Biomechanical properties of the mid-shaft femur in middle-aged hypophysectomized rats

ORIGINAL ARTICLE

Biomechanical properties of the mid-shaft femur in middle-aged hypophysectomized rats as assessed by bending test

Clarisa Bozzini ?Emilio O.Picasso ?

Graciela M.Champin ?Rosa Mar?

′a Alippi ?

Carlos E.Bozzini

Received:17October 2011/Accepted:23January 2012/Published online:3February 2012óSpringer Science+Business Media,LLC 2012

Abstract Both stiffness and strength of bones are thought to be controlled by the ‘‘bone mechanostat’’.Its natural stimuli would be the strains of bone tissue (sensed by osteocytes)that are induced by both gravitational forces (body weight)and contraction of regional muscles.Body weight and muscle mass increase with age.Biomechanical performance of load-bearing bones must adapt to these growth-induced changes.Hypophysectomy in the rat slows the rate of body growth.With time,a great difference in body size is established between a hypophysectomized rat and its age-matched control,which makes it dif?cult to establish the real effect of pituitary ablation on bone bio-mechanics.The purpose of the present investigation was to compare mid-shaft femoral mechanical properties between hypophysectomized and weight-matched normal rats,which will show similar sizes and thus will be exposed to similar habitual loads.Two groups of 10female rats each (H and C)were established.H rats were 12-month-old that had been hypophysectomized 11months before.C rats were 2.5-month-old normals.Right femur mechanical properties were tested in 3-point bending.Structural (load-bearing capacity and stiffness),geometric (cross-sectional area,cortical sectional area,and moment of inertia),and material (modulus of elasticity and maximum elastic stress)properties were evaluated.The left femur was ashed for calcium https://www.sodocs.net/doc/b814749882.html,parisons between parameters were performed by the Student’s t test.Average body

weight,body length,femur weight,femur length,and gastrocnemius weight were not signi?cantly different between H and C rats.Calcium content in ashes was sig-ni?cantly higher in H than in C rats.Cross-sectional area,medullary area,and cross-sectional moment of inertia were higher in C rats,whereas cortical area did not differ between groups.Structural properties (diaphyseal stiffness,elastic limit,and load at fracture)were about four times higher in hypophysectomized rats,as were the bone material stiffness or Young’s modulus and the maximal elastic stress (about 79).The femur obtained from a middle-aged H rat was stronger and stiffer than the femur obtained from a young-adult C rat,both specimens show-ing similar size and bone mass and almost equal geometric properties.The higher than normal structural properties shown by the hypophysectomized femur were entirely due to changes in the intrinsic properties of the bone;it was thus stronger at the tissue level.The change of the femoral bone tissue was associated with a high mineral content and an unusual high modulus of elasticity and was probably due to a diminished bone and collagen turnover.Keywords Bone biomechanics áHypophisis áRat femur áBone quality

Introduction

The effect of hypophysectomy on several physiological variables in the rat has been extensively studied.In relation to bone,adenohypophyseal hormones are important for normal growth of bone as well as maintenance of skeletal mass.Hypophysectomy in young rats slopes the rate of growth with diminution of longitudinal and radial bone growth [1–5],loss of cancellous bone [4],and diminution

C.Bozzini áG.M.Champin áR.M.Alippi áC.E.Bozzini (&)Department of Physiology,Faculty of Odontology,University of Buenos Aires,Buenos Aires,Argentina e-mail:cebozi@?sio.odon.uba.ar

E.O.Picasso

Department of Advanced Statistics,Faculty of Engineering,University of Buenos Aires,Buenos Aires,Argentina

Endocrine (2012)42:411–418DOI 10.1007/s12020-012-9616-0

of cortical bone gain[3,5].The causes of skeletal altera-tions in hypophysectomized rats are associated with decreases in growth-and modeling-dependent bone gain and bone turnover[3,5].Additional biological changes associated with hypophysectomy are reduction in body weight gain and lean body mass[6,7]and development of permanent physiological anemia[8].

