Radial Contractions Research Articles

Nonlinear elasticity and short-range mechanical coupling govern the rate and symmetry of mouth opening in Hydra.

Hydra has a tubular bilayered epithelial body column with a dome-shaped head on one end and a foot on the other. Hydra lacks a permanent mouth: its head epithelium is sealed. Upon neuronal activation, a mouth opens at the apex of the head which can exceed the body column diameter in seconds, allowing Hydra to ingest prey larger than itself. While the kinematics of mouth opening are well characterized, the underlying mechanism is unknown. We show that Hydra mouth opening is generated by independent local contractions that require tissue-level coordination. We model the head epithelium as an active viscoelastic nonlinear spring network. The model reproduces the size, timescale and symmetry of mouth opening. It shows that radial contractions, travelling inwards from the outer boundary of the head, pull the mouth open. Nonlinear elasticity makes mouth opening larger and faster, contrary to expectations. The model correctly predicts changes in mouth shape in response to external forces. By generating innervated : nerve-free chimera in experiments and simulations, we show that nearest-neighbour mechanical signalling suffices to coordinate mouth opening. Hydra mouth opening shows that in the absence of long-range chemical or neuronal signals, short-range mechanical coupling is sufficient to produce long-range order in tissue deformations.

Characterization of properties and deterioration by termites in the Pinus elliottii Engelm. wood

The technological properties of wood are constituted by parameters, which after being analyzed, make it possible to define an appropriate use for this material. However, the deterioration of the wood due to the attack of termites, which find their food source in the chemical components, ends up altering these original technological characteristics, reducing their useful life and compromising their use. Thus, this study aimed to determine some technological properties of Pinus elliottii, as well as to evaluate the influence of deterioration caused by Nasutitermes termites in this wood. Specimens with dimensions of 20 x 20 x 150 mm (tangential x radial x longitudinal) were used as specimens. The physical properties evaluated were the basic density and linear shrinkage (tangential and radial contractions, and anisotropy coefficient), while the mechanical properties were represented through the Janka hardness test and compression parallel to the fibers. After 40 days of the biodeterioration test with Nasutitermes termites, changes in the equilibrium moisture content, retractability, water absorption rate and mechanical properties were evaluated. While the physical and mechanical properties evaluated showed values similar to those found in the literature, the deterioration caused by termites caused a reduction in hardness and parameters related to compression, increasing the dimensional instability of the wood, represented by the variation in the anisotropy coefficient. This made it possible to conclude that the biodeterioration resulting from the attack of termites directly affected the technological parameters of the wood, and consequently, its quality for the use in the purpose it could initially be destined.

SoGut: A Soft Robotic Gastric Simulator.

The human stomach breaks down and transports food by coordinated radial contractions of the gastric walls. The radial contractions periodically propagate through the stomach and constitute the peristaltic contractions, also called the gastric motility. The force, amplitude, and frequency of peristaltic contractions are relevant to massaging and transporting the food contents in the gastric lumen. However, existing gastric simulators have not faithfully replicated gastric motility. Herein, we report a soft robotic gastric simulator (SoGut) that emulates peristaltic contractions in an anatomically realistic way. SoGut incorporates an array of circular air chambers that generate radial contractions. The design and fabrication of SoGut leverages principles from the soft robotics field, which features compliance and adaptability. We studied the force and amplitude of the contractions when the lumen of SoGut was empty or filled with contents of different viscosity. We examined the contracting force using manometry. SoGut exhibited a similar range of contracting force as the human stomach reported in the literature. Besides, we investigated the amplitude of the contractions through videofluoroscopy where the contraction ratio was derived. The contraction ratio as a function of inflation pressure is found to match the observations of in vivo situations. We demonstrated that SoGut can achieve in vitro peristaltic contractions by coordinating the inflation sequence of multiple air chambers. It exhibited the functions to massage and transport the food contents. SoGut can simulate the physiological motions of the human stomach to advance research of digestion.

Hicks neutrality and homotheticity in technologies with multiple inputs and multiple outputs

We analyze two popular notions in production theory: the notion of Hicks neutral technical change and the notion of homothetic technology. Both of these notions are characterized by the radial expansions or contractions of the relevant isoquants, yet in different ways. In the case of multiple-input and multiple-output, an isoquant is characterized by either the input or output combinations. Thus, for each of these notions, there are two types of conditions: one is based on the input isoquants and the other is based on the output isoquants. We show that for each notion, these two conditions are equivalent under the α-returns to scale technology. From this result, we also derive several implications for the properties of well-known productivity indexes, such as the Malmquist productivity index and the Hicks-Moorsteen productivity index.

