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Results for “Elastic Modulus”

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PubMed2006

Microelastic mapping of living endothelial cells exposed to shear stress in relation to three-dimensional distribution of actin filaments.

The surface topography and local elastic moduli of endothelial cells exposed to shear stress were measured using atomic force microscopy. Bovine aortic endothelial cells were exposed to shear stress of 2Pa for 6, 12 or 24h. In addition, a confocal laser-scanning microscope used in conjunction with the atomic force microscope was used to observe the actin filament structure of these endothelial cells to elucidate the relationship between mechanical properties and cytoskeletal structure. The elastic modulus, calculated using the Hertz model, was measured at 50x50 points at 1mum intervals within 40min. For endothelial cells sheared for 6h and 12h, the elastic modulus at the upstream region was found to be higher than that at the downstream region. For endothelial cells sheared for 24h, the elastic modulus at both the upstream and downstream regions increased. Fluorescent images showed thick, elongated actin filaments oriented in the direction of flow at the ventral surface of the cells. In the middle plane of the cells, actin filaments developed around the nucleus, while in the upper plane, short, thick actin filaments were observed but thick stress fibers were not present. The high elastic modulus came from the stress fibers. These results indicate that the higher elastic modulus observed in the upstream and downstream regions of sheared endothelial cells is mainly due to the development of stress fibers at the ventral surface and middle plane of the cell.

Actin Cytoskeleton↗

PubMed1996

The modulus of elasticity of equine hoof wall: implications for the mechanical function of the hoof.

During normal weight-bearing and locomotion, the equine hoof wall deforms in a consistent pattern; the proximal dorsal wall rotates caudo-ventrally about the distal dorsal border and there is latero-medial flaring posteriorly. The aim of this study is to examine whether there are regional differences in the modulus of elasticity of hoof wall material and whether such differences correlate with the pattern of deformation which occurs in vivo. The modulus of elasticity of equine hoof wall was determined in tension and compression for samples from six forefeet. Samples were tested at the mid-point of the inner and outer halves of the wall thickness at two positions along the proximo-distal axis of the dorsal wall, and from the mid-point of its thickness at the lateral and medial quarters. Test samples were oriented both parallel and perpendicular to the tubules that characterise the microstructure of the wall. The colour of each sample was noted, and the moisture content measured. The range in the mean modulus of elasticity for all samples and tests was 460-1049 MPa, the dorsal outer wall having the highest values, the dorsal inner wall the lowest, and the quarters having intermediate values. The mean value obtained for the quarters was similar to the average of the values for the dorsal inner and outer walls. At all sites, the modulus of elasticity was marginally higher in compression than in tension, possibly owing to microstructural defects. The difference in stiffness between the outer wall and the inner wall was inversely related to moisture content. The difference in stiffness between the dorsal outer and inner walls demonstrates that the equine hoof wall has a comparatively rigid external capsule with a lining of lower stiffness. This arrangement presumably provides some stress protection to the internally adjacent living tissues. The similarity in stiffness between the samples from the quarters and the mean of the two dorsal wall sites suggests that the wall at the quarters has a similar change in stiffness across its thickness as the dorsal wall. However, the reduced thickness of the wall at the quarters compared with the dorsal wall means that, functionally, the quarters are more flexible than the dorsal wall. This will facilitate the flaring of the lateral and medial walls which occurs during weight-bearing. Anisotropy was evident only in tensile tests of the dorsal wall samples. Contrary to popular assertions that white hooves are mechanically inferior, horn pigmentation had no detectable effect on stiffness.

Animals↗

PubMed2000

Effect of collagen denaturation on the toughness of bone.

The purpose of this study was to explore the relationship between the integrity of collagen and biomechanical properties of bone. In this study, age (range, 5-26 years old) and gender related changes in cortical bone samples from 33 baboon femurs (15 males and 18 females) were examined. The percentage of denatured collagen was determined using a selective digestion technique. The fracture toughness, elastic modulus, yield and ultimate strength, and energy to fracture of bone were determined in three-point bending configurations. The porosity and weight fractions of the mineral and organic phase also were measured. A two-way analysis of variance showed that age dependent changes were reflected primarily in the amount of denatured collagen, fracture toughness, energy to fracture, and elastic modulus, whereas gender had effects on the fracture toughness, elastic modulus, and porosity of bone. In addition, regression analyses indicated that the percentage of denatured collagen had an inverse correlation with the toughness of bone and a positive correlation with its elastic modulus, whereas mineral content had positive correlation with the strength and elastic modulus of bone. The results of this study suggest collagen influences the toughness of bone, whereas mineral content predominantly contributes to bone stiffness and strength.