It is assumed that the mechanical properties of long bones integrated as organs are directly related to the amount(bone mass),the architectural disposition of bone material,and the mechanical quality of bone material[9, 10].The structural stiffness(measurable as a load/defor-mation ratio)is usually kept high enough to withstand the every day bone deformation to avoid damage and hence fracture.The structural stiffness,and indirectly the strength of bones,is thought to be controlled by the‘‘bone me-chanostat’’[11].This is a feedback mechanism,which optimizes the bone’s design through a permanent re-dis-tribution of the mineralized tissue.

Both body mass and regional muscles mass increase with age in a normal rat.Therefore,a weight-bearing bone, like the femur,will increase its mass and adapt its mechanical properties with time in order to satisfy the mechanical demands imposed by growth.Hypophysectomy is characterized by growth failure,which will be respon-sible,from a theoretical point of view,for the lack of the age and growth-related increment in both body and bone mass.As a consequence,the latter parameters will be signi?cantly lower in a pituitary ablated rat when compared to an age-matched normal rat.The difference will increase in relation to the time after surgery until the normal rat attains its peak of growth.The different growth patterns between normal and hypophysectomized rats create a great dif?culty in analyzing the real effect of hypophysectomy on mechanical bone quality in the rat.In general,bones of different sizes should not be compared.One way to mini-mize the different structural properties that are observed between bones with different mass is the standardization of those properties by relating them to some allometric vari-ables(the body weight of the animals,the mid-diaphyseal cross-sectional area,the bone ash content,etc.).This has been the procedure occasionally employed to compare results from rats of different body size.

In spite of the diminution of linear growth that follows hypophysectomy in the juvenile rat,we have observed that the biomechanical quality of the femoral shaft changes with time:the juvenile femur is transformed in a type of adult bone that is characterized by a high mineral density and an unusual large modulus of elasticity[12].These ?ndings suggest that the femur of the hypophysectomized rat is‘‘overdesigned’’in relation to the mechanical loads acting on it.A similar‘‘stiffening’’response was also evident in the mandible,which is not a weight-bearing bone but subjected to the loads created during mastication (load-bearing bone)[13].The increased elastic modulus of cortical bone in75-day-old hypophysectomized rats has been also observed by Feldman et al.[14].

In order to determine the real effects of hypophysectomy on femoral bone biomechanics,it would be desirable to compare bones obtained from normal and hypophysecto-mized rats both having similar body weights and regional muscular mass.Under these conditions,bones should be exposed to similar load-induced strains and the effects of the absence of adenohypophyseal hormones on bone quality could thus be estimated,by assuming that hypophysectomy does not change the skeletal response to mechanical loading.This brings on to another situation: femora obtained from pituitary-ablated and control rats sharing similar body and muscle masses should have been obligatory obtained from rats of different ages.In relation to age,rats can be considered as young adults(3-month old),mature adults(6-month-old),middle-aged adults(12-month-old),and aged adults(24-month-old).In general,the elastic deformation of aged rats was signi?cantly impaired both at the tissue and the organ levels with increasing age, probably associated with increased mineralization,crys-tallinity,and type-B carbonate substitution[15].However, the maximum breaking force required to fracture femurs at mid-shaft did not change with age because architectural compensations,even though the normalized tissue strength decreased with age[16].The above changes with age were observed in aged adult animals and were not apparent neither in young adults nor in mature adults.In the experiments reported here,we used normal rats aged 2.5months(young adults)and hypophysectomized rats aged12months(middle-aged adults).The ages examined in the present study avoid the large amount of bone mod-eling and skeletal growth characteristic of very young rats (\2-month-old)and ensure the achievement of peak bone mass in older rats,which occurs at*10months in female rats.Concerning these particular ages,it has been demon-strated[15,16]that(1)periosteal and endosteal diameters were not signi?cant different between young and middle-aged rats;(2)that the cross-sectional area of the mid-femoral diaphysis signi?cantly increased with age,being about20%higher in middle-aged rats than in young rats;

(3)moment of inertia about the bending axis of middle-aged rats was about25%higher than in young rats;and(4) that structural stiffness,yield stress,resilience,and bending modulus were not different between young rats and mid-dle-aged rats Thus,by mainly considering the?ndings mentioned in the last paragraph,it is possible to assume that any difference in bone quality found between both types of animals should not be related to age.

