Calculation of thermally caused blood flow changes in a finger using thermographic skin temperature measurements (author's transl)]

The skin temperature changes of the third finger were registered with the help of an infrared camera during a cooling process of the hand and forearm of a male, 38-years-old subject. Using the system of formulae, explained in previous publications [4-7], it was possible to describe the blood flow changes in the finger. The results are: 1. A formula for the "pseudo thermal conductivity" (material constant of the thermal conductivity plus the convective contribution), which is similar to the formula used for theat release of the whole body [4], describes well the experimental results. The "pseudo thermal conductivity" is a measure for the specific blood flow and can be converted into it. 2. The "pseudo thermal conductivity" has a local maximum. 3. The position of the maximum is independent of the tissue temperature. The anatomical properties of the finger seem to determine the position of the maximum. 4. The maximum of the "pseudo thermal conductivity"--and therefore the maximal blood flow--increases stronger than linearly with the tissue temperature.     

An assessment of skin temperature gradients in a tropical primate using infrared thermography and subcutaneous implants

Infrared thermography has become a useful tool to assess surface temperatures of animals for thermoregulatory research. However, surface temperatures are an endpoint along the body's core-shell temperature gradient. Skin and fur are the peripheral tissues most exposed to ambient thermal conditions and are known to serve as thermosensors that initiate thermoregulatory responses. Yet relatively little is known about how surface temperatures of wild mammals measured by infrared thermography relate to subcutaneous temperatures. Moreover, this relationship may differ with the degree that fur covers the body. To assess the relationship between temperatures and temperature gradients in peripheral tissues between furred and bare areas, we collected data from wild mantled howling monkeys (Alouatta palliata) in Costa Rica. We used infrared thermography to measure surface temperatures of the furred dorsum and bare facial areas of the body, recorded concurrent subcutaneous temperatures in the dorsum, and measured ambient thermal conditions via a weather station. Temperature gradients through cutaneous tissues (subcutaneous-surface temperature) and surface temperature gradients (surface-ambient temperature) were calculated. Our results indicate that there are differences in temperatures and temperature gradients in furred versus bare areas of mantled howlers. Under natural thermal conditions experienced by wild animals, the bare facial areas were warmer than temperatures in the furred dorsum, and cutaneous temperature gradients in the face were more variable than the dorsum, consistent with these bare areas acting as thermal windows. Cutaneous temperature gradients in the dorsum were more closely linked to subcutaneous temperatures, while facial temperature gradients were more heavily influenced by ambient conditions. These findings indicate that despite the insulative properties of fur, for mantled howling monkeys surface temperatures of furred areas still demonstrate a relationship with subcutaneous temperatures. Given that most mammals possess dense fur, this provides insight for using infrared imaging in thermoregulatory studies of wild animals lacking bare skin.     

Elastic properties of the cell surface and trafficking of single AMPA receptors in living hippocampal neurons

Although various approaches are routinely used to study receptor trafficking, a technology that allows for visualizing trafficking of single receptors at the surface of living cells remains lacking. Here we used atomic force microscope to simultaneously probe the topography of living cells, record the elastic properties of their surface, and examine the distribution of transfected alpha-amino-3-hydroxy-5-methylisoxazole-4-proprionic acid (AMPA)-type glutamate receptors (AMPAR). On nonstimulated neurons, AMPARs were located in stiff nanodomains with high elasticity modulus relative to the remaining cell surface. Receptor stimulation with N-methyl-D-aspartate (NMDA) provoked a permanent disappearance of these stiff nanodomains followed by a decrease (53%) of the number of surface AMPARs. Blocking electrical activity before NMDA stimulation recruited the same number of AMPARs for internalization, preceded by the loss of the stiff nanodomains. However, in that case, the stiff nanodomains were recovered and AMPARs were reinserted into the membrane shortly after. Our results show that modulation of receptor distribution is accompanied by changes in the local elastic properties of cell membrane. We postulate, therefore, that the mechanical environment of a receptor might be critical to determine its specific distribution behavior in response to different stimuli.     

