Academic literature on the topic 'Four step technique to be free from addiction'

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Journal articles on the topic "Four step technique to be free from addiction"

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Sebold, Miriam, Daniel J. Schad, Stephan Nebe, Maria Garbusow, Elisabeth Jünger, Nils B. Kroemer, Norbert Kathmann, et al. "Don't Think, Just Feel the Music: Individuals with Strong Pavlovian-to-Instrumental Transfer Effects Rely Less on Model-based Reinforcement Learning." Journal of Cognitive Neuroscience 28, no. 7 (July 2016): 985–95. http://dx.doi.org/10.1162/jocn_a_00945.

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Behavioral choice can be characterized along two axes. One axis distinguishes reflexive, model-free systems that slowly accumulate values through experience and a model-based system that uses knowledge to reason prospectively. The second axis distinguishes Pavlovian valuation of stimuli from instrumental valuation of actions or stimulus–action pairs. This results in four values and many possible interactions between them, with important consequences for accounts of individual variation. We here explored whether individual variation along one axis was related to individual variation along the other. Specifically, we asked whether individuals' balance between model-based and model-free learning was related to their tendency to show Pavlovian interferences with instrumental decisions. In two independent samples with a total of 243 participants, Pavlovian–instrumental transfer effects were negatively correlated with the strength of model-based reasoning in a two-step task. This suggests a potential common underlying substrate predisposing individuals to both have strong Pavlovian interference and be less model-based and provides a framework within which to interpret the observation of both effects in addiction.
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Shams, Mudassir, Naila Rafiq, Babar Ahmad, and Nazir Ahmad Mir. "Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications." Journal of Mathematics 2021 (January 2, 2021): 1–10. http://dx.doi.org/10.1155/2021/6643514.

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We introduce here a new two-step derivate-free inverse simultaneous iterative method for estimating all roots of nonlinear equation. It is proved that convergence order of the newly constructed method is four. Lower bound of the convergence order is determined using Mathematica and verified with theoretical local convergence order of the method introduced. Some nonlinear models which are taken from physical and engineering sciences as numerical test examples to demonstrate the performance and efficiency of the newly constructed modified inverse simultaneous methods as compared to classical methods existing in literature are presented. Dynamical planes and residual graphs are drawn using MATLAB to elaborate efficiency, robustness, and authentication in its domain.
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Begum, Arifa, AKM Asaduzzaman, Md Humayun Kabir Talukder, Md Shakil Hossan, and Syeda Mahmuda Akhter. "Extracurricular Activities Influencing Academic Performance of Undergraduate Medical Students of Bangladesh: Teachers’ and Students’ Views." Bangladesh Journal of Medical Education 11, no. 1 (September 17, 2020): 32–42. http://dx.doi.org/10.3329/bjme.v11i1.49241.

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This descriptive cross sectional study was conducted to identify the teachers’ & students’ views according to extracurricular activities influencing academic performance of undergraduate medical students. The study period was July 2017 to June 2018.The study was carried out among four phases of undergraduate medical students & teachers of basic science, para clinical & clinical subjects of four (04) government & four (04) non-government selected medical colleges of Dhaka & outside Dhaka. Medical colleges were selected purposively & convenience sampling technique was adopted for data collection. A self-administered semi-structured questionnaire using five points Likert scale were administered on 58 teachers & 1020 students to collect data & an interview schedule was used to conduct in-depth interviews with 15 medical teachers. Study revealed that according to views of the medical students, factors like drug addiction 922(90.6%) & student politics 835(82.0%) were negatively influencing academic performance of undergraduate medical students. On the other hand, factors like indoor-outdoor games 791(77.7%), cultural activities 611(60.0%) & social activities 658(64.7%) were positively influencing on their academic performance. Findings of the students’ views were consistent with the teachers’ views. In-depth interview of the teachers revealed that students should take part in extra-curricular activities alongside their study. But it should be in a balanced way so that they do not hamper their study. Teachers should encourage students to participate in extra-curricular activities. Study recommended that medical campus should be kept free from the unhealthy student politics. Study also recommended to prevent drug addiction, the parents should be aware & the college authority should have adequate monitoring in the student hostels & should strictly implement any measure if required. Bangladesh Journal of Medical Education Vol.11(1) 2020: 32-42
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Kovalnogov, Vladislav N., Ruslan V. Fedorov, Tamara V. Karpukhina, Theodore E. Simos, and Charalampos Tsitouras. "Runge–Kutta Pairs of Orders 5(4) Trained to Best Address Keplerian Type Orbits." Mathematics 9, no. 19 (September 27, 2021): 2400. http://dx.doi.org/10.3390/math9192400.