Animals↗

PubMed2003

Transthoracic echocardiographic assessment of proximal ascending aorta elasticity in familial heterozygous hypercholesterolemia patients.

BACKGROUND: Decreased elasticity of the aorta is associated with aging and several risk factors of atherosclerosis. The data regarding this phenomenon in patients with familial hypercholesterolemia are rather sparse. OBJECTIVES: To evaluate non-invasively the elasticity of the proximal ascending aorta of 51 heterozygous FH patients compared to 42 normal age and gender-matched controls. METHODS: Aortic elasticity was estimated by transthoracic echocardiography using the "pressure-strain" elastic modulus and aortic strain formulas. RESULTS: The elastic modulus score was higher in the FH group than in the controls (1.12 +/- 0.91 10(6) dynes/cm2 vs. 0.65 +/- 0.46 10(6) dynes/cm2 respectively, P = 0.01). This was consistent in both the pediatric (0.5 +/- 0.2 10(6) dynes/cm2 vs. 0.4 +/- 0.1 10(6) dynes/cm2 respectively, P = 0.009) and adult subgroups (1.3 +/- 1.0 10(6) dynes/cm2 vs. 0.8 +/- 0.5 10(6) dynes/cm2 respectively, P = 0.0004). Aortic strain was significantly lower in patients with FH than in controls (6 +/- 4% vs. 9 +/- 5% respectively, P = 0.0002). These findings reflected decreased elasticity of the proximal ascending aorta in the FH patients. In multivariate analysis, age, serum cholesterol level and serum triglycerides level were the independent predictors of the elastic modulus score, whereas age was the predictor of aortic strain. CONCLUSIONS: The elasticity of the proximal ascending aorta is decreased in heterozygous FH patients.

Adolescent↗

PubMed2005

Dynamic visco-elastic properties of dental composite resins.

OBJECTIVES: This study aimed to examine the visco-elastic properties of dental composites by dynamic mechanical analysis under the influence of clinically relevant temperatures and variable frequencies, after being stored in air or distilled water for up to 3 months. METHODS: Two direct (Diamond Lite and Grandio) and two indirect (Artglass and Vita Zeta LC) composites were used. Samples were immediately tested (baseline) or stored at 37 degrees C, either in air or distilled water for 1 day, 7 or 90 days before testing. During dynamic testing, elastic modulus, viscous modulus and loss tangent were determined over a frequency range from 0.1 to 10 Hz at constant temperatures between 5 and 55 degrees C. RESULTS: Results were analyzed by one-way ANOVA and Turkey's-test. Elastic and viscous moduli were higher for direct than for indirect composites. No such evidence was found for loss tangent. Only the elastic modulus showed statistically relevant differences in the direct and indirect materials groups: Grandio showed higher modulus than Diamond Lite, while Artglass had higher modulus than Vita Zeta LC. The elastic modulus reduced with increasing temperature and decreasing frequency, while the loss tangent showed the opposite trend. The influence of temperature and frequency on viscous modulus was not conclusive. The elastic modulus was more sensitive to moisture than viscous modulus and loss tangent but all three properties showed no overall consistent trend in the results following the storage periods. SIGNIFICANCE: Dynamic mechanical analysis was a valuable tool to characterize the visco-elastic properties of dental composites, thus giving us a greater insight into material behavior.

Air↗

PubMed1988

Physical properties of addition silicones as a function of composition.

The effects of molecular weight of the base silicone, filler and copolymer concentrations on compression set, strain, creep and dynamic elastic modulus were determined. The molecular weight of the base silicone had the least effect on these properties although low molecular weights showed better properties. Chain extenders were detrimental to physical properties of creep, compression set and dynamic elastic modulus. Increased copolymer concentrations decreased compression set, strain and creep and increased the dynamic elastic modulus. The useful copolymer/base functional group ratio was from 1:1 to 3:1. Filler affected properties to a lesser extent than copolymer ratio. Compression set, strain, and creep decreased and the dynamic elastic modulus increased with increasing filler with the properties being directly proportional to the weight fraction. All properties were interrelated with ln strain linearly related to ln compression set, creep proportional to set, and the dynamic elastic modulus was inversely correlated with strain and creep.