Characterization of nAChRs in Nematostella vectensis supports neuronal and non-neuronal roles in the cnidarian\u2013bilaterian common ancestor

BackgroundNicotinic and muscarinic acetylcholine receptors likely evolved in the cnidarian–bilaterian common ancestor. Both receptor families are best known for their role at chemical synapses in bilaterian animals, but they also have described roles as non-neuronal signaling receptors within the bilaterians. It is not clear when either of the functions for nicotinic or muscarinic receptors evolved. Previous studies in cnidarians suggest that acetylcholine’s neuronal role existed prior to the cnidarian–bilaterian divergence, but did not address potential non-neuronal functions. To determine the origins of neuronal and non-neuronal functions of nicotinic acetylcholine receptors, we investigated the phylogenetic position of cnidarian acetylcholine receptors, characterized the spatiotemporal expression patterns of nicotinic receptors in N. vectensis, and compared pharmacological studies in N. vectensis to the previous work in other cnidarians.ResultsConsistent with described activity in other cnidarians, treatment with acetylcholine-induced tentacular contractions in the cnidarian sea anemone N. vectensis. Phylogenetic analysis suggests that the N. vectensis genome encodes 26 nicotinic (nAChRs) and no muscarinic (mAChRs) acetylcholine receptors and that nAChRs independently radiated in cnidarian and bilaterian linages. The namesake nAChR agonist, nicotine, induced tentacular contractions similar to those observed with acetylcholine, and the nAChR antagonist mecamylamine suppressed tentacular contractions induced by both acetylcholine and nicotine. This indicated that tentacle contractions are in fact mediated by nAChRs. Nicotine also induced the contraction of radial muscles, which contract as part of the peristaltic waves that propagate along the oral–aboral axis of the trunk. Radial contractions and peristaltic waves were suppressed by mecamylamine. The ability of nicotine to mimic acetylcholine responses, and of mecamylamine to suppress acetylcholine and nicotine-induced contractions, supports a neuronal function for acetylcholine in cnidarians. Examination of the spatiotemporal expression of N. vectensis nAChRs (NvnAChRs) during development and in juvenile polyps identified that NvnAChRs are expressed in neurons, muscles, gonads, and large domains known to be consistent with a role in developmental patterning. These patterns are consistent with nAChRs functioning in both a neuronal and non-neuronal capacity in N. vectensis.ConclusionOur data suggest that nAChR receptors functioned at chemical synapses in N. vectensis to regulate tentacle contraction. Similar responses to acetylcholine are well documented in cnidarians, suggesting that the neuronal function represents an ancestral role for nAChRs. Expression patterns of nAChRs are consistent with both neuronal and non-neuronal roles for acetylcholine in cnidarians. Together, these observations suggest that both neuronal and non-neuronal functions for the ancestral nAChRs were present in the cnidarian–bilaterian common ancestor. Thus, both roles described in bilaterian species likely arose at or near the base of nAChR evolution.

Non-overlapping Neural Networks in Hydra vulgaris

To understand the emergent properties of neural circuits, it would be ideal to record the activity of every neuron in a behaving animal and decode how it relates to behavior. We have achieved this with the cnidarian Hydra vulgaris, using calcium imaging of genetically engineered animals to measure the activity of essentially all of its neurons. Although the nervous system of Hydra is traditionally described as a simple nerve net, we surprisingly find instead a series of functional networks that are anatomically non-overlapping and are associated with specific behaviors. Three major functional networks extend through the entire animal and are activated selectively during longitudinal contractions, elongations in response to light, and radial contractions, whereas an additional network is located near the hypostome and is active during nodding. These results demonstrate the functional sophistication of apparently simple nerve nets, and the potential of Hydra and other basal metazoans as a model system for neural circuit studies.

Geometry-Related Right Ventricular Systolic Function Assessed by Longitudinal and Radial Right Ventricular Contractions.