The present investigation was designed to estimate the mechanical quality of two bones showing similar sizes and

exposed to similar habitual loads.One of them was obtained from a normal young-adult rat,the other bone from a middle-aged hypophysectomized rat.The purpose of the study was to increase our knowledge in an attempt to explain the reasons that transform a normal bone into an ‘‘overdesigned’’bone after hypophysectomy.

Materials and methods

Experimental design

Two groups of10female Sprague–Dawley rats each (hypophysectomized[H]and control[C])were established.

H rats were12-month old(middle-aged adults)and had been hypophysectomized11months before by the standard parapharyngeal approach.They were purchased from Charles River Laboratory International Inc.,Wilmington, USA.C rats were2.5-month-old(young adults).H rats weighed138.4±7.06g,and C rats weighed139.0±7.97g(P[0.05)at the time of autopsy.C rats were thus weight-matched with H ones,but not age-matched.During the pre-autopsy period(10months for the H rats, 2.5months for the C rats),all animals were allowed free access to water and to a standard pelleted chow diet that has been shown to meet all necessary requirements to allow normal growth and development of rats[17].Animals were maintained under local vivarium conditions(temperature 22–23°C,12-h on/off light cycle).At the time of autopsy, both body weight and length were established.Body length was taken as the distance between nose and tip of tail.Rats were then sacri?ced by ether overdose.The femurs were dissected,cleaned of adhering soft tissue,weighed in a Mettler scale and their lengths measured.They were then stored at-20°C wrapped in gauze soaked with Ringer’s solution in sealed plastic bags,in accordance with Turner and Burr[18].Gastrocnemius muscles were dissected and weighed immediately.

Mechanical testing of femurs

On the day of testing,each bone was thawed at room temperature before analysis.To assess cortical bone mechanical properties,the right femur was tested in3-point bending[19].Each bone was placed horizontally with the anterior side facing down on two transverse support (L=13mm span)and central along its length.Load was applied perpendicularly to the long axis on the bone until fracture.The test machine(Instron model4442,Instron Corp.,Canton,MA,USA)was operated in stroke control at a constant rate of5mm/min,which is useful for describing the static properties of the bone structure.For this biome-chanical test,load/deformation(W/d)curves(Fig.1)showing both the elastic(Hookean behavior)and the plastic(non-Hookean behavior)phases separated by the yielding point,enabled graphic assessment of the main structural mechanical properties of the bone shafts as beams[18]which essentially measures the resistance to both deformation(stiffness)and fracture(strength)and the ability to absorb energy by deforming.They are(a)struc-tural properties(whole-bone properties,as derived from the slope of the W/d curve in the linear region of the elastic behavior):(1)maximal stress de?ection(yield de?ection d y,elastic limit or load at the yielding point W y)represents the endpoint of elastic deformation(yielding point)and de?nes a threshold above which unrecoverable permanent deformation occur,marking the initiation of damage accumulation with the appearance of the?rst microcracks

that occur on the periosteal surface of the bone;it is a measure of the bone strength;(2)structural elastic stiffness (load/de?ection relationship,diaphyseal stiffness,bone beam’rigidity,or slope of the linear phase of the W/d curve)represents the rigidity of the beam or the resistance to deformation;(3)elastic absorption of energy by the whole bone(the total energy absorbed by the specimen up to the yielding point)represents the energy necessary to initiate the?rst microcracks and permanently affect bone structure,and(4)structural strength(whole-bone strength, maximal supported load,ultimate load,load at fracture W f) represents the value of the load at fracture and expresses directly the resistance of the whole bone to fracture, incorporating both the elastic and the plastic behaviors.

(b)geometric properties(bone design characteristics). They are:(1)bone length and diameters:the bone length was measured directly using a digital caliper(Digginess, Geneva,Switzerland)with an accuracy of±100l m;(2) mid-diaphyseal cross-sectional area,CSA:using an Isomet low-speed diamond saw(Buheler,Lake Bluff,IL,USA) the fracture section was regularized to perform micro-morphometrical determinations of the vertical(load direction)and horizontal(right angle to load direction) outer(VOD,HOD)and inner(VID,HID)diameters of the elliptic-shaped fracture sections(Table1).Measurements were taken directly using a stereomicroscope(Stenu DV4, Carl Zeiss Microimagen,Gottingen,Germany)with an accuracy of±0.01mm.CSA was calculated by applying the equation:CSA=3.14(VODáVID-HODáHID)/4;

