Weierstrass's criterion and compact solitary waves

Weierstrass's theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to identify some differential equations for which compact and even semicompact traveling solitary waves exist. In the framework of continuum mechanics, these differential equations correspond to bulk shear waves for a special class of constitutive laws.Comment: 4 page

On the Mathematical and Geometrical Structure of the Determining Equations for Shear Waves in Nonlinear Isotropic Incompressible Elastodynamics

Using the theory of $1+1$ hyperbolic systems we put in perspective the mathematical and geometrical structure of the celebrated circularly polarized waves solutions for isotropic hyperelastic materials determined by Carroll in Acta Mechanica 3 (1967) 167--181. We show that a natural generalization of this class of solutions yields an infinite family of \emph{linear} solutions for the equations of isotropic elastodynamics. Moreover, we determine a huge class of hyperbolic partial differential equations having the same property of the shear wave system. Restricting the attention to the usual first order asymptotic approximation of the equations determining transverse waves we provide the complete integration of this system using generalized symmetries.Comment: 19 page

Measurement of thermal properties of biological tissues and tissue-mimicking phantom with a dual-needle sensor

This work presents the measurement of the thermal properties of ex vivo biological tissues (i.e., porcine liver and kidney tissues) as a function of temperature, along with the thermal characterization of a tissue-mimicking agar-based phantom. The evaluation of the thermal properties was performed by the dual needle technique, adopting a sensor equipped with two needles, capable to deliver thermal energy to the biomaterial and monitor the related tissue thermal behavior. Measurements of thermal conductivity, thermal diffusivity, and volumetric heat capacity were conducted at room temperature and at temperatures relevant from a biological point of view, namely, body temperature and temperatures of similar to 60 degrees C- 65 degrees C, which are typically correlated to instantaneous thermal damage in tissue. Thermal properties of biological tissue remained rather constant at the investigated temperatures: average values of thermal conductivity ranged from 0.515 W/(m.K) to 0.575 W/(m.K), thermal diffusivity ranged from 0.144 mm(2)/s to 0.163 mm2/s, whilst the average volumetric heat capacity was from 3.48 MJ/(m(3).K) to 3.72 MJ/(m(3).K). Furthermore, the thermal properties of the realized agar phantom were comparable to the ones of biological tissues. The results of this study provide valuable information for the characterization of porcine liver and kidney tissues, in terms of their thermal properties, to be used in predictive mathematical models of thermal therapies and validate the usage of agar phantoms as tissue-mimicking materials

Characterization of Susceptibility Artifacts in MR-thermometry PRFS-based during Laser Interstitial Thermal Therapy

Magnetic Resonance Thermometry (MRT) is demonstrating huge abilities to guide laser interstitial thermal therapy (LITT) in several organs, such as the brain. Among the methods to perform MRT, Proton Resonance Frequency (PRF) shift holds significant benefits, like tissue independence. Despite its potential, PRF shift-based MRT holds significant challenges affecting the accuracy of reconstructed temperature maps. In particular, susceptibility artifacts due to gas-bubble formation are an important source of error in temperature maps in MRT-guided LITT. This work presents the characterization of the susceptibility artifacts in MRT-guided LITT and the measurement of its size. LITT was performed in gelatin-based phantoms, at 5 W, 2 W, 1 W, and 0.5 W under MRI guidance with a 1.5 T clinical MRI scanner. Temperature images were obtained with a 3D EPI (Echo planar imaging) prototype sequence. Areas of temperature errors were defined as zones of negative temperature variation <-2 degrees C. Moreover, we have analyzed the artifact shape in sagittal, axial and coronal planes. The analysis demonstrates a double-lobe shape for the susceptibility artifact mainly distributed in the sagittal plane. Also, the higher laser power caused a bigger artifact area. Temperature errors of similar to 80 degrees C proved the necessity to avoid susceptibility artifact generation during MRT-guided LITT. The analysis of the influence of the laser power on the artifact has suggested that using low laser power (0.5 W) helps avoid this measurement error

Experimental Assessment of a Variable Orifice Flowmeter for Respiratory Monitoring