Chemical Phenomena↗

PubMed2003

[Realtime elastography. A new ultrasound procedure for the reconstruction of tissue elasticity].

It is well known that some diseases, such as cancer, lead to a change of tissue hardness (i.e. the so-called elasticity modulus). The reconstruction of tissue elasticity provides the sonographer with important additional information which can be applied for the diagnosis of these diseases. Elasticity imaging has recently attracted attention as a technique which directly reveals the physical property of tissue and enables us to determine the change of tissue hardness caused by diseases. The elasticity modulus, i.e. the tissue elasticity distribution can be calculated from the strain and the stress of the examined structures. While the strain field can be estimated from the RF signals returned from tissue structures before and after compression, it is impossible to measure the stress field directly within the tissue. Another problem is that the compression of harder tissue structures is often followed by a lateral displacement of these structures. It is nearly impossible to represent the volume of this sideslip with conventional 2D methods but its calculation is indispensable for an accurate determination of the tissue elasticity of the examined structures. To overcome these problems, we propose the so-called Extended CA-method (Extended Combined Autocorrelation Method) which allows the reconstruction of the tissue elasticity of the examined structures on the basis of the 3-dimensional finite element model. The new technique enables a highly accurate estimation of the tissue elasticity distribution and the adequate compensation of sideslips. The realtime elasticity imaging described in this article, can easily be performed with the SonoElastography module that can be integrated into the platform of the HITACHI EUB-8500 system. Like colour Doppler examinations, tissue elasticity imaging can easily be performed with conventional ultrasound probes and does not require additional instruments (e.g. for measuring pressure or vibrations). The calculation of tissue elasticity distribution is performed in realtime and the examination results are represented in colour over the conventional B-mode image. The results of the simulations and phantom experiments performed verify that with the information obtained by the new realtime elasticity imaging method, lesions can be detected and represented more rapidly and with higher accuracy than with conventional methods based on the 2D Model, and that even lesions invisible on B-mode images can be detected.

Breast Neoplasms↗

PubMed1992

Mechanical fragility of erythrocyte membrane in neonates and adults.

The shortened life span of neonatal red blood cells (RBC) is associated with accelerated membrane loss. The present study was designed to measure the critical shear force that causes membrane failure and the rate of membrane failure for neonatal and adult RBC. A micropipette technique was used to determine the membrane extensional (shear) elastic modulus (i.e. resistance of the membrane to extensional elastic deformation), the rate of extensional membrane deformation (i.e. surface viscosity), and the tension for local membrane fragmentation. A flow channel system was used to determine the critical shear force of plastic membrane deformation (i.e. beginning of membrane tether formation), the rate of plastic deformation, and the plastic shear viscosity coefficient. The extensional elastic modulus of neonatal RBC was 18% smaller and the rate of elastic deformation was 25% longer compared with adult cells (p less than 0.05). Membrane surface viscosity was similar for both cell types. The tension for local membrane fragmentation in the micropipette was 23% lower in neonates than in adults. However, the strain (i.e. extent of membrane deformation calculated as ratio of the stress resultant and the elastic modulus) at which membrane rupture in the micropipette occurred was similar for neonatal and adult RBC. This indicates that the smaller critical tension for neonatal RBC membrane failure was due to increased membrane elastic deformability.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

PubMed2007

In vivo areal modulus of elasticity estimation of the human tympanic membrane system: modelling of middle ear mechanical function in normal young and aged ears.