Modelling a historic oil-tank fire allows an estimation of the sensitivity of the infrared receptors in pyrophilous Melanophila beetles

Pyrophilous jewel beetles of the genus Melanophila approach forest fires and there is considerable evidence that these beetles can detect fires from great distances of more than 60 km. Because Melanophila beetles are equipped with infrared receptors and are also attracted by hot surfaces it can be concluded that these infrared receptors are used for fire detection.The sensitivity of the IR receptors is still unknown. The lowest threshold published so far is 0.6 W/m(2) which, however, cannot explain the detection of forest fires by IR radiation from distances larger than approximately 10 km. To investigate the possible sensitivity of the IR receptors we assumed that beetles use IR radiation for remote fire detection and we made use of a historic report about a big oil-tank fire in Coalinga, California, in 1924. IR emission of an oil-tank fire can be calculated by "pool fire" simulations which now are used for fire safety and risk analysis. Assuming that beetles were lured to the fire from the nearest forests 25 and 130 km away, our results show that detection from a distance of 25 km requires a threshold of the IR receptors of at least 3×10(-2) W/m(2). According to our investigations most beetles became aware of the fire from a distance of 130 km. In this case the threshold has to be 1.3×10(-4) W/m(2). Because such low IR intensities are buried in thermal noise we suggest that the infrared sensory system of Melanophila beetles utilizes stochastic resonance for the detection of weak IR radiation. Our simulations also suggest that the biological IR receptors might be even more sensitive than uncooled technical IR sensors. Thus a closer look into the mode of operation of the Melanophila IR receptors seems promising for the development of novel IR sensors.     

Revealing structural modifications in thermomechanical reshaping of collagenous tissues using optical coherence elastography

Moderate heating of such collagenous tissues as cornea and cartilages by infra‐red laser (IR laser) irradiation is an emerging technology for nondestructive modification of the tissue shape and microstructure for a variety of applications in ophthalmology, otolaryngology and so on. Postirradiation high‐resolution microscopic examination indicates the appearance of microscopic either spheroidal or crack‐like narrow pores depending on the tissue type and irradiation regime. Such examinations usually require special tissue preparation (eg, staining, drying that affect microstructure themselves) and are mostly suitable for studying individual pores, whereas evaluation of their averaged parameters, especially in situ, is challenging. Here, we demonstrate the ability of optical coherence tomography (OCT) to visualize areas of pore initiation and evaluate their averaged properties by combining visualization of residual irradiation‐induced tissue dilatation and evaluation of the accompanying Young‐modulus reduction by OCT‐based compressional elastography. We show that the averaged OCT‐based data obtained in situ fairly well agree with the microscopic examination results. The results obtained develop the basis for effective and safe applications of novel nondestructive laser technologies of tissue modification in clinical practice. PICTURE: Elastographic OCT‐based images of an excised rabbit eye cornea subjected to thermomechanical laser‐assisted reshaping. Central panel shows resultant cumulative dilatation in cornea after moderate (~45‐50°C) pulse‐periodic heating by an IR laser together with distribution of the inverse Young modulus 1/E before (left) and after (right) IR irradiation. Significant modulus decrease in the center of irradiated region is caused by initiated micropores. Their parameters can be extracted by analyzing the elastographic images.      

Thermographic mapping of the skin surface of the head in bald-headed male subjects

Thermal patterns on the skin are related to skin blood perfusion. While knowledge concerning thermal distribution patterns of the face are well established, the thermal distribution patterns of the skin surface of other aspects of the head has only been investigated once previously in a study employing low resolution thermographic equipment [van Dulken, H., van Voss, S.F.C.H, 1971. The normal thermographic patterns of the human head. Acta Neurochir. 23, 247–58.] The purpose of the study was to re-examine the thermal distribution patterns of the surface of the entire head in 12 healthy bald headed male subjects (mean age 39±7.8 (SD) years) using a high definition infrared (IR) thermographic camera. The thermal distribution patterns were monitored using dynamic infrared thermography (DIRT) before, during and after a 2 min local skin cooling procedure with a pair of fans. Infrared thermal images (thermograms) were taken of the superior, anterior, lateral and posterior aspects of the head. The thermal patterns in general followed the anatomical location of the main superficial arteries and veins of the head as described in anatomy books although there were some variations, especially with regard to the forehead and top of the head (superior aspect), ranging from an asymmetrical distribution pattern to a lack of a clear thermal pattern. The thermal patterns in the left and right lateral thermograms in each individual were relatively symmetrical. During the rewarming period the helix, auricular lobule of the auricles and the nose were relatively cold. The frontal thermograms were characterized by cool nasal and cheek areas and a clear warm area surrounding the eyes, especially around the inner canthus.     