The aim of our study was to evaluate the geometry-related right ventricular (RV) systolic function under normal hemodynamics by assessing the longitudinal and the radial RV contractions in children. We examined 953 healthy children. We measured tricuspid annular plane systolic excursion (TAPSE), RV anterior wall displacement from the interventricular septum (RVWD), and RV to left ventricular diameter ratio (RV/LV ratio) using M-mode echocardiography. The z-values were calculated as geometrical parameters of the TAPSE (z-TAPSE), the RVWD (z-RVWD), and the RV/LV ratio (z-RV/LV). The RV stroke volume (RVSV) was measured using Doppler echocardiography and standardized using the z-value (z-RVSV). The z-TAPSE was no or weakly negatively correlated with both the z-RVWD (r=-0.18, P<0.0001) and the z-RV/LV (r=-0.12, P<0.0001). In contrast, the z-RV/LV correlated positively with the z-RVWD (r=0.61, P<0.0001). The z-RVSV correlated only with the z-TAPSE (r=0.30, P<0.0001). Although the radial RV motion increases with the progression of RV dilatation, the RVSV is not associated with radial RV motion. In contrast, the RVSV relates to the longitudinal RV motion independently of the radial RV motion under the normal physiological condition. We presume that the RV contraction patterns change related to the RV geometry under various hemodynamic conditions.

Z-Value of Mitral Annular Plane Systolic Excursion Is a Useful Indicator to Predict Left Ventricular Stroke Volume in Children: Comparing Longitudinal and Radial Contractions.

The purpose of our study was to explore the pumping mechanism of the left ventricle (LV) and to examine the role of longitudinal LV contraction in LV stroke volume (LVSV) compared to a radial LV contraction. We examined 890 consecutive children without structural heart disease including 395 patients with a history of Kawasaki disease (KD). We measured the mitral annular plane systolic excursion (MAPSE), the LV end-diastolic and end-systolic dimension (LVDd), the LV radial wall displacement (LVRWD) and the LV stroke volume (LVSV). The LVSV was determined by the Doppler method. The z-values of MAPSE, LVDd, LVRWD and LVSV were calculated by the mean values and standard deviations (SDs) based upon BSA every 0.1 m(2) . We evaluated the relationship between the z-LVSV and the geometrical factors. The z-value of the MAPSE was the most powerful determinant for the z-values of the LVSV of all of the geometrical factors (β = 0.36, P < 0.0001). However, the z-values of the LVRWD did not contribute to those of the LVSV. The longitudinal LV contraction contributes more to the LVSV than the radial LV contraction, even in subjects without heart failure. Evaluation of longitudinal LV contraction using the MAPSE z-value is useful for assessing global LV function in children with various body sizes.

On metric-preserving functions and fixed point theorems

Kirk and Shahzad have recently given, in this journal, fixed point theorems concerning local radial contractions and metric transforms. In this article, we replace the metric transforms by metric-preserving functions. This in turn gives several extensions of the main results given by Kirk and Shahzad. Several examples are given. The fixed point sets of metric transforms and metric-preserving functions are also investigated.

Alternation of right ventricular contraction pattern in healthy children-shift from radial to longitudinal direction at approximately 15 mm of tricuspid annular plane systolic excursion.

Many studies have investigated tricuspid annular plane systolic excursion (TAPSE) as a longitudinal right ventricular (RV) contraction. The aim of this study was to clarify the mechanism of RV systolic function compared with longitudinal and radial RV contractions in healthy children. A total of 815 consecutive healthy children and adolescents were enrolled. We measured TAPSE on M-mode echocardiography as a longitudinal RV contraction. RV wall displacement (RVWD) toward the center of the left ventricle (LV) was measured in the short-axis view on M-mode echocardiography. RV stroke volume (RVSV) was obtained using pulse Doppler echocardiography as an indicator of RV global systolic function. RVSV and TAPSE had a positive but non-linear correlation with a definite inflection point around 15 mm of TAPSE. Subjects were stratified into 2 groups according to TAPSE (≤ 15 mm or >15 mm). In subjects with TAPSE ≤ 15 mm, RVWD and TAPSE were identified as independent predictors of RVSV. In contrast, in subjects with TAPSE >15 mm, TAPSE were identified as an independent predictor of RVSV. Normal RV contraction pattern shifts from radial to longitudinal directions at approximately 15 mm of TAPSE. RVSV is primarily generated by longitudinal contraction, but in neonates, RVSV is supported not only by longitudinal contraction but also by radial contraction.