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The derivation of Runge–Kutta pairs of orders five and four that effectively uses six stages per step is considered. The coefficients provided by such a method are 27 and have to satisfy a system of 25 nonlinear equations. Traditionally, various solutions have been tried. Each of these solutions makes use of some simplified assumptions and offers different families of methods. Here, we make use of the most celebrated family to appear in the literature, where we may use as the last stage the first function evaluation from the next step (FSAL property). The family under consideration has the advantage of being solved explicitly. Actually, we arrive at a subsystem where all the coefficients are found with respect to five free parameters. These free parameters are adjusted (trained) in order to deliver a pair that outperforms other similar pairs of orders 5(4) in Keplerian type orbits, e.g., Kepler, perturbed Kepler, Arenstorf orbit or Pleiades. The training uses differential evolution technique. The finally proposed pair has a remarkable performance and offers on average more than a digit of accuracy in a variety of orbits.
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Haque, MS, and K. Hattori. "Detection of viruses of Bangladeshi and Japanese garlic and their elimination through root meristem culture." Progressive Agriculture 28, no. 2 (August 9, 2017): 55–63. http://dx.doi.org/10.3329/pa.v28i2.33465.

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A number of viruses cause considerable yield loss and quality deterioration in garlic. Root meristems of virus infected plants are known to be free from detectable viruses. This potentiality could be exploited to obtain virus free clones at a high frequency by culturing excised root meristems in vitro. We have developed efficient methods of direct and somatic embryo derived shoot regeneration from root meristems of garlic. The objectives of this work were to detect viruses infecting Bangladeshi and Japanese garlic clones and find an easy and efficient method of eliminating the viruses for the improvement of both yield and quality of garlic. At first, we confirmed the presence of detectable viruses in three Bangladeshi and one Japanese clones. The clones were infected with four different types of viruses: Garlic viruses (GarVs), Onion yellow dwarf virus (OYDV), Leek yellow stripe virus (LYSV), and Garlic common latent virus (GCLV). To eliminate those viruses, as per our previous method, root meristems were cultured on MS medium supplemented with 1.0 µM NAA and 10.0 µM BA. Shoot primordia developed from the cultured explants within 1 month. The regenerated individual shoot buds (2-5 mm) were separated from the mother explants and transferred to growth regulators free medium. RT-PCR confirmed that the viruses present in the mother garlic plants were absent in the shoots found after two-step culture. The regenerated shoots were rooted on growth regulator free medium and transferred to pots. Results indicated that the plants remained free from LYSV. Virus elimination through root meristem culture emerged as an efficient novel technique for the eradication of multiple viruses as confirmed by RT-PCR in this study. This technique has the potential for the production and supply of virus free propagules (plants/bulblets) for the yield and quality improvement of garlic.Progressive Agriculture 28 (2): 55-63, 2017
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Kovalnogov, Vladislav N., Ruslan V. Fedorov, Tamara V. Karpukhina, Theodore E. Simos, and Charalampos Tsitouras. "Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions." Mathematics 9, no. 21 (October 29, 2021): 2756. http://dx.doi.org/10.3390/math9212756.

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Numerov-type methods using four stages per step and sharing sixth algebraic order are considered. The coefficients of such methods are depended on two free parameters. For addressing problems with oscillatory solutions, we traditionally try to satisfy some specific properties such as reduce the phase-lag error, extend the interval of periodicity or even nullify the amplification. All of these latter properties come from a test problem that poses as a solution to an ideal trigonometric orbit. Here, we propose the training of the coefficients of the selected family of methods in a wide set of relevant problems. After performing this training using the differential evolution technique, we arrive at a certain method that outperforms the other ones from this family in an even wider set of oscillatory problems.
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Lee, Won-Chul, Jong-Yeon Shin, Chang Woo Kim, Minsuk Kwon, Sangmoon Lee, Erin Connolly-Strong, Brian Baek-Lok Oh, and Young Seok Ju. "Advancing cancer MRD monitoring through tumor whole-genome informed, duplex ctDNA sequencing." Journal of Clinical Oncology 42, no. 16_suppl (June 1, 2024): e15044-e15044. http://dx.doi.org/10.1200/jco.2024.42.16_suppl.e15044.

