Spectral characterization of ciliary beating: variations of frequency with time

1985 ◽  
Vol 249 (1) ◽  
pp. C160-C165 ◽  
Author(s):  
D. Eshel ◽  
Y. Grossman ◽  
Z. Priel

Ciliary beating frequency in tissue culture from frog palate and isolated lung was optically examined using instrumentation that was adjusted to measure a fraction of the surface area of a single ciliary cell. Consecutive 1-s segments of the analogue signal were fast Fourier transformed (FFT) to obtain a power spectrum. At room temperature, these power spectra changed over time from 1 s to the next. Each spectrum contained several dominant frequencies of similar intensities. Cooling the preparation resulted in a single-peak spectrum that was constant over time. A mathematical model is proposed to simulate these findings. The results and the mathematical model support the hypothesis that ciliary beating frequency fluctuates over short periods of time.

Viruses ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 547
Author(s):  
Veronika Bernhauerová ◽  
Veronica V. Rezelj ◽  
Marco Vignuzzi

Mathematical models of in vitro viral kinetics help us understand and quantify the main determinants underlying the virus–host cell interactions. We aimed to provide a numerical characterization of the Zika virus (ZIKV) in vitro infection kinetics, an arthropod-borne emerging virus that has gained public recognition due to its association with microcephaly in newborns. The mathematical model of in vitro viral infection typically assumes that degradation of extracellular infectious virus proceeds in an exponential manner, that is, each viral particle has the same probability of losing infectivity at any given time. We incubated ZIKV stock in the cell culture media and sampled with high frequency for quantification over the course of 96 h. The data showed a delay in the virus degradation in the first 24 h followed by a decline, which could not be captured by the model with exponentially distributed decay time of infectious virus. Thus, we proposed a model, in which inactivation of infectious ZIKV is gamma distributed and fit the model to the temporal measurements of infectious virus remaining in the media. The model was able to reproduce the data well and yielded the decay time of infectious ZIKV to be 40 h. We studied the in vitro ZIKV infection kinetics by conducting cell infection at two distinct multiplicity of infection and measuring viral loads over time. We fit the mathematical model of in vitro viral infection with gamma distributed degradation time of infectious virus to the viral growth data and identified the timespans and rates involved within the ZIKV-host cell interplay. Our mathematical analysis combined with the data provides a well-described example of non-exponential viral decay dynamics and presents numerical characterization of in vitro infection with ZIKV.


2021 ◽  
pp. 1-47
Author(s):  
Mohamed Raafat ◽  
Amr Baz

Abstract A theoretical and experimental investigation of a new class of a tensegrity-based structural damper is presented. The damper is not only capable of attenuating undesirable structural vibrations, as all conventional dampers, but also capable of completely blocking the transmission of vibration over specific frequency bands by virtue of its periodicity. Such dual functionality distinguishes the tensegrity damper over its counterparts of existing structural dampers. Particular emphasis is placed here in presenting the concept and developing the mathematical model of the dynamics of a unit cell the damper. The model is then coupled with a Floquet-Bloch analysis in order to identify the bandgap characteristics of the damper. The predictions of the mathematical model are validated experimentally using a prototype of the damper which is built using 3D printing. A comprehensive material characterization of the damper is performed followed by a detailed extraction of the static and dynamic behavior of the damper in order to validate the theoretical predictions. Close agreement is observed between theory and experiments. The developed theoretical and experimental techniques provide invaluable means for the design of this new class of dampers particularly for critical structural applications.


2014 ◽  
Vol 915-916 ◽  
pp. 277-280
Author(s):  
Yao Chen Shi ◽  
Zhan Guo Li ◽  
Xiu Guang Yang

The vibration of belt affected the transmission stability of automotive synchronous belt. The mathematical model of longitudinal vibration was established through analyzing the longitudinal vibration of automotive synchronous belt. Developed the vibration dynamic measurement device, aiming at RU style arc teethed synchronous belt transmission process, measured the variety of amplitude over time at the middle of the belt span obtained the rules of amplitude and frequency change along with the rotation speed. It is of certain importance to improving the transmission stability of arc teethed synchronous belt.


2006 ◽  
Vol 522-523 ◽  
pp. 93-102 ◽  
Author(s):  
C. Anghel ◽  
Gunnar Hultquist ◽  
Qian Dong ◽  
J. Rundgren ◽  
Isao Saeki ◽  
...  