Energy and Environmental Efficiency of China’s Transportation Sector: A Multidirectional Analysis Approach

With the rapid economic development, the transportation sector becomes one of the high-energy-consumption and high-CO2-emissions sectors in China. In order to ensure efficient use of energy and to reduce CO2pollution, it is important to gain the best performance standards in China’s transportation sector. Data envelopment analysis (DEA) has been accepted as a popular tool of efficiency measurement. However, previous studies based on DEA are mainly restricted to the radial expansions of outputs or radial contractions of inputs. In this paper, we present a nonradial DEA model with multidirectional efficiency analysis (MEA) involving undesirable outputs for the measurement of regional energy and environmental efficiency of China’s transportation sector during the period 2006–2010. We not only evaluate the energy and environmental efficiency level and trend of China’s transportation sector but also investigate the efficiency patterns of 30 regions and three major areas of China. Additionally, we identify the energy saving potential and CO2emissions reduction potential for each province and area in China in this study.

Mucosal microfolds augment mixing at the wall of the distal ileum of the brushtail possum

Recent work suggests that mixing in the small intestine takes place in central luminal and peripheral compartments. However, while movements of villi have been described, the mechanisms by which peripheral mixing are engendered remain unclear. We examined the disposition and movement of mucosa and associated villi during contractions of the everted terminal ileum of the brushtail possum. We then simulated the effect of these movements on peripheral mixing. Compression of the intestinal mucosa by phasic longitudinal or radial contractions created short-lived microfolds, which were of similar scale to the attached villi. The packing density of the villous tips increased in the concavities and decreased on the crests of these microfolds. Simulations showed that these caused liquid digesta to be expelled from, or drawn into, intervillous spaces, significantly augmenting peripheral, but not bulk, luminal mixing. We describe a mechanism by which peripheral mixing may be engendered by mucosal microfolds without requiring the coordinated contraction of individual villi or groups of villi.

Selectively Enhanced Motion Perception in Core Video Gamers

In this study we examined the effects of action video game play on performance for encoding global motion. There were no significant differences between video game player (VGP) and non-video game player (NVGP) performance for either translational or rotational motion. For radial motion, VGPs were significantly better than NVGPs at discriminating contracting, but not expanding, elements. We postulate that VGPs are selectively sensitive to radial contractions because, while this type of optic flow information is abundant in action video games, it is not encountered in abundance in the real world.

Energy and emissions efficiency patterns of Chinese regions: A multi-directional efficiency analysis

Evaluation of the energy and emissions efficiency of Chinese regions has recently attracted increasing interest. A number of previous studies have contributed to the measurement of energy efficiency using various types of data envelopment analysis (DEA) techniques. However, most of these DEA-based energy efficiency analyses were restricted to the radial expansions of outputs or radial contractions of inputs. In this paper, we utilize the multi-directional efficiency analysis (MEA) approach instead of the traditional radial DEA to investigate Chinese regional energy and emissions efficiency. Since MEA selects benchmarks such that the input contractions or output expansions are proportional to the potential improvement identified by considering the improvement potential in each input or output variable separately, not just the efficiency status but also the efficiency patterns of different Chinese regions and areas can be detected. The empirical study results indicate that, in general, the MEA efficiency of China experienced an increasing process over the study period 1997–2010; the east area overall is more MEA efficient than the central area and the west area of China during the study period; the significant higher MEA efficiency of the east area to the central area and the west area are due to both the higher energy specific efficiency and the higher emissions specific efficiency of the east area compared to the other two areas; the provinces of Hebei, Shanxi, Inner Mongolia, Shandong, Henan, and Hubei etc. have both high energy saving potentials and high emissions reduction potentials, thus they will play the most important roles in China’s effort on energy conservation and CO2 emissions mitigation.

Electric-field-induced volume change and room temperature phase stability of (Bi1/2Na1/2)TiO3-x mol. % BaTiO3 piezoceramics

Phase stability of (1 − x) (Bi1/2Na1/2)TiO3-x BaTiO3 (0 ≤ x ≤ 0.15) under electric field was investigated by measuring volume changes during a bipolar poling cycle. The unique nature of field-dependent phase stability with three distinctive regions is revealed by comparative studies using commercial soft PZT and relaxor PLZT. For x ≤ 0.06 and x ≥ 0.13, similarly with PZT and PLZT, the axial strain expands with the contracting radial strain, but the former results in a remanent volume demonstrating an electric-field-induced phase transition. For 0.08 ≤ x ≤ 0.12, this field-induced phase transition is distinguished by negligible radial contractions implying polarization rotation. A “poling-induced” morphotropic phase boundary forms at x = 0.07.