The quasi-static elastic properties of the tympanic membrane system can be described by the areal modulus of elasticity determined by a middle ear model. The response of the tympanic membrane to quasi-static pressure changes is determined by its elastic properties. Several clinical problems are related to these, but studies are few and mostly not comparable. The elastic properties of membranes can be described by the areal modulus, and these may also be susceptible to age-related changes reflected by changes in the areal modulus. The areal modulus is determined by the relationship between membrane tension and change of the surface area relative to the undeformed surface area. A middle ear model determined the tension-strain relationship in vivo based on data from experimental pressure-volume deformations of the human tympanic membrane system. The areal modulus was determined in both a younger (n = 10) and an older (n = 10) group of normal subjects. The areal modulus for lateral and medial displacement of the tympanic membrane system was smaller in the older group (mean = 0.686 and 0.828 kN m(-1), respectively) compared to the younger group (mean = 1.066 and 1.206 kN m(-1), respectively), though not significantly (2p = 0.10 and 0.11, respectively). Based on the model the areal modulus was established describing the summated elastic properties of the tympanic membrane system. Future model improvements include exact determination of the tympanic membrane area accounting for its shape via 3D finite element analyses. In vivo estimates of Young's modulus in this study were a factor 2-3 smaller than previously found in vitro. No significant age-related differences were found in the elastic properties as expressed by the areal modulus.

Adult↗

PubMed2000

Age, gender, and bone lamellae elastic moduli.

To enhance preventative and therapeutic strategies for metabolic bone diseases and bone fragility disorders, we began to explore the physical properties of bone tissue at the cellular level. Proximal femurs were harvested from 27 cadavera (16 male and 11 female) for in vitro measurement of the mechanical properties. We measured the variations in lamellar-level elastic modulus and hardness in human bone as a function of age and gender to identify microstructural properties responsible for age and gender-related reductions in the mechanical integrity. The lateral femoral necks were examined, and age, gender, height, body mass, and body mass index were not found to correlate with lamellar-level elastic modulus or hardness. This result was consistent for osteonal, interstitial, and trabecular tissue. These data suggest that increased bone mass maintenance, known to occur in heavier individuals, is not accompanied by increases in the lamellar-level elastic modulus or hardness. The independence of elastic modulus and hardness from age and gender suggests that age and gender-related decreases in mechanical integrity do not involve alterations in elastic modulus or hardness of the extracellular matrix. Lamellar-level ultimate, fatigue, and fracture toughness properties should also be investigated. Other factors, such as tissue mass and organization, may also contribute to age and gender-related decreases in the mechanical integrity.

Adult↗

PubMed2006

Three-dimensional finite element analysis of weakened roots restored with different cements in combination with titanium alloy posts.

BACKGROUND: It is very difficult and relatively unpredictable to preserve and restore severely weakened pulpless roots. To provide much needed benefit basis for clinical practice, this study was carried out to analyze the stress distribution in weakened roots restored with different cements in combination with titanium alloy posts. Finite element analysis (FEA) was employed in the study. METHODS: A pseudo three-dimensional model of a maxillary central incisor with flared root canal, theoretically restored with titanium alloy posts in combination with different cements, was established. The analysis was performed by use of ANSYS software. The tooth was assumed to be isotropic, homogenous and elastic. A load of 100 N at an angle of 45 degrees to the longitudinal axis was applied at the palatal surface of the crown. The distributions of stresses in weakened roots filled with cements of different elastic modulus were analyzed by the three-dimensional FEA model. RESULTS: Several stress trends were observed when the stress cloud atlas obtained in the study was analyzed. With the increase of the elastic modulus of cements from 1.8 GPa to 22.4 GPa, the stress values in dentin decreased from 39.58 MPa to 31.43 MPa and from 24.51 MPa to 20.76 MPa (respectively, for maximum principle stress values and Von Mises stress values). When Panavia F and zinc phosphate cement were used, the stress peak values in dentin were very small with no significant difference observed, and the Von Mises stress values were 20.87 MPa and 20.76 MPa respectively. On the other hand, maximum principle stress value and Von Mises stress value in cement layer increased with the increase of the elastic modulus of cements. CONCLUSIONS: The result of this study demonstrated that elastic modulus was indeed one of the important parameters to evaluate property of the cements. Our three-dimensional FEA model study also found that the cement with elastic modulus similar to that of dentin could reinforce weakened root and reduce the stress in dentin. Thus, it may be a better choice for the restoration of weakened roots in clinical practice.

Adult↗

PubMed1987

The elasticity of uniform, unilamellar vesicles of acidic phospholipids during osmotic swelling is dominated by the ionic strength of the media.