A parametric study of thermal therapy of skin tissue

A thermal therapy for cancer in skin tissue is numerically investigated using three bioheat conduction models, namely Pennes, thermal wave and dual-phase lag models. A laser is applied at the surface of the skin for cancer ablation, and the temperature and thermal damage distributions are predicted using the three bioheat models and two different modeling approaches of the laser effect. The first one is a prescribed surface heat flux, in which the tissue is assumed to be highly absorbent, while the second approach is a volumetric heat source, which is reasonable if the scattering and absorption skin effects are of similar magnitude. The finite volume method is applied to solve the governing bioheat equation. A parametric study is carried out to ascertain the effects of the thermophysical properties of the cancer on the thermal damage. The temperature distributions predicted by the three models exhibit significant differences, even though the temperature distributions are similar when the laser is turned off. The type of bioheat model has more influence on the predicted thermal damage than the type of modeling approach used for the laser. The phase lags of heat flux and temperature gradient have an important influence on the results, as well as the thermal conductivity of the cancer. In contrast, the uncertainty in the specific heat and blood perfusion rate has a minor influence on the thermal damage.     

Theoretical and experimental exclusion of errors in the determination of the elasticity and water transport parameters of plant cells by the pressure probe technique

The volumetric elastic modulus of the cell wall and the hydraulic conductivity of the cell membranes were measured on ligatured compartments of different sizes of Chara corallina internodes using the pressure probe technique. The ratio between intact cell surface area and the area of puncture in the cell wall and membrane introduced by the microcapillary of the pressure probe was varied over a large range by inserting microcapillaries of widely varying diameters in different sized compartments. The relationship of the elastic modulus and the hydraulic conductivity to turgor pressure was independent of the ratio of intact cell surface area to the area of injury. The increase in the hydraulic conductivity below 2 bar turgor pressure and the volume dependence of the elastic modulus were shown to be the same as those observed in intact nonligatured cells. Theoretical considerations of the possible influence of injury of the cell wall and cell membrane around the inserted microcapillary on the measurement of the water transport and cell wall parameters do not explain the experimental findings. Thus, mechanical artifacts, if at all present, are too small to account for the observed dependence of the hydraulic conductivity and the elastic modulus on turgor pressure. The pressure probe technique thus represents an accurate method for measuring water transport parameters in both giant algal cells and in tissue cells of higher plants.     

Thermoelasticity of red blood cell membrane.

The elastic properties of the human red blood cell membrane have been measured as functions of temperature. The area compressibility modulus and the elastic shear modulus, which together characterize the surface elastic behavior of the membrane, have been measured over the temperature range of 2-50 degrees C with micropipette aspiration of flaccid and osmotically swollen red cells. In addition, the fractional increase in membrane surface area from 2-50 degrees C has been measured to give a value for the thermal area expansivity. The value of the elastic shear modulus at 25 degrees C was measured to be 6.6 X 10(-3) dyne/cm. The change in the elastic shear modulus with temperature was -6 X 10(-5) dyne/cm degrees C. Fractional forces were shown to be only on the order of 10-15%. The area compressibility modulus at 25 degrees C was measured to be 450 dyne/cm. The change in the area compressibility modulus with temperature was -6 dyne/cm degrees C. The thermal area expansivity for red cell membrane was measured to be 1.2 X 10(-3)/degrees C. With this data and thermoelastic relations the heat of expansion is determined to be 110-200 ergs/cm2; the heat of extension is 2 X 10(-2) ergs/cm2 for unit extension of the red cell membrane. The heat of expansion is of the order anticipated for a lipid bilayer idealized as twice the behavior of a monolayer at an oil-water interface. The observation that the heat of extension is positive demonstrates that the entropy of the material increases with extension, and that the dominant mechanism of elastic energy storage is energetic. Assuming that the red cell membrane shear rigidity is associated with "spectrin," unit extension of the membrane increases the configurational entropy of spectrin by 500 cal/mol.     