Early impairment of systolic function in patients with systemic hypertension: An echocardiographic study of myocardial deformation

Objective The purpose of this study was to examine left ventricular (LV) systolic longitudinal and radial contractions in patients with essential hypertension with normal LV ejection fraction (EF) and fractional shortening (FS). Design The study consisted of 40 control subjects and 40 patients with hypertension, with normal LV EF. Tissue Doppler echocardiography was performed to assess LV longitudinal systolic strain from the apical views and LV radial strain from parasternal short axis view. Mean longitudinal strain was calculated from the basal and mid segments. Radial strain was measured from the mid segment of the inferior wall. Results In the hypertension group, mean longitudinal and radial strains were significantly reduced compared with controls: (mean [SD] −16.9% [3] vs −20.9% [1.3], P < 0.001 for longitudinal strain) (28.6% [10.5] vs 34.7% [12.9] P = 0.03 for radial strain). Longitudinal strain appears to be correlated with LV mass index (r = −0.43) but not radial strain (r = 0.12). Conclusions Patients with hypertension and normal EF were demonstrated to have reduced LV systolic longitudinal and radial functions. There is a significant association between LV mass index, impaired diastolic function and reduced LV longitudinal contractility.

Towards in vivo flow cytometry

Cytometry is the characterization and measurement of cells and cellular constituents for biological, diagnostic and therapeutic purposes, embracing the fields of cell and molecular biology, biochemistry, biophysics, cell physiology, pathology, immunology, genetics, biotechnology, plant biology and microbiology. Cytometry is based on quantitative measurements of the molecular and phenotypic properties of cells using flow and image cytometry, microarrays, and proteomics. Cytomics (molecular cell systems research) aims at the understanding of the molecular architecture and functionality of cell systems (cytomes) by single-cell analysis in combination with exhaustive bioinformatic knowledge extraction. The cytomics concept has been significantly advanced by a multitude of current developments like confocal and laser scanning microscopy, multiphoton fluorescence excitation, spectral imaging, fluorescence resonance energy transfer (FRET), fast imaging in flow, optical stretching in flow, and miniaturized flow and image cytometry within laboratories on a chip or laser microdissection, as well as the use of bead arrays [1, 2]. Data sieving or data mining of the vast amounts of collected multiparameter data for exhaustive multilevel bioinformatic knowledge extraction avoids the inadvertent loss of information from unknown molecular relations being inaccessible to an a priori hypothesis. These approaches will become powerful tools for such important fields as individualized medicine, drug discovery and drug development [3–6]. This special issue is focused on state-of-the-art research in advanced cytometry and application areas with particular emphasis on novel biophotonic methods, disease diagnosis, and monitoring of disease treatment at single-cell level in stationary and flow conditions. It seeks to advance scholarly research that spans from fundamental interactions between light, cells, vascular tissue, and labeling particles, to strategies and opportunities for preclinical and clinical research. Recent advances in slide-based cytometry for in vitro application are summarized by Gerstner et al. [7]. They show that single cell based quantitation using microscope based cytometry instruments is making its way from basic research into clinical use. Calibration and quality control are essential in every cytometric analysis. Basics of standardization and calibration in cytometry are comprehensively summarized by Mittag and colleague [8]. Leif [9] demonstrates how data formats produced by cytometric measurements can be integrated into clinical diagnostic system standards for improved data management in the clinical environment. Flow cytometry (FCM) is based both on cell detection as whole and the use of high-speed imaging of individual cells and nanoparticles. Tychinski and co-workers [10] analyze the metabolic component of cellular refractivity and its importance for optical cytometry. The refractivity decrease in response to energy depletion was demonstrated for mitochondria, chloroplasts, spores, and cancer cells using the coherent phase microscope “Airyscan”. Estimations indicated high values for the equivalent refractive index of structured water in cells. To reduce the interference from tissue light scattering background, gold nanoparticles with strong plasmon scattering resonance properties can be applied as in vivo FCM contrast agents. This technique requires an understanding of light interaction features of cells with and without nanoparticles. Tanev and coworkers [11] compare light scattering of these cells in controlled refractive index matching conditions. They analyze the optical schematics including phase contrast microscopy as a prospective modality for in vivo FCM. Jacobs et al. [12] consider some important features of the diffraction imaging of spheres and melanoma cells with a microscope objective. Using a confocal imaging-based method to reconstruct and analyze the 3D structure, they demonstrated that genetic modifications in these cells can induce morphological changes, and the modified cells can be used as an experimental model to study the correlation between 3D morphology features and diffraction image data. Galanzha et al. [13, 14] introduce in vivo FCM with photoacoustic and photothermal detection schematics. Conventional FCM provides fast multi-parameter quantification of the biological properties of individual cells at subcellular and molecular levels. Nevertheless, the invasive extraction of cells from a living system modifies their properties, preventing their long-term study in their native environment. In vivo FCM of blood and lymph vessels with natural bioflows overcomes these problems. Cells can be detected label-free, by endogenous chromophores and pigments or by advanced strongly absorbing nanoparticles as novel labels. Both approaches are demonstrated for noninvasive rapid detection and treatment of metastases in lymph flow and sentinel lymph nodes by an integrated system of multicolor photoacoustic lymph FCM/lymphography and photothermal therapy. Bykov et al. [15] employ Doppler OCT imaging of cytoplasm shuttle flow in a slime mold Physarum polycephalum. Radial contractions of the gel-like walls of the strands and the velocity distributions in the sol-like endoplasm streaming along the plasmodial strands are imaged. The motility inhibitor effect of carbon dioxide on the cytoplasm shuttle flow and strand wall contraction is shown.