Uniform, unilamellar vesicles have been prepared by the pH-modification technique. The initial sizes of the vesicles were from 200 to 700 nm and were measured to within 1-3% by photo correlation spectroscopy. Vesicles were made of the dioleoyl esters of phosphatidic acid, phosphatidylcholine, phosphatidylglycerol, phosphatidylethanolamine, the diphytanyl ethers of phosphatidylglycerol, Escherichia coli lipids, and lac permease reconstituted into E. coli lipids. The vesicle suspensions were prepared and then diluted with electrolyte (KCl) and/or nonelectrolyte (sucrose, trehalose, pentaerythritol) impermeants. The amplitude of the swelling is linearly proportional to the osmotic pressure difference across the bilayer. We have determined the elastic modulus, the elastic limit (percent surface expansion at bursting), and the transbilayer pressure difference at bursting for each of these vesicles at constant osmolarity but at different ionic strengths. We find that the elastic properties of the bilayer vary by a factor of 10 in electrolyte media as compared to isosmolal nonelectrolyte media and that this variation appears to be related to both the charge density at the surface and the ionic strength of the media. Anionic lipid vesicles in 150 mM KCl have a significantly higher modulus (50 X 10(7) dyn/cm2) and transbilayer pressure difference (40 mosM) at bursting with a small capacity to stretch (3-4% surface expansion) compared to the same vesicles suspended in nonelectrolyte impermeants. The latter vesicles undergo a significant surface expansion (8-10%), display a low modulus (3 X 10(7) dyn/cm2), and burst at 3-4 mosM bilayer pressure difference. Vesicles suspended in media of constant osmolarity at various ionic strengths display properties with proportional values.(ABSTRACT TRUNCATED AT 250 WORDS)

Elasticity↗

PubMed2005

Clustering and mechanics in dense depletion and thermal gels.

We report on the microstructure and mechanical properties (elastic modulus) of concentrated depletion and thermal gels of octadecyl-coated silica particles for different values of the strength of interaction--polymer concentration for depletion gels and temperature for thermal gels. The depletion gels are composed of dense clusters and voids, while the thermal gels are devoid of clusters. Shear breaks up clusters in depletion gels while it induces clustering in the thermal gels. In both of these gels, the microstructure recovers to the presheared state upon cessation of shear. The recovery of the elastic modulus mimics the microstructure in the sense that the elastic modulus recovers to the presheared sheared state after shearing is stopped. Calculations of the gel boundary by modeling the interactions with an effective one-component square-well model reveals that suspensions with similar ranges of attraction gel at the same volume fraction at a fixed strength of attraction. Calculations of the elastic modulus using the naïve mode coupling theory for depletion gels are in good agreement with experimental measurements provided clustering is taken into account and have the same magnitude as the elastic moduli of thermal gels with similar strengths of attraction. These calculations, in addition to the experimental observations reinforce the point that the microscopic parameter determining the elastic modulus of dense gels and its recovery is the localization length which is only a fraction of the particle diameter and not the structure on the length scale of the particle diameter and larger.

Colloids↗

PubMed1972

Early increase in left ventricular compliance after myocardial infarction.

The left ventricular (LV) pressure-volume (P-V) relationship is a resultant of several determinants, including initial ventricular volume, geometry, and wall stiffness. A quantitative index of one of these determinants, LV wall stiffness, was developed from a mathematical analysis of the isolated P-V relationship. Since this relationship was exponential, stiffness (dP/dV) could be expressed by the equation dP/dV = aP + b, where a and b are constants. The a constant, termed the passive elastic modulus, was independent of both pressure and volume, was modified only slightly by changes in geometry, and thus was primarily affected by changes in wall stiffness. LV wall stiffness was assessed by determination of the passive elastic modulus in eight normal canine hearts and in five hearts 1 hr after acute myocardial infarction. The value of the passive elastic modulus for the normal canine LV was found to be 0.099+/-0.006 cc(-1). In the five infarcted hearts there was a modest, but statistically insignificant, shift of the P-V curves from control, such that for the same pressure the infarcted hearts contained greater volume. However, the passive elastic modulus decreased 41% to 0.057+/-0.006 cc(-1) (P < 0.001). Thus, although LV wall stiffness may increase later in the course of myocardial infarction, it is concluded that it was significantly decreased 1 hr after infarction. Calculation of the passive elastic modulus provided a sensitive means of detecting such changes, whereas P-V curves alone were generally insensitive.

Animals↗

PubMed2000

Heterogeneity of bone lamellar-level elastic moduli.