Thermal motion of whole protein molecules in protein solids

A preliminary analysis is presented of whether and to what extent thermal motion of protein molecules as rigid bodies contributes to the mobility found in X-ray and M?ssbauer studies. A simple theory is advanced enabling the estimation of mean-square amplitudes of translational and librational motion of the protein molecules in crystals and amorphous glasses from the experimental data on the elastic properties of these solids. The values calculated and their dependence on the crystal packing, temperature and hydration level were found to be in good accord with the data of X-ray analysis and M?ssbauer spectroscopy. The external modes were concluded to contribute significantly to the values of mean value of chi 2 measured by the last two methods meaning that the conventional amplitudes of internal motion in proteins were overestimated. The real average amplitude of thermal motion of atoms in the protein interior should be close to that in molecular crystals, in accordance with the crystal-like packing of atoms inside the protein globule and some other "crystal-like" physical characteristics such as Young's modulus, adiabatic compressibility and thermal expansion coefficient. Factors are discussed which determine the temperature dependence of the amplitudes of external and internal modes of protein motion.     

Effects of water-filtered infrared A irradiation on human fibroblasts

Infrared radiation is a substantial part of the solar energy output reaching the earth surface. Therefore, exposure of humans to infrared radiation is common. However, whether and how infrared (IR) or infrared A acts on human skin cells is still under debate. Recently the generation of reactive oxygen species by water-filtered infrared A (wIRA) irradiation was postulated. wIRA shows a spectral distribution similar to that of solar irradiation at the earth's surface. Thus, the need for protection of human skin from both solar- and artificially generated infrared A irradiation was concluded. Here we demonstrate that in human dermal fibroblasts this reactive oxygen species generation is dependent on heat formation by infrared A and can be reproduced by thermal exposure. On the other hand wIRA irradiation had no detectable effect if the temperature in the cells was kept constant, even if irradiance exceeded the extraterrestrial solar irradiance in the IR range by a factor of about 4 and the maximum at noontime in the tropics by a factor up to about 6. This could be demonstrated by the measurement of oxidant formation using H₂DCFDA and the determination of protein carbonyls. In additional experiments we could show that during thermal exposure the mitochondria contribute significantly to oxidant production. Further experiments revealed that the major absorbance of infrared is due to absorption of the energy by cellular water.     

The effect of the interface on the bone stresses beneath tibial components

It was proposed that the stresses in the layer of bone immediately beneath a tibial component are an important determinant of fixation durability. Using finite element analysis, (ANSYS), the stresses were determined as a function of the amount of bone resection, the localization or completeness of implant-bone contact, and the interface material. The model was of two-dimensional sagittal slices consisting of quadrilateral elements (1 mm) with a range of seventeen material properties determined by CT scans. Typical prosthesis designs shifted the center of pressure more centrally rather than posteriorly, and thus increased anterior bone stresses. Resection up to 10 mm could actually decrease bone stresses due to an increase in bone surface area as long as complete coverage was obtained. A cement interface or direct metal on bone produced identical stresses. However a 1 mm complian: interface significantly reduced stresses in regions of high elastic modulus gradient. For rigid interfaces, the contact can be irregular, which leads to areas of over and understressing of bone. These conclusions have implications related to implant design.     

Characterising the micro-mechanical behaviour of the carious dentine of primary teeth using nano-indentation

A better appreciation of the properties of carious dentine would be of clinical advantage in carious assessment and management. The aim of this study is to understand the deterioration of the mechanical properties of carious dentine as a result of bacterial demineralising process as well as change in dentine structures observed under scanning electronic microscope. Eight primary molar teeth with untreated carious dentine were axially sectioned and fine polished for nano-indentation. On each specimen, six lines of indentation, evenly distributed through the lesion, were made from the pulp to lesion cavity floor parallel to tubule direction using nano-indentation (Ultra Micro Indentation System, UMIS-2000), while another two indentation lines were made on an adjacent region of sound dentine in the same manner. All tests were conducted on hydrated specimens. Hardness and elastic modulus decreased significantly and progressively toward the cavity floor varying from 0.56 to 0.001 GPa and 14.55 to 0.015 GPa, respectively. The change in mechanical properties was in a specific pattern as a function of lesion depth, in which the hardness could be fitted to an exponential function, while the variation of the elastic modulus across the entire lesion was fitted to a power law relationship. More critical evaluation of the elastic modulus data indicated that two distinct exponential functions provided an excellent fit to the results. These changes in elastic modulus also matched the structural changes seen across a lesion, which were associated with a change from primarily peritubular to intertubular dissolution.     