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e15044 Background: Circulating tumor DNA (ctDNA), a cell-free DNA (cfDNA) present in the plasma of cancer patients, originates from cancer cells and serves as a crucial biomarker during cancer treatment. Despite its importance, the current limit of detection (LoD) of conventional ctDNA assays is suboptimal (0.01%; 10-4) for detecting ctDNA from microscopic residual and recurrent cancer tissues. To address this, we integrated two cutting-edge techniques: whole-genome sequencing (WGS) of primary cancer tissue (a mutation capture step) and duplex DNA sequencing-based cfDNA sequencing (mutation recapture steps). Methods: Thirteen colorectal cancer patients participated in this study. Primary tumor tissues and matched normal blood tissues were collected for WGS in the mutation capture step, while plasma samples for cfDNA sequencing in the mutation recapture steps were obtained just prior to colorectal cancer surgery and 1-month post-surgery follow-up. Tumor DNA and germline DNA were analyzed using CancerVision, a CLIA-certified clinical-grade cancer WGS platform, in the mutation capture step. In the mutation recapture steps, somatically acquired mutations from the previous step were tracked in cfDNA samples using the Concatenating Original Duplex for Error Correction (CODEC) technique, a duplex DNA sequencing technique that examines both Watson and Crick strands of double-stranded DNA molecules to discern true mutations from sequencing noise. Results: The median WGS depth of tumor and germline tissues was 40x and 20x, respectively. The mean depth of cfDNA WGS with CODEC was 25x, with a median duplex sequencing rate of 70%. Overall, 4,828-301,434 somatic base substitutions (SBSs) per sample were discovered in the capture step. Four of the thirteen tumors exhibited hypermutator characteristics with microsatellite instability features. The CODEC technique demonstrated excellent capability in tracing cancer-specific mutations in cfDNA sequencing with a technical sequencing error rate of 4 x 10-7, defining the maximum technical LoD, which is 250-fold lower errors than conventional sequencing. In our sample cohort, tumor fractions in cfDNA sequencing were robustly estimated from 0.001% (10-5), below the LoD of conventional MRD methods. Conclusions: Our integration of tumor-WGS-informed duplex cfDNA sequencing methods significantly enhances the sensitivity of sequencing-based MRD assays, achieving a technical LoD limit of 10-7 for detecting ctDNA in cancer patients. These approaches represent a breakthrough in monitoring MRD in real-world cancer patients.
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Gorban, Iryna, and Anna Korolova. "APPLICATION OF THE METHOD OF DISCRETE SINGULARITIES TO THE CALCULATION OF THE EVOLUTION OF SURFACE GRAVITY WAVES OVER BOTTOM IRREGULARITIES." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 1 (August 1, 2023): 82–88. http://dx.doi.org/10.20998/2222-0631.2023.01.12.

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The numerical technique for simulation of viscous non-linear interactions between a solitary wave and a non-regular bottom was developed. It couples the boundary integral method used to determine the free surface deformations and the vortex scheme for integrating the fluid dynamic equations. To verify the model, a series of test calculations was carried out, where the obtained results were compared with our own experimental data and results known from similar studies by other authors. A good coincidence of the free surface elevation, as well as the velocity fields during the passage of a solitary wave over a thin submerged plate, was obtained. Systematic calculations of the interaction of a solitary wave with a submerged step in a wide range of wave amplitudes and step heights were performed. It is shown that when a wave emerges from deep water into the shallows, its evolution is determined by energy losses due to reflection, dispersion effects, and the generation of a vortex field. The dynamics of the wave on the submerged step depends on the coefficient of interaction, which is the ratio of the wave amplitude to the water depth above the step. Four types of wave behavior are possible above the step. Those are the weak interaction, when the wave gently splits into transmitted and reflected solitons; fission with development of two solitons behind the irregularity; fission with the generation of a dispersion chain of waves in the shallow water; and the collapse of a wave. The obtained critical value of the coefficient of interaction, at which the solitary wave is always breaking, is about 0.8, which is in congruence with the experimental data. Studies of patterns of vorticity generated by a solitary wave at the edge of a submerged step revealed two oppositely directed vortices with a horizontal axis, the scale of which is proportional to the water depth in a shallow channel. Their dynamics causes intensive exchange processes between deep water and shallows, as well as water flows from the bottom to the top and water mixing. The obtained data make it possible to predict in advance the development of processes and dangers caused by long nonlinear waves reaching the shelf.
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Audia, Biagio, Pasquale Pagliusi, Alfredo Mazzulla, and Gabriella Cipparrone. "Multi-Wavelength Optical Patterning for Multiscale Materials Design." Photonics 8, no. 11 (October 28, 2021): 481. http://dx.doi.org/10.3390/photonics8110481.