(3)second moment of inertia of cortical bone(with reference to the anterior–posterior bending axis,xCSMI) as estimating by the equation:xCSMI=(3.14 [VOD3áHOD-VID3áHID/64]).CSMI captures both bone mass and distribution on the cross section.The larger the CSMI,the further the disposition of bone cortical mass from a given reference axis.As bones were tested in anterior-posterior bending,the selected reference axis was the‘‘horizontal’’diameter of the bone cross section,and(4) bone volume between supports:(L p[HOD-HID]);and (4)bone material properties(intrinsic properties of the mineralized tissue)as calculated from structural and geo-metric properties.Thus,bone material properties were not directly determined by mechanical means.They are:(1) Young’s modulus of elasticity(bone material stiffness, intrinsic stiffness,strain–stress relationship)calculated by the formula:E=W yáL3/48ád yáI x(W y=load at the yielding point,L=distance between supports, d y=maximal elastic de?ection,I x=second moment of inertia in relation to the horizontal axis);(2)maximal elastic stress,which expresses the reacting force opposed by the deformed bone to the deforming load(estimation of tissue strength).It was calculated by the formula: r=LáVODáW y/8I x;and(3)energy absorbing capacity (EAC,expressed per unit of bone tissue volume,EAC/vol). It should be pointed out that estimating intrinsic material properties using3-point bending and beam theory is not without limitations[18].Notable sources of artifact include displacement due to indenting at the contact points and nonuniformity of the cross-sectional geometry in the loa-ded portion of the diaphysis.Although these undoubtedly

Table1Femur diaphyseal geometric properties

VOD VID

HOD HID

Parameter C H P

Horizontal OD(mm) 3.47±0.20 3.02±0.28\0.001 Horizontal ID(mm) 2.48±0.26 1.58±0.25\0.0001 Vertical OD(mm) 2.48±0.15 2.13±0.09\0.0001 Vertical ID(mm) 1.64±0.170.94±0.18\0.0001 CSA(mm2) 6.76±0.65 5.05±0.52\0.0001 CtA(mm2) 3.53±0.48 3.86±0.37[0.05 MA(mm2) 3.23±0.68 1.19±0.34\0.0001 WLR0.46±0.10 1.15±0.39\0.0001 xCSMI(mm4) 2.058±0.38 1.36±0.21\0.0002 VOL(mm3)45.90±6.3050.2±4.80[0.05

All data are expressed as mean±SD

CSA cross-sectional area,CtA cortical area,MA medullary area,WLR wall/lumen rati,xCSMI cross-sectional moment of inertia,VOL volume between supports(see text for explanation of the upper diagram)

diminish the accuracy of the derived quantities as true material properties in an absolute term,they are still deemed useful and meaningful for comparative purposes.

Bone ash determination

The left femur of each animal was ashed at600°C in a muf?e furnace for18h and the ash weight obtained.The bone ash was dissolved in2N HCl and calcium content determined by atomic absorption spectrophotometry[20]. Femoral calcium content corresponds to the amount of calcium in ashes.

Statistics

Results were summarized as mean±SD and differences were considered statistically signi?cant at the level of P\https://www.sodocs.net/doc/b814749882.html,parisons between parameters were per-

formed by the Student’s t test by using GraphPad Prism Software(GraphPad Software Inc.,San Diego,CA,USA).

The experiment was conducted in accordance with the principles outlined in the National Institute of Health Guide for the Care and Management of Laboratory Animals,and approved by the University of Buenos Aires Ethics Committee.

Results

At the time of autopsy,average body weight was139.0±7.97g in C rats and138.4±7.06g in H rats(P[ 0.05).Body length(C=30.35±0.70cm;H=30.85±0.34cm),femur weight(C=501.3±30.2mg;H= 528.9±36.2mg),and femur length(C=24.51±0.52mm;H=25.1±0.34mm)were not signi?cantly different between C and H rats.Femoral calcium content was signi?cantly greater(P\0.0003)in H than in C rats (137.9±36.2vs.62.6±16.6mg,respectively).The weight of the gastrocnemius was249.2±30.3mg and 225.4±32.2mg in C and H rats,respectively(P[0.05).