Advances in our ability to assess fracture risk, predict implant success, and evaluate new therapies for bone metabolic and remodeling disorders depend on our understanding of anatomically specific measures of local tissue mechanical properties near and surrounding bone cells. Using nanoindentation, we have quantified elastic modulus and hardness of human lamellar bone tissue as a function of tissue microstructures and anatomic location. Cortical and trabecular bone specimens were obtained from the femoral neck and diaphysis, distal radius, and fifth lumbar vertebra of ten male subjects (aged 40-85 years). Tissue was tested under moist conditions at room temperature to a maximum depth of 500 nm with a loading rate of 10 nm/sec. Diaphyseal tissue was found to have greater elastic modulus and hardness than metaphyseal tissues for all microstructures, whereas interstitial elastic modulus and hardness did not differ significantly between metaphyses. Trabecular bone varied across locations, with the femoral neck having greater lamellar-level elastic modulus and hardness than the distal radius, which had greater properties than the fifth lumbar vertebra. Osteonal, interstitial, and primary lamellar tissues of compact bone had greater elastic moduli and hardnesses than trabecular bone when comparing within an anatomic location. Only femoral neck interstitial tissue had a greater elastic modulus than its osteonal counterpart, which suggests that microstructural distinctions can vary with anatomical location and may reflect differences in the average tissue age of cortical bone or mineral and collagen organization.

Adult↗

PubMedDate not supplied

The fracture resistance of all-ceramic crowns on supporting structures with different elastic moduli.

This in vitro study evaluated the fracture resistance of all-ceramic crowns as a function of the elastic modulus of the supporting die. All-ceramic crowns were made for dies with three different elastic moduli and two different crown lengths. The occlusal surface was loaded in compression with a 12.7-mm steel ball. The fracture load increased markedly with the increase in elastic modulus. The largest increase was seen when only the occlusal surface of the crown was covered. The characteristic fracture load of the complete-crown restorations was more than double that of the occlusal-cover restorations in the dies with the lowest modulus of elasticity, while for the dies with the highest modulus of elasticity the difference in the characteristic fracture load for the two configurations was not significant.

Chemical Phenomena↗

PubMed1999

Resin composites for foundation restorations.

This study focused on the compressive properties of two core buildup materials, Ti-Core, (EDS, Inc.) and FluoroCore, (L.D. Caulk). Specimens were 0.6 x 1.2 cm cylinders, Prior to testing, the specimens were aged in a moist environment for one, seven, or 28 day(s). The properties of interest were compressive strength, modulus of elasticity and toughness. The data set for each of the three compressive properties was subjected to a separate two-way analysis of variance. Scheffé F-tests were used to compare means. Whereas the effect of material on each of the three properties was significant (p < 0.002), the effects of specimen age (p > 0.400) and material x specimen age (p > 0.350) were not significant. FluoroCore was stronger and tougher than Ti-Core. On the other hand, Ti-Core displayed the highest stiffness, but ruptured brittley. The moderately low strength of Ti-Core, and the insufficient elastic modulus of FluoroCore, avert favorable recommendations pertaining to the construction of foundation restorations.

Analysis of Variance↗

PubMed1998

Compressive properties of chemically cured, resin modified glass ionomer luting cements.

This study compared the responses of three proprietary chemically cured hybrid glass ionomer luting cements to compressive loading. These cements bear the trade names Advance, Fuji DUET and Vitremer Luting Cement, and are distributed and sold through ordinary domestic and international channels of dental commerce. The findings are as follows: 1. Advance, and Fuji DUET were stronger and stiffer than Vitremer Luting Cement. On the other hand, Vitremer exhibited the highest toughness. 2. The compressive properties of Advance were not affected significantly by increasing the specimen aging period to 28 days from seven days. 3. Prolonged aging of Fuji DUET and Vitremer specimens in a humid environment elicited significant changes in compressive strength and modulus of elasticity. Whereas the strength and elastic modulus changes for Fuji DUET were negative, the changes experienced by Vitremer were positive. 4. Extending the specimen aging period to 28 days from seven days did not affect significantly the toughness of either Fuji DUET or Vitremer Luting Cement. Relatively low elastic moduli limit the application of the chemically cured hybrid glass ionomers to the cementation of one- to three-unit cast fixed restorations.

Analysis of Variance↗