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Laser interferometry is a consolidated technique for materials structuring, enabling single step and large area patterning. Here we report the investigation of the morphological modification encoded on a thin film of a photosensitive material by the light interference pattern obtained from a laser operating in multiline mode. Four lines with equal intensity are retained, with the same p linear polarization. An azopolymer is exploited as medium for the holographic recording. Optical microscopy and profilometer measurements analyze the modification induced in the bulk and on the surface of the irradiated area. We show that the intensity profile of the interference patterns of two laser beams is the one obtained assuming each line of the laser as an independent oscillator of given intensity and wavelength, and how these light structures are faithfully replicated in the material bulk and on the topography of the free surface. Patterns at different length scales are achievable in a single step, that can be traced back to both interference fringes and wave envelopes. The proposed multi-wavelength holographic patterning provides a simple tool to generate complex light structures, able to perform multiscale modifications of photoresponsive materials
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Sekiguchi, Yuki, Tomotaka Oroguchi, Yuki Takayama, and Masayoshi Nakasako. "Data processing software suiteSITENNOfor coherent X-ray diffraction imaging using the X-ray free-electron laser SACLA." Journal of Synchrotron Radiation 21, no. 3 (March 15, 2014): 600–612. http://dx.doi.org/10.1107/s1600577514003439.

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Coherent X-ray diffraction imaging is a promising technique for visualizing the structures of non-crystalline particles with dimensions of micrometers to sub-micrometers. Recently, X-ray free-electron laser sources have enabled efficient experiments in the `diffraction before destruction' scheme. Diffraction experiments have been conducted at SPring-8 Angstrom Compact free-electron LAser (SACLA) using the custom-made diffraction apparatus KOTOBUKI-1 and two multiport CCD detectors. In the experiments, ten thousands of single-shot diffraction patterns can be collected within several hours. Then, diffraction patterns with significant levels of intensity suitable for structural analysis must be found, direct-beam positions in diffraction patterns determined, diffraction patterns from the two CCD detectors merged, and phase-retrieval calculations for structural analyses performed. A software suite namedSITENNOhas been developed to semi-automatically apply the four-step processing to a huge number of diffraction data. Here, details of the algorithm used in the suite are described and the performance for approximately 9000 diffraction patterns collected from cuboid-shaped copper oxide particles reported. Using theSITENNOsuite, it is possible to conduct experiments with data processing immediately after the data collection, and to characterize the size distribution and internal structures of the non-crystalline particles.
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Books on the topic "Four step technique to be free from addiction"

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Desai, Deepakbhai, ed. The Way to Get Rid of Addictions (In Gujarati). Dada Bhagwan Vignan Foundation, 2023.

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Conference papers on the topic "Four step technique to be free from addiction"

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Alam, M. S., K. Jemili, and M. A. Karim. "Modified signed-digit quaternary arithmetic using optical symbolic substitution." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.fpp1.

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Modified signed-digit (MSD) arithmetic can be efficiently performed by using two-step symbolic substitution (SS) for carry-free addition and borrow-free subtraction, where the to-be-added pair of numbers is first mapped into an intermediate pair such that the addition of the latter pair will prohibit carry propagation. Kozaitis1 presented the addition rules for a higherorder (two-bit) SS scheme allowing four bits to be processed at the same time. However, this technique depends on the length of the bit string, thereby producing an unnecessary constraint on the computation speed for operations involving long operands. To incorporate more information in fewer digits and at the same time perform arithmetic operations independent of the length of the bit strings, in this paper we study the higher-order SS technique employing MSD quaternary arithmetic. The necessary SS rules for both addition and subtraction using the proposed technique have been derived by taking into consideration a pair of reference bits from the next-lower-order bit position. Finally, the performances of the higher-order MSD binary, trinary, and quaternary arithmetic with the optical SS technique are compared.
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Lingelbach, Katharina, Daniel Diers, Michael Bui, and Mathias Vukelić. "Investigating Feature Set Decisions for Mental State Decoding in Virtual Reality based Learning Environments." In 14th International Conference on Applied Human Factors and Ergonomics (AHFE 2023). AHFE International, 2023. http://dx.doi.org/10.54941/ahfe1003014.