Doppler OCT imaging of cytoplasm shuttle flow in Physarum polycephalum

The Doppler optical coherence tomography technique was applied to image the oscillatory dynamics of protoplasm in the strands of the plasmodium of slime mould Physarum polycephalum. Radial contractions of the gel-like walls of the strands and the velocity distributions in the sol-like endoplasm streaming along the plasmodial strands are imaged. The motility inhibitor effect of carbon dioxide on the cytoplasm shuttle flow and strand-wall contraction is shown. The optical attenuation coefficient of cytoplasm is estimated.

Visualisation of the oscillation dynamics of cytoplasm in a living cell of Physarum mixomycete plasmodium by the method of optical coherence Doppler tomography

The method of optical coherence Doppler tomography is used for the first time to visualise the oscillatory amoeboid mobility in strands of Physarum polycephalum mixomycete plasmodium and to record periodic radial contractions of the strands and spatiotemporal variations in the velocity of the cytoplasmic flow inside them.

SHRINKAGE AND DENSITY VARIATIONS OF FRESH GREEN BEANS DURING DRYING IN AN INERT MEDIUM FLUIDIZED BED

ABSTRACT In this article, the shrinkage and density variations of cylindrical fresh green beans were investigated in a fluidized bed dryer with energy carriers. A pilot‐scaled fluidized bed dryer was set up for performing the drying experiments. Glass bead particles were used as inert materials. The drying experiments were done with fresh green beans of several lengths using hot air as a heating agent with the temperature range of 30–50C, and the effects of various parameters, such as the presence of inert materials, temperature and sample length, were investigated. It was found that the shrinkage or volume changes, and radial and axial contractions of fresh green beans could be well correlated as linear functions of moisture content during drying. Calculated and experimental values were in good agreement with mean absolute errors (MAEs) of 3.56, 2.48 and 1.22 for volume changes, and axial and radial contractions, respectively. By considering that the change in the volume of the samples was equal to the volume of evaporated water, mathematical models were proposed for volume and density variations. Comparison of the predicted values for volume and density by the proposed model with experimental date showed that the uniform model of shrinkage could explain the shrinkage and density variations of fresh green beans with MAEs of 5.190 and 4.250 for volume and density variations, respectively. The shrinkage coefficients were evaluated by considering their measurement uncertainties.PRACTICAL APPLICATIONSAny attempt to characterize drying behavior must inevitably address the physical parameters of the material such as shrinkage and density. The shrinkage phenomenon occurring during the drying process affects the physical properties of the solids, as well as the transport phenomena properties. The shrinkage of vegetables during drying is important not only from the viewpoint of material end use but also for simulation problems.