A better understanding of the transport properties of gases in oxides is certainly very important in many applications. In the case of metals, a general protection measure against corrosion implies formation of a dense metal oxide scale. The scale should act as a barrier against gas transport and consequently it needs to be gas-tight. This is often assumed but rarely, if ever, confirmed. Hence there is a need for characterization of micro- and/or meso- pores formed especially during the early oxidation stage of metallic materials. This paper presents a novel and relatively straightforward method for characterization of gas release from an oxide previously equilibrated in a controlled atmosphere. The geometry of the sample is approximated to be a plate. The plate can be self-supporting or constitute a scale on a substrate. A mathematical model for calculation of diffusivity and gas content is given for this geometry. A desorption experiment, involving a mass spectrometer placed in ultra high vacuum, can be used to determine diffusivity and amount of gas released with aid of the mathematical model. The method is validated in measurements of diffusivity and solubility of He in quartz and applied in characterization of two Zroxides and one Fe oxide. From the outgassed amounts of water and nitrogen the H2O/N2 molar ratio can be used to estimate an effective pore size in oxides.


2021 ◽  
Vol 2131 (3) ◽  
pp. 032034
Author(s):  
O Lebedev ◽  
I Lipatov

Abstract Determination of the ship’s course width necessary for the ships safe operation is an urgent task due to the increase in the modern ships’ dimensions. The existing methods for assessing the fairway are calculated with a full re-positioning of the propulsion-rudder complex, according to the maximum drift angle. The vessel movement is considered to be steady, that is, the speed, the drift angles do not depend on time. The relevance of this study is associated with the assessment of determining the width of the fairway at any time interval. This is due to the fact that when passing the river sections, the vessels perform maneuvering with the rudder gear shifted for short periods of time and not at the maximum shift angle. Determination of the parameters of the ship’s movement over time when the navigator manipulates the ship’s controls (control of the rudder device, changing the parameters of the main engines) can be determined by the mathematical model of the ship’s movement. This article discusses the issues of creating a model that adequately describe the processes of vessel movement, including in the conditions of vessel movement along a limited ship’s course. The adequacy of the model was verified using the data of field and model experiments. According to the compiled mathematical model, the calculations were made for various projects of dry cargo ships.


Blood ◽  
2015 ◽  
Vol 126 (23) ◽  
pp. 130-130 ◽  
Author(s):  
David M. Kurtz ◽  
Florian Scherer ◽  
Aaron M. Newman ◽  
Alexander F. Lovejoy ◽  
Daniel M. Klass ◽  
...  

Abstract Background: The prognosis for diffuse large B-cell lymphoma (DLBCL) patients who fail initial therapy remains poor. Current prognostic methods to identify patients destined for failure employ baseline molecular profiles or imaging data at fixed milestones, thus sub-optimally capturing functional response dynamics. Noninvasive detection of tumor-specific DNA sequences in the plasma, or circulating tumor DNA (ctDNA), provides a window of opportunity to observe these changes early during therapy. We sought to relate early ctDNA kinetics during therapy to tumor volume, therapeutic responses, and ultimate clinical outcomes. Methods: Using CAPP-Seq, a next-generation sequencing platform for detection of ctDNA (Newman Nature Medicine 2014), we prospectively profiled patients with DLBCL receiving combination immunochemotherapy at Stanford University. Tumor samples were used to define tumor specific somatic alterations, which were then monitored in plasma. We examined two methods of assessing ctDNA change over time: a simple heuristic model (assessing the change in ctDNA concentration from cycle 1 to cycle 2), and a biologically based mathematical model of ctDNA dynamics to predict tumor volume and patient outcomes. Results: We sequenced tumor and plasma samples (n=135) from ten patients receiving Rituximab-containing regimens. Plasma samples were collected prior to, during, and immediately after chemotherapy, with a median of 7 samples per patient during the first therapy cycle. Across patients, ctDNA concentrations varied over a 6-log range (Figure 1). The change in ctDNA concentration between cycle 1 and cycle 2 generally tracked with FDG PET/CT response - patients achieving a PR or CR had an average decrease of 2.9±0.8 logs in ctDNA concentration, compared to an increase of 0.3±0.8 logs for those with SD or PD (p<0.001). However, this metric failed to capture some patients who ultimately relapsed after radiographic remission. We therefore developed a multi-compartmental ordinary-differential equation (ODE) model of tumor dynamics capturing tumor volume, ctDNA, and the effect of chemotherapy. We performed nonlinear regression to fit data to this model using serial ctDNA measurements from individual patients, thereby creating continuous, patient-specific models of both ctDNA and tumor volume (Figure 1a-b). This mathematical model significantly fit ctDNA measurements and predicted tumor volumes across patients and samples (Figure 1c). Using ctDNA measurements from the first 2 cycles of therapy, this model accurately predicted clinical outcomes for all ten patients, including relapse after radiographic remission. An additional cohort of patients will be presented at this meeting. Conclusions: Given its high specificity and large dynamic range, ctDNA provides an opportunity to monitor the dynamics of therapeutic response in patients with DLBCL. Methods capturing these dynamics correlate with radiographic response. Given the complexity of tumor dynamics, heuristic models of ctDNA may less faithfully capture ultimate clinical outcomes. Personalized mathematical models of ctDNA can potentially reflect tumor dynamics and predict clinical outcomes for individual patients. Figure 1. Personalized tumor modeling from ctDNA tumor dynamics. a) An example of a model of ctDNA fit to observed data for a single patient (DLBCL010). b) The corresponding tumor volume prediction over time for patient DLBCL010. c) Summary of the mathematical model across ten patients, demonstrating the fit between measured data and the model. Figure 1. Personalized tumor modeling from ctDNA tumor dynamics. a) An example of a model of ctDNA fit to observed data for a single patient (DLBCL010). b) The corresponding tumor volume prediction over time for patient DLBCL010. c) Summary of the mathematical model across ten patients, demonstrating the fit between measured data and the model. Disclosures Newman: Roche: Consultancy. Klass:Roche: Employment. Gambhir:CellSight: Consultancy. Diehn:Roche: Consultancy. Alizadeh:Genentech: Consultancy; Roche: Consultancy; Celgene: Consultancy.