Values of cross-sectional geometry of the femur mid-diaphysis are shown in Table1that includes a schematic diagram showing an approximate representation of the cross-sectional area in C and H rats.The shaded region of each diagram roughly represents the thickness of the cor-tical mineralized area(CtA),which was higher(44%)in H than in C rats.Both horizontal and vertical diameters were signi?cantly higher in the C than in the H groups,as were the cross-sectional area(CSA)and the medullary area (MA).The cortical area(CtA)did not signi?cantly differ between both groups and thus explains the higher cortical wall thickness and the wall/lumen ratio observed in the H animals.The cross-sectional moment of inertia(xCSMI),which was calculated by considering the four diameters measured at the regularized cross-section,was higher in C than in H rats.Structural properties,as derived from the slope of the load/deformation curve in the linear region of the elastic behavior,are shown in Table2.The values for diaphyseal stiffness,the elastic limit,and the load at fracture were4.48,4.44and4.00times higher,respec-tively,in H than in C rats.The elastic absorption of energy by the whole bone was also signi?cantly higher in the former than in the latter(2.08times).Bone material or intrinsic properties of the mineralized tissue,as derived from structural and geometric properties,are also shown in Table2.Bone material stiffness or Young’s modulus of elasticity E and the maximal elastic stress were7.55and 7.89times higher,respectively,in H than in C rats.The elastic energy absorption related to bone tissue volume, was also higher in the former than in the latter(2.08times). Discussion

During the course of the current investigation,we evalu-ated the biomechanical properties of the femoral mid-diaphysis of bones obtained from rats sharing similar body weights but different ages and endocrine-metabolic status: one group of animals was formed by normal young adult rats,the other being integrated by middle-aged adult ani-mals that had been hypophysectomized11months before. Based on previously reported studies[15,16],we have assumed that the differences found between both groups in relation to their femoral biomechanical quality were inde-pendent of the age of the animals.This assumption is further enhanced by data shown in our previously pub-lished work of the subject:the elastic modulus E was2.5 times greater in rats after5months of hypophysectomy Table2Femur diaphyseal mechanical properties in normal and hypophysectomized rats

Parameter C H P Extrinsic

Stiffness(N/mm)63.89±25.60286.39±37.87\0.0001 Elastic limit(N)17.40±4.2977.36±10.82\0.0001 Fracture load(N)23.73±5.7495.01±12.60\0.0001 EEA(N/mm) 3.05±2.019.80±1.78\0.0001 Intrinsic

E(N/mm2)1348.0±356.010182.0±413.0\0.0001 S el(N m2) 1.94±0.7315.31±1.99\0.0001 EEA/vol

(N/mm/mm3)

0.085±0.0510.177±0.062\0.01

All data are expressed as mean±SD

EEA elastic energy absorption,E elastic modulus,S el limit elastic stress

than in age-matched normal rats.Body weight in the latter group was4.18times higher than that in the hypophysec-tomized group[12].However,it should be remembered that for a similar body weight,the body composition of the hypophysectomized rat differs from that of a normal rat, the increment of fat and the diminution of protein contents being the main observations[6,7].It is not known whether these differences could be responsible,at least partially,for the changes induced by hypophysectomy on bone biome-chanics.Finally,bone size and strength are usually related not only to body weight but also to regional muscle mass and strength(customary strain stimulus)[10,21].The weight of the gastrocnemius,one of the regional muscles involucrated,did not differ signi?cantly between C and H rats in this study.These considerations should indicate that the chosen experimental model was suitable for the pur-poses of the current investigation.

For a similar body weight and regional muscle mass,the femoral diaphysis of the middle-aged hypophysectomized rat was stronger than that of a young-adult normal rat.The indicators of whole-bone quality(assimilable to resistance to fracture)were signi?cantly higher in the former than in the latter.Bones fracture when external stresses exceed the local capacity of the material to withstand them[22].

Multiple factors contribute to bone strength.For the present discussion,it is pertinent to brie?y consider only those factors that can make a bone stronger that,according to Turner[23],are the increment of the bone mass,its more ef?cient distribution,and the improvement of the bone material properties(stronger at the tissue level).Thus,it seems necessary to consider the changes,if any,induced on those factors by hypophysectomy in an attempt to give a plausible explanation for the bone effects described here.