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In modern workplaces with rapidly changing skill requirements, suitable training and learning environments play a key role for companies to remain competitive, effective and ensure job satisfaction. To provide an immersive, interactive, and engaging learning experience, Virtual Reality (VR) has emerged as a revolutionary technology. Especially when erroneous behaviour is associated with severe consequences or great resources, VR offers the opportunity to explore actions and visualize consequences in safely and at affordable costs. In addition, it provides an easy way to personalize educational content, learning speed, and/or format to the individual to guarantee a good fit with skills and needs. This is decisive, since insufficient or excessive workload during training sessions results in demotivation and reduced performance. In the latter case, persistent professional exhaustion, pressure to succeed and stress can lead to long-term psychological consequences for employees. Besides skill and ability, current physical conditions (e.g., illness or fatigue) and psychological states (e.g., motivation) also affect the learning performance. To identify and monitor individual mental states, Brain-Computer Interfaces (BCI) measuring neurophysiological activation patterns, e.g., with an electroencephalography (EEG), or functional near-infrared spectroscopy (fNIRS) can be integrated in a VR-learning environment. Recently, fNIRS, a mobile optical brain imaging technique, has become popular for real-world applications due to its good usability, portability, and ease of use. For the reliable online decoding of mental states, informative neuronal patterns, suitable methods for pre-processing and artefact removal, as well as efficient machine learning algorithms for the classification need to be explored. We, therefore, investigated and decoded different working memory states in a free moving fNIRS experiment presented in VR. different working memory states in a free moving fNIRS VR experiment and the possibility of decoding these states properly. 11 volunteers (four female, right-handed, mean age of 23.73, SD = 1.42, range = 21−26 years) participated in the study. The experimental task was a colour-based visuo-spatial n-back paradigm adapted from Lühmann and colleagues (2019) with a low (1-back) and high working memory load condition (3-back) and a 0-back condition as active baseline. Brain activity was recorded using the mobile NIRx NIRSport2. To capture brain activation patterns associated with working memory load, optode montage was designed to optimally cover the prefrontal cortex (PFC; in particular, dorso- and ventrolateral parts of the PFC) with some lateral restriction by the VR head-mounted display (HMD). fNIRS signals were processed using the python-toolbox mne and mne-nirs. For the decoding of working memory load, we extracted statistical features, that are peak, minimum, average, slope, peak-to-peak, and time-to-peak, from epochs of oxygenated (HbO) and deoxygenated (HbR) hemoglobin concentration per channel. A Linear Discriminant Analysis (LDA), Support Vector Machine (SVM) and Gradient Boosting classifier (XGBoost) were explored and compared to a Dummy classifier (empirical chance level). We also investigated which cortical regions contributed to the decoding when choosing single features and which feature combination was suggested to optimize performance. With this study, we aim to provide empirically supported decision recommendations to reach the next step towards future online decoding pipelines in real-world VR-based learning applications.
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Darvish, Kurosh, Erik G. Takhounts, and Jeff R. Crandall. "A Dynamic Method to Develop Nonlinear Viscoelastic Model of Brain Tissue." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0122.