Influence of blood flow and millimeter wave exposure on skin temperature in different thermal models

Recently we showed that the Pennes bioheat transfer equation was not adequate to quantify mm wave heating of the skin at high blood flow rates. To do so, it is necessary to incorporate an "effective" thermal conductivity to obtain a hybrid bioheat equation (HBHE). The main aim of this study was to determine the relationship between non-specific tissue blood flow in a homogeneous unilayer model and dermal blood flow in multilayer models providing that the skin surface temperatures before and following mm wave exposure were the same. This knowledge could be used to develop multilayer models based on the fitting parameters obtained with the homogeneous tissue models. We tested four tissue models consisting of 1-4 layers and applied the one-dimensional steady-state HBHE. To understand the role of the epidermis in skin models we added to the one- and three-layer models an external thin epidermal layer with no blood flow. Only the combination of models containing the epidermal layer was appropriate for determination of the relationship between non-specific tissue and dermal blood flows giving the same skin surface temperatures. In this case we obtained a linear relationship between non-specific tissue and dermal blood flows. The presence of the fat layer resulted in the appearance of a significant temperature gradient between the dermis and muscle layer which increased with the fat layer thickness.     

Effect of hydroperoxides on red blood cell membrane mechanical properties

We investigate the effect of oxidative stress on red blood cell membrane mechanical properties in vitro using detailed analysis of the membrane thermal fluctuation spectrum. Two different oxidants, the cytosol-soluble hydrogen peroxide and the membrane-soluble cumene hydroperoxide, are used, and their effects on the membrane bending elastic modulus, surface tension, strength of confinement due to the membrane skeleton, and 2D shear elastic modulus are measured. We find that both oxidants alter significantly the membrane elastic properties, but their effects differ qualitatively and quantitatively. While hydrogen peroxide mainly affects the elasticity of the membrane protein skeleton (increasing the membrane shear modulus), cumene hydroperoxide has an impact on both membrane skeleton and lipid bilayer mechanical properties, as can be seen from the increased values of the shear and bending elastic moduli. The biologically important implication of these results is that the effects of oxidative stress on the biophysical properties, and hence the physiological functions, of the cell membrane depend on the nature of the oxidative agent. Thermal fluctuation spectroscopy provides a means of characterizing these different effects, potentially in a clinical milieu.     

A covalently cross-linked gel derived from the epidermis of the pilot whale Globicephala melas

The rheological properties of the stratum corneum of the pilot whale (Globicephala melas) were investigated with emphasis on their significance to the self-cleaning abilities of the skin surface smoothed by a jelly material enriched with various hydrolytic enzymes. The gel formation of the collected fluid was monitored by applying periodic-harmonic oscillating loads using a stress-controlled rheometer. In the mechanical spectrum of the gel, the plateau region of the storage modulus G' (<1200 Pa) and the loss modulus G" (>120 Pa) were independent of frequency (omega = 43.98 to 0.13 rad x s(-1), tau = 15 Pa, T = 20 degrees C), indicating high elastic performance of a covalently cross-linked viscoelastic solid. In addition, multi-angle laser light scattering experiments (MALLS) were performed to analyse the potential time-dependent changes in the weight-average molar mass of the samples. The observed increase showed that the gel formation is based on the assembly of covalently cross-linked aggregates. The viscoelastic properties and the shear resistance of the gel assure that the enzyme-containing jelly material smoothing the skin surface is not removed from the stratum corneum by shear regimes during dolphin jumping. The even skin surface is considered to be most important for the self-cleaning abilities of the dolphin skin against biofouling.     

Elastic modulus of tree frog adhesive toe pads

Previous work using an atomic force microscope in nanoindenter mode indicated that the outer, 10- to 15-??m thick, keratinised layer of tree frog toe pads has a modulus of elasticity equivalent to silicone rubber (5?C15?MPa) (Scholz et al. 2009), but gave no information on the physical properties of deeper structures. In this study, micro-indentation is used to measure the stiffness of whole toe pads of the tree frog, Litoria caerulea. We show here that tree frog toe pads are amongst the softest of biological structures (effective elastic modulus 4?C25?kPa), and that they exhibit a gradient of stiffness, being stiffest on the outside. This stiffness gradient results from the presence of a dense network of capillaries lying beneath the pad epidermis, which probably has a shock absorbing function. Additionally, we compare the physical properties (elastic modulus, work of adhesion, pull-off force) of the toe pads of immature and adult frogs.     

