Optimal financial and ordering decisions of a firm with insurance contract

This paper examines the impact of a bank’s risk limit on the financial and ordering decisions of a capital-constrained firm with insurance contract. All our major results can be computed via explicit expressions. It is shown that the bank will control its risk to be below the risk limit through setting a loan limit and the firm can make the loan limit increase by buying a deductible insurance policy. It is also shown that the repayment demand level needed to avoid bankruptcy will not be affected by the insurance policy. We derive the firm’s optimal ordering quantity and insurance coverage level under a downside risk measurement and a variance risk measurement separately. It is shown that the firm should pay more attention to whether to buy insurance or not under the downside risk measurement and how much insurance coverage to buy under the variance risk measurement. Under the downside risk measurement, once the firm decides to buy insurance, the optimal coverage level is independent of the bank’s risk limit. We also show that the insurance contract has a more obvious effect on the profit increases when the selling price is high or the bank’s risk limit is low. First published online: 18 Jun 201

Imaging the Mechanics and Electromechanics of the Heart

Abstract-The heart is a mechanical pump that is electrically driven. We have previously shown that the contractility of the cardiac muscle can reliably be used in order to assess the extent of ischemia using myocardial elastography. Myocardial elastography estimates displacement and strain during the natural contraction of the myocardium using signal processing techniques on echocardiograms in order to assess the change in mechanical properties as a result of disease. In this paper, we showed that elastographic techniques can be used to estimate and image both the mechanics and electromechanics of normal and pathological hearts in vivo. In order to image the mechanics throughout the entire cardiac cycle, the minimum frame rate was determined to be on the order of 150 fps in a long-axis view and 300 fps in a short-axis view. The incremental and cumulative displacement and strains were measured and imaged for the characterization of normal function and differentiation from infracted myocardium. In order to image the electromechanical function, the incremental displacement was imaged in consecutive cardiac cycles during end-systole in both dogs and humans. The contraction wave velocity in normal dogs was found to be twice higher than in normal humans and twice lower than in ischemic dogs. In conclusion, we have demonstrated that elastographic techniques can be used to detect and quantify the mechanics and electromechanics of the myocardium in vivo. Ongoing investigations entail assessment of myocardial elastography in characterizing and quantifying ischemia and infarction in vivo

In vivo characterization of the aortic wall stress–strain relationship

a b s t r a c t Arterial stiffness has been shown to be a good indicator of arterial wall disease. However, a single parameter is insufficient to describe the complex stress-strain relationship of a multi-component, non-linear tissue such as the aorta. We therefore propose a new approach to measure the stress-strain relationship locally in vivo noninvasively, and present a clinically relevant parameter describing the mechanical interaction between aortic wall constituents. The slope change of the circumferential stress-strain curve was hypothesized to be related to the contribution of elastin and collagen, and was defined as the transition strain (e T h ). A two-parallel spring model was employed and three Young's moduli were accordingly evaluated, i.e., corresponding to the: elastic lamellae (E 1 ), elastin-collagen fibers (E 2 ) and collagen fibers (E 3 ). Our study was performed on normal and Angiotensin II (AngII)-treated mouse abdominal aortas using the aortic pressure after catheterization and the local aortic wall diameters change from a cross-correlation technique on the radio frequency (RF) ultrasound signal at 30 MHz and frame rate of 8 kHz. Using our technique, the transition strain and three Young's moduli in both normal and pathological aortas were mapped in 2D. The slope change of the circumferential stress-strain curve was first observed in vivo under physiologic conditions. The transition strain was found at a lower strain level in the AngII-treated case, i.e., 0.029 ± 0.006 for the normal and 0.012 ± 0.004 for the AngII-treated aortas. E 1 , E 2 and E 3 were equal to 69.7 ± 18.6, 214.5 ± 65.8 and 144.8 ± 55.2 kPa for the normal aortas, and 222.1 ± 114.8, 775.0 ± 586.4 and 552.9 ± 519.1 kPa for the AngII-treated aortas, respectively. This is because of the alteration of structures and content of the wall constituents, the degradation of elastic lamella and collagen formation due to AngII treatment. While such values illustrate the alteration of structure and content of the wall constituents related to AngII treatment, limitations regarding physical assumptions (isotropic, linear elastic) should be kept in mind. The transition strain, however, was shown to be a pressure independent parameter that can be clinically relevant and noninvasively measured using ultrasound-based motion estimation techniques. In conclusion, our novel methodology can assess the stress-strain relationship of the aortic wall locally in vivo and quantify important parameters for the detection and characterization of vascular disease