Author(s):  
A. I. Malyshev

This paper reports the estimation of the predictability of seismicity and large earthquakes in Kamchatka as inferred from data in the Kamchatka regional catalog for 1962–2014. The mathematical model uses a second-order nonlinear differential equation, while the optimization algorithm and the estimates of predictability are the author’s own. The estimates show a high predictability of seismicity; the extrema of prediction nonlinearity typical of large earthquakes usually occur simultaneously with similar extrema of seismicity as a whole. Overall, 220 large (K ≥ 13.3) Kamchatka earthquakes were analyzed to find that foreshock predictability was available for 200 earthquakes (~30000 determinations) and aftershock predictability for 215 earthquakes (~300000 determinations). The predictability related to large earthquakes began to be seen and was rapidly increasing at intermediate (7.5–30 km) radii of hypocenter samples. The prediction distances over time were some tens and hundreds of days for foreshock predictability and some hundreds and thousands of days for aftershock predictability. These results demonstrate very good promise for the approximation extrapolation approach to the prediction of both large earthquakes themselves and of subsequent aftershock decay of seismic activity.


Author(s):  
A. I. Malyshev

This paper reports the estimation of the predictability of seismicity and large earthquakes in Kamchatka as inferred from data in the Kamchatka regional catalog for 1962–2014. The mathematical model uses a second-order nonlinear differential equation, while the optimization algorithm and the estimates of predictability are the author’s own. The estimates show a high predictability of seismicity; the extrema of prediction nonlinearity typical of large earthquakes usually occur simultaneously with similar extrema of seismicity as a whole. Overall, 220 large (K ≥ 13.3) Kamchatka earthquakes were analyzed to find that foreshock predictability was available for 200 earthquakes (~30000 determinations) and aftershock predictability for 215 earthquakes (~300000 determinations). The predictability related to large earthquakes began to be seen and was rapidly increasing at intermediate (7.5–30 km) radii of hypocenter samples. The prediction distances over time were some tens and hundreds of days for foreshock predictability and some hundreds and thousands of days for aftershock predictability. These results demonstrate very good promise for the approximation extrapolation approach to the prediction of both large earthquakes themselves and of subsequent aftershock decay of seismic activity.


Author(s):  
S Cafferty ◽  
K Worden ◽  
G Tomlinson

In a previous paper [see reference (4)], it was shown that the restoring force surface (RFS) procedure provides a direct and clear method for characterizing the dynamic properties of automotive shock absorbers or dampers. The procedure was based on repetitive harmonic testing of the absorbers at fixed frequency but with varying amplitude. The current paper describes how the surfaces can be obtained from tests using random excitation. The merits and demerits are discussed relative to the harmonic test procedure. It is shown that the random excitation approach offers a useful alternative but produces force surfaces which are corrupted by small stochastic components; an explanation of the distortion is given in terms of the mathematical model proposed in the previous paper. The implications for identification of shock absorbers are discussed


1991 ◽  
Vol 37 (2) ◽  
pp. 265-269
Author(s):  
James P AuBuchon

Abstract Proficiency testing (PT) programs may fail to establish a range of acceptable performance in a challenge when an insufficient number of participants use a particular method. In this study I analyzed a mathematical approach to establish acceptable performance in alanine aminotransferase (ALT; EC 2.6.1.2) PT challenges. This approach was derived from the mathematical model used in establishing a nationwide ALT standardization system for blood-collection facilities in 1988. A ratio of results was derived between each method in the PT program and an arbitrarily chosen "standard" method. The intent of this approach was to transform a target value for a challenge as determined in the "standard" method to units applicable to methods utilized less often. However, the high degree of variability over time in the ratios for some methods precluded general application of this approach. Therefore, although this simple mathematical method was successful in implementing an ALT standardization system across different methods, a derivation of this approach did not afford comparison of results in PT challenges.


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