Mechanical properties of cultured human airway smooth muscle cells from 0.05 to 0.4 Hz.

We investigated the rheological properties of living human airway smooth muscle cells in culture and monitored the changes in rheological properties induced by exogenous stimuli. We oscillated small magnetic microbeads bound specifically to integrin receptors and computed the storage modulus (G') and loss modulus (G") from the applied torque and the resulting rotational motion of the beads as determined from their remanent magnetic field. Under baseline conditions, G' increased weakly with frequency, whereas G" was independent of the frequency. The cell was predominantly elastic, with the ratio of G" to G' (defined as eta) being approximately 0. 35 at all frequencies. G' and G" increased together after contractile activation and decreased together after deactivation, whereas eta remained unaltered in each case. Thus elastic and dissipative stresses were coupled during changes in contractile activation. G' and G" decreased with disruption of the actin fibers by cytochalasin D, but eta increased. These results imply that the mechanisms for frictional energy loss and elastic energy storage in the living cell are coupled and reside within the cytoskeleton.     

Low-temperature methyl bromide fumigation of emerald ash borer (Coleoptera: Buprestidae) in ash logs

Ash (Fraxinus spp.) logs, infested with fully developed, cold-acclimated larval and prepupal emerald ash borer, Agrilus planipennis Fairmaire (Coleoptera: Buprestidae), were fumigated with methyl bromide (MeBr) at 4.4 and 10.0 degrees C for 24 h. Concentrations X time dosages of MeBr obtained were 1579 and 1273 g-h/m3 (24-h exposure) at 4.4 and 10.0 degrees C after applied doses of 112 and 96 g/m3, respectively. MeBr concentrations were simultaneously measured with a ContainIR infrared monitor and Fumiscope thermal conductivity meter calibrated for MeBr to measure the effect of CO2 on Fumiscope concentration readings compared with the infrared (IR) instrument. The presence of CO2 caused false high MeBr readings. With the thermal conductivity meter, CO2 measured 11.36 g/m3 MeBr per 1% CO2 in clean air, whereas the gas-specific infrared ContainIR instrument measured 9.55% CO2 as 4.2 g/m3 MeBr (0.44 g/m3 per 1% CO2). The IR instrument was 0.4% as sensitive to CO2 as the thermal conductivity meter. After aeration, fumigated and control logs were held for 8 wk to capture emerging beetles. No A. planipennis adults emerged from any of the fumigated logs, whereas 262 emerged from control logs (139 and 123/m2 at 4.4 and 10.0 degrees C, respectively). An effective fumigation dose and minimum periodic MeBr concentrations are proposed. The use of a CO2 scrubber in conjunction with nonspecific thermal conductivity instruments is necessary to more accurately measure MeBr concentrations.     

Coherent Timescales and Mechanical Structure of Multicellular Aggregates

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics in specifying multicellular reorganization during embryonic developments and malignant invasion. Tissue-like spheroids, when subjected to a compressive force, are known to exhibit liquid-like behaviors at long timescales (hours), largely because of cell rearrangements that serve to effectively dissipate the applied stress. At short timescales (seconds to minutes), before cell rearrangement, the mechanical behavior is strikingly different. The current work uses shape relaxation to investigate the structural characteristics of aggregates and discovers two coherent timescales: one on the order of seconds, the other tens of seconds. These timescales are universal, conserved across a variety of tested species, and persist despite great differences in other properties such as tissue surface tension and adhesion. A precise mathematical theory is used to correlate the timescales with mechanical properties and reveals that aggregates have a relatively strong envelope and an unusually “soft” interior (weak bulk elastic modulus). This characteristic is peculiar, considering that both layers consist of identical units (cells), but is consistent with the fact that this structure can engender both structural integrity and the flexibility required for remodeling. In addition, tissue surface tension, elastic modulus, and viscosity are proportional to each other. Considering that these tissue-level properties intrinsically derive from cellular-level properties, the proportionalities imply precise coregulation of the latter and in particular of the tension on the cell-medium and cell-cell interfaces.