used to model propagation through the fluid and the beam patterns of arrays of transducers are studied. In the first problem, a method is presented to determine the omni-directional and directional far-field pressures radiated by a cylindrical transducer array in an infinite rigid cylindrical baffle. The solution to the Helmholtz equation and the displacement continuity condition at the interface between the array and the surrounding water are used to determine the pressure. The displacement of the surface of each transducer is in the direction of the normal to the array and is assumed to be uniform. Expressions are derived for the pressure radiated by a sector of the array vibrating in-phase, the entire array vibrating in-phase, and a sector of the array phase-shaded to simulate radiation from a rectangular piston. It is shown that the uniform displacement required for generating a source level of 220 dB ref. μPa @ 1m that is omni directional in the azimuthal plane is in the order of 1 micron for typical arrays. Numerical results are presented to show that there is only a small difference between the on-axis pressures radiated by phased cylindrical arrays and planar arrays. The problem is of interest because cylindrical arrays of projectors are often used to search for underwater objects. In the second problem, the errors, when using data-independent, classical, energy and split beam correlation methods, in finding the direction of arrival (DOA) of a plane acoustic wave, caused by the presence of a solid circular elastic cylindrical stiffener near a linear array of hydrophones, are investigated. Scattering from the effectively infinite cylinder is modeled using the exact axisymmetric equations of motion and the total pressures at the hydrophone locations are computed. The effect of the radius of the cylinder, a, the distance between the cylinder and the array, b, the number of hydrophones in the array, 2H, and the angle of incidence of the wave, α, on the error in finding the DOA are illustrated using numerical results. For an array that is about 30 times the wavelength and for small angles of incidence (α<10), the error in finding the DOA using the energy method is less than that using the split beam correlation method with beam steered to α; and in some cases, the error increases when b increases; and the errors in finding the DOA using the energy method and the split beam correlation method with beam steered to α vary approximately as a7 / 4 . The problem is of interest because elastic stiffeners – in nearly acoustically transparent sonar domes that are used to protect arrays of transducers – scatter waves that are incident on it and cause an error in the estimated direction of arrival of the wave. In the third problem, a high-frequency ray-acoustics method is presented and used to determine the interior pressure field when a plane wave is normally incident on a fluid cylinder embedded in another infinite fluid. The pressure field is determined by using geometrical and physical acoustics. The interior pressure is expressed as the sum of the pressures due to all rays that pass through a point. Numerical results are presented for ka = 20 to 100 where k is the acoustic wavenumber of the exterior fluid and a is the radius of the cylinder. The results are in good agreement with those obtained using field theory. The directional responses, to the plane wave, of sectors of a circular array of uniformly distributed hydrophones in the embedded cylinder are then computed. The sectors are used to simulate linear arrays with uniformly distributed normals by using delays. The directional responses are compared with the output from an array in an infinite homogenous fluid. These outputs are of interest as they are used to determine the direction of arrival of the plane wave. Numerical results are presented for a circular array with 32 hydrophones and 12 hydrophones in each sector. The problem is of interest because arrays of hydrophones are housed inside sonar domes and acoustic plane waves from distant sources are scattered by the dome filled with fresh water and cause deterioration in the performance of the array.

Adrenergic and muscarinic receptor subtypes functional regulation during diabetogenesis: Effect of curcumin and vitamin D3 pre-treatment

In the present study, the initial phase was directed to confirm the effects of curcumin and vitamin D3 in preventing or delaying diabetes onset by studying the blood glucose and insulin levels in the pre-treated and diabetic groups. Behavioural studies were conducted to evaluate the cognitive and motor function in experimental rats. The major focus of the study was to understand the cellular and neuronal mechanisms that ensure the prophylactic capability of curcumin and vitamin D3. To elucidate the mechanisms involved in conferring the antidiabetogenesis effect, we examined the DNA and protein profiles using radioactive incorporation studies for DNA synthesis, DNA methylation and protein synthesis. Furthermore the gene expression studies of Akt-1, Pax, Pdx-1, Neuro D1, insulin like growth factor-1 and NF-κB were done to monitor pancreatic beta cell proliferation and differentiation. The antioxidant and antiapoptotic actions of curcumin and vitamin D3 were examined by studying the expression of antioxidant enzymes - SOD and GPx, and apoptotic mediators like Bax, caspase 3, caspase 8 and TNF-α. In order to understand the signalling pathways involved in curcumin and vitamin D3 action, the second messengers, cAMP, cGMP and IP3 were studied along with the expression of vitamin D receptor in the pancreas. The neuronal regulation of pancreatic beta cell maintenance, proliferation and insulin release was studied by assessing the adrenergic and muscarinic receptor functional regulation in the pancreas, brain stem, hippocampus and hypothalamus. The receptor number and binding affinity of total muscarinic, muscarinic M1, muscarinic M3, total adrenergic, α adrenergic and β adrenergic receptor subtypes were studied in pancreas, brain stem and hippocampus of experimental rats. The mRNA expression of muscarinic and adrenergic receptor subtypes were determined using Real Time PCR. Immunohistochemistry studies using confocal microscope were carried out to confirm receptor density and gene expression results. Cell signalling alterations in the pancreas and brain regions associated with diabetogenesis and antidiabetogenesis were assessed by examining the gene expression profiles of vitamin D receptor, CREB, phospholipase C, insulin receptor and GLUT. This study will establish the anti-diabetogenesis activity of curcumin and vitamin D3 pre-treatment and will attempt to understand the cellular, molecular and neuronal control mechanism in the onset of diabetes.Administration of MLD-STZ to curcumin and vitamin D3 pre-treated rats induced only an incidental prediabetic condition. Curcumin and vitamin D3 pretreated groups injected with MLD-STZ exhibited improved circulating insulin levels and behavioural responses when compared to MLD-STZ induced diabetic group. Activation of beta cell compensatory response induces an increase in pancreatic insulin output and beta cell mass expansion in the pre-treated group. Cell signalling proteins that regulate pancreatic beta cell survival, insulin release, proliferation and differentiation showed a significant increase in curcumin and vitamin D3 pre-treated rats. Marked decline in α2 adrenergic receptor function in pancreas helps to relent sympathetic inhibition of insulin release. Neuronal stimulation of hyperglycemia induced beta cell compensatory response is mediated by escalated signalling through β adrenergic, muscarinic M1 and M3 receptors. Pre-treatment mediated functional regulation of adrenergic and cholinergic receptors, key cell signalling proteins and second messengers improves pancreatic glucose sensing, insulin gene expression, insulin secretion, cell survival and beta cell mass expansion in pancreas. Curcumin and vitamin D3 pre-treatment induced modulation of adrenergic and cholinergic signalling in brain stem, hippocampus and hypothalamus promotes insulin secretion, beta cell compensatory response, insulin sensitivity and energy balance to resist diabetogenesis. Pre-treatment improved second messenger levels and the gene expression of intracellular signalling molecules in brain stem, hippocampus and hypothalamus, to retain a functional neuronal response to hyperglycemia. Curcumin and vitamin D3 protect pancreas and brain regions from oxidative stress by their indigenous antioxidant properties and by their ability to stimulate cellular free radical defence system. The present study demonstrates the role of adrenergic and muscarinic receptor subtypes functional regulation in curcumin and vitamin D3 mediated anti-diabetogenesis. This will have immense clinical significance in developing effective strategies to delay or prevent the onset of diabetes.