Accurate measurement of gas exchanges is essential in mechanical ventilation and in respiratory monitoring. Among the large number of commercial flowmeters, only few kinds of sensors are used in these fields. Among them, variable orifice meters (VOMs) show some valuable characteristics, such as linearity, good dynamic response, and low cost. This paper presents the characterization of a commercial VOM intended for application in respiratory monitoring. Firstly, two nominally identical VOMs were calibrated within ±10 L·min−1, to assess their metrological properties. Furthermore, experiments were performed by humidifying the air, to evaluate the influence of vapor condensation on sensor’s performances. The condensation influence was investigated during two long lasting trials (i.e., 4 hours) by delivering 4 L·min−1 and 8 L·min−1. Data show that the two VOMs’ responses are linear and their response is comparable (sensitivity difference of 1.4%, RMSE of 1.50 Pa); their discrimination threshold is <0.5 L·min−1, and the settling time is about 66 ms. The condensation within the VOM causes a negligible change in sensor sensitivity and a very slight deterioration of precision. The good static and dynamic properties and the low influence of condensation on sensor’s response make this VOM suitable for applications in respiratory function monitoring

Weak Transversality and Partially Invariant Solutions

New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.Comment: 23 pages, preprint CRM-284

Smart textile for respiratory monitoring and thoraco-abdominal motion pattern evaluation

The use of wearable systems for monitoring vital parameters has gained wide popularity in several medical fields. The focus of the present study is the experimental assessment of a smart textile based on 12 fiber Bragg grating sensors for breathing monitoring and thoraco‐abdominal motion pattern analysis. The feasibility of the smart textile for monitoring several temporal respiratory parameters (ie, breath‐by‐breath respiratory period, breathing frequency, duration of inspiratory and expiratory phases), volume variations of the whole chest wall and of its compartments is performed on 8 healthy male volunteers. Values gathered by the textile are compared to the data obtained by a motion analysis system, used as the reference instrument. Good agreement between the 2 systems on both respiratory period (bias of 0.01 seconds), breathing frequency (bias of −0.02 breaths/min) and tidal volume (bias of 0.09 L) values is demonstrated. Smart textile shows good performance in the monitoring of thoraco‐abdominal pattern and its variation, as well

Equivalence of conservation laws and equivalence of potential systems

We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are considered as examples. Using reducibility of them to the one-dimensional linear heat equation, we construct complete hierarchies of local and potential conservation laws for them and describe, in some sense, all their potential symmetries. Known results on the subject are interpreted in the proposed framework. This paper is an extended comment on the paper of J.-q. Mei and H.-q. Zhang [Internat. J. Theoret. Phys., 2006, in press].Comment: 10 page

Smart Textile Based on Fiber Bragg Grating Sensors for Respiratory Monitoring: Design and Preliminary Trials.

Continuous respiratory monitoring is important to assess adequate ventilation. We present a fiber optic-based smart textile for respiratory monitoring able to work during Magnetic Resonance (MR) examinations. The system is based on the conversion of chest wall movements into strain of two fiber Bragg grating (FBG) sensors, placed on the upper thorax (UT). FBGs are glued on the textile by an adhesive silicon rubber. To increase the system sensitivity, the FBGs positioning was led by preliminary experiments performed using an optoelectronic system: FBGs placed on the chest surface experienced the largest strain during breathing. System performances, in terms of respiratory period (TR), duration of inspiratory (TI) and expiratory (TE) phases, as well as left and right UT volumes, were assessed on four healthy volunteers. The comparison of results obtained by the proposed system and an optoelectronic plethysmography highlights the high accuracy in the estimation of TR, TI, and TE: Bland-Altman analysis shows mean of difference values lower than 0.045 s, 0.33 s, and 0.35 s for TR, TI, and TE, respectively. The mean difference of UT volumes between the two systems is about 8.3%. The promising results foster further development of the system to allow routine use during MR examinations.Continuous respiratory monitoring is important to assess adequate ventilation. We present a fiber optic-based smart textile for respiratory monitoring able to work during Magnetic Resonance (MR) examinations. The system is based on the conversion of chest wall movements into strain of two fiber Bragg grating (FBG) sensors, placed on the upper thorax (UT). FBGs are glued on the textile by an adhesive silicon rubber. To increase the system sensitivity, the FBGs positioning was led by preliminary experiments performed using an optoelectronic system: FBGs placed on the chest surface experienced the largest strain during breathing. System performances, in terms of respiratory period (TR), duration of inspiratory (TI) and expiratory (TE) phases, as well as left and right UT volumes, were assessed on four healthy volunteers. The comparison of results obtained by the proposed system and an optoelectronic plethysmography highlights the high accuracy in the estimation of TR, TI, and TE: Bland-Altman analysis shows mean of difference values lower than 0.045 s, 0.33 s, and 0.35 s for TR, TI, and TE, respectively. The mean difference of UT volumes between the two systems is about 8.3%. The promising results foster further development of the system to allow routine use during MR examinations