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Abstract The objective of this paper is to present an instrumentation and data analysis method developed to determine a nonlinear viscoelastic model of brain tissue using a forced vibration technique. The application of this model is mainly for studying the injury mechanisms of brain tissue resulting from impacts to the head. Since the early 1950s several attempts have been recorded to model the mechanical behavior of brain tissue. Investigators have used a variety of quasi-static and dynamic experimental techniques in their studies and there is a general agreement that brain exhibits viscoelastic characteristics (Galford and McElhaney, 1969). However, there are three major limitations associated with most of the previous studies. First is the limitation of boundary and environmental conditions. By applying small strains (less than 10%), most researchers have explained their experimental results with linear models (Shuck and Advani, 1972). However, biomechanical models show that shear strains up to 100% occur in brain in impact situations (Ueno et al., 1996). To include finite deformation, a nonlinear model is needed to characterize the biomechanics of impact and injury of the brain tissue. Although viscoelastic material properties are generally very sensitive to temperature (Haddad, 1995), the effect of temperature on brain material properties has not been investigated in the previous studies. Most in vitro tests have been performed in the room temperature and only a few in vivo studies have been reported (Fallenstein et al., 1969; Wang and Wineman, 1972). The effect of gravity has not been addressed in the previous studies. The brain sample is so soft that it creeps under its own weight, which causes pre-stress and pre-strain in the sample (Takhounts, 1998). The second limitation is with regard to the constitutive models. A few researchers, who have investigated the nonlinear behavior of the brain tissue, have presented the results of their studies in some special forms of stress-strain relationships (Donnely, 1993). These relationships are generally dependent on the type of experiment and can not be used for other types of loading and deformation. In order to develop an analytical or numerical model of brain, a three-dimensional constitutive relation is required that is independent of the type of experiment. The third limitation is the experimental methods. In the stress relaxation test method, due to hardware and inertial limitations, the jump of ideal step input is usually simulated with high-speed ramp input (Takhounts, 1998). Therefore, time constants that are shorter than the ramp time interval (about 0.04 s) can not be identified in the relaxation response. The small time constants have a significant effect in the short time response of the material, which is of primary interest in the biomechanics of impact and injury. On the other hand, due to inertial effects, the transient vibration of the system perturbs the first portion (about 400 ms) of the relaxation curve (Takhounts, 1998). In the ramp test method also, due to the initial acceleration period, the short time constants can not be measured correctly (Donnely, 1993). Previous studies based on the forced vibration technique, due to hardware limitations, have been performed in the frequency range of 5–350 Hz with strain levels of up to 35% (Shuck and Advani, 1972; Arbogast et al., 1997). These results have been used to develop linear viscoelastic models for shear with time constants in the range of 0.4 to 32 milliseconds. In the method presented in this paper, the goal was to develop a viscoelastic model of brain tissue that is free from the constraints discussed above. The samples are taken from fresh human and bovine brain tissues (maximum 24 hours after death or slaughter). Samples are cut with cylindrical metal cores (5–20 mm diameter) from different parts of the brain tissue and in transverse and vertical anatomic directions. Using the same experimental apparatus, cylindrical samples with the length of 5–30 mm are studied in both simple extension and in simple shear modes. In order to study the effect of temperature, canceling the effect of gravity and minimizing material deterioration, each sample is placed in a temperature controlled slow flow of saline solution throughout the experiment. An electromechanical vibrator with frequency response of dc-6500 Hz and maximum force of 65lb is used to apply the input displacement to one end of the specimen. The characteristics of the vibrator allow the identification of a wide range of time constants of the brain tissue (from 80 μs to 1.6 s) in a wide range of strain inputs (infinitesimal to 100%). The reaction force at the other end of the specimen is recorded via a miniature high precision load cell. As shown in figure 1, the analog signals of the load cell, an accelerometer that measures the motion of the vibrator, and a thermocouple that measures the temperature of the sample are collected via an isolated analog to digital converter in a personal computer. Via a digital to analog converter, the computer also controls the motion of the vibrator. The whole system works as a closed loop control system. The resultant forces of a simple harmonic displacement input and also the superposition of a series of simple harmonic inputs are analyzed in the frequency domain to generate linear, quasilinear and nonlinear third order Green-Rivlin viscoelastic models of the brain tissue (Fung, 1993 and Lockett, 1972). In addition, square wave and triangular wave inputs are applied to study the relaxation and hysteresis phenomena. The lateral movement of the samples is recorded with a high-speed camera and digital image analysis. The results obtained from the samples in transverse and vertical directions are used to develop three-dimensional transversely isotropic models. Preliminary experiments, as shown in figure 2, show that for low strain levels below 10%, linear viscoelastic model describes the short time behavior of brain tissue to a high degree of accuracy. For strain levels between 10% to 40% and short relaxation times below 100 ms, a quasilinear model can be used that only considers the strain nonlinearity of the material. Assuming that the effect of a single relaxation exponential function, after passing four time constants, is negligible, 100 ms relaxation time corresponds to the frequency of 6.4 Hz. For higher strain levels (up to 100%) and longer relaxation times (up to 5 s) or lower frequencies (below 6.4 Hz), a third order Green-Rivlin model, which includes both strain and time nonlinearity, should be used. The discrete spectrum approximation is used to represent the relaxation functions. It is shown that by using this form, the nonlinear models can be easily implemented in numerical algorithms that can be used in finite element programs (Puso and Weiss, 1998). A complete set of tests on a single specimen takes between 15–30 minutes. Therefore, multiple sections from a whole brain can be analyzed in a few hours, which minimizes the effect of material deterioration.
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