Bone size is recognized as an important component of bone strength[24].Structural dimensions or geometry determine the stresses that bones can handle under loading conditions[22].From a mechanical standpoint,increasing the external diameter of a cylinder increases resistance to ?exion[18].When loads act on a long bone in?exion or traction,the ef?ciency of the sectional design depends on the endosteal and periosteal diameters,the absolute and relative(wall/lumen ratio)thickness of the cortical mineralized tissue,and the cross-sectional moments of inertia.Neither the femur size(weight and length)nor the mineralized cortical area(mm2)measured at the mid-shaft cross-section signi?cantly differed between H and C rats. However,both the endosteal and periosteal diameters and the cross-sectional moment of inertia were higher in C than in H rats,whereas the thickness of the cortical mineralized tissue and the wall/lumen ratio were higher in H than in C animals.According to Frost[25],the‘‘mass’’factor (amount of bone in a bone’s cross-section)and the ‘‘architectural’’factor(cross-sectional and longitudinal shapes and size of a bone and the distribution of its com-pacta)affect its strength.Therefore,from the analysis of both factors in the bones of C and H rats,it would be pos-sible,from the geometrical point of view,that the femoral mid-shafts of the C rats should be stronger than that of the H rats because of the higher cross-sectional area and the cross-sectional moment of inertia.The latter appears to be the most important of the geometric factors in the determina-tion of the resistance to deformation under elastic condi-tions.However,if one analyze the equation for the calculation of deformation(d=WL3/(48EI)(W=load, L=distance between supports,E=elastic modulus, I=moment of inertia)one will observe that E is in the denominator,whose value is extremely high in the H rat and thus will cancel the importance of the CSMI as the main geometric determinant of the resistance to deformation.

Although it seems that the‘‘architectural’’factor may apparently favor the bending strength of the femoral diaphysis in the C rats,the measured strength in the bending test indicated that the‘‘whole bone’’stiffness and strength were far superior in H than in C rats.From the analysis of the load/deformation curve,the H femur showed an increased stiffness in elastic conditions,an increased maximal stress de?ection,an increased elastic absorption of energy,and an increased structural strength.

These indicators of the increased whole-bone strength in the H rats in relation to C rats have to be primarily related to changes occurring in the bone material properties after hypophysectomy since they do not appear to be greatly associated to the architectural properties described above.

Focusing on the intrinsic material properties,the dif-ferences found between H and C rats were dramatic.The Young’s modulus of elasticity,the maximal elastic stress, and the EAC expressed per unit of bone tissue volume were signi?cantly higher in H than in C rats.

Bone tissue is a two-phase porous composite material comprised primarily of inorganic bone apatite crystals that mineralize an organic type I collagen matrix,which toge-ther provide its mechanical properties[26].An increase in tissue mineral density increases the stiffness but sacri?ces ?exibility[27].Mineralization of bone matrix is a2-fold process:(1)mineralization of new collagen matrix that starts*5–10days after deposition in the resorption site (primary mineralization);and(2)a much slower process of secondary mineralization that begins after completion of the bone remodeling unit,which progressively adds *50–60%of mineral content on bone matrix over the ensuing months[22].Changes in the bone remodeling rate can in?uence the degree of mineralization of bone[28]. During rapid remodeling,full mineralization cannot occur because resorption resumes before the process is complete.

A similar phenomenon occurs during the modelation phase

of the growth period in which the median degree of min-eralization is low.In the adult,the median degree of mineralization depends on the remodeling rate,or bone turnover[29].When it is low,there is more time for sec-ondary mineralization to proceed,whereas in high turnover rates,recently formed bone is removed before there is time for prolonged secondary mineralization.Reduced bone turnover increases mean tissue age[26].In the present experiments,the young adult rats used as controls had not terminated their growth period and thus their modeling rate may be high.In contrast,Mart?′nez et al.[3]have suggested that bone turnover is lowered in hypophysectomized rats and proved that the total mineral density is thus larger in the cortical bone,suggesting an increase in the normal maturation of the mineralized matrix.The‘‘remodelatory space’’should thus be decreased and the time for secondary mineralization increased.The difference in bone turnover rate between C and H rats in the present study could explain the?nding of the signi?cantly higher(2.29) amount of Ca in the ashes of the whole femur of the H rat in relation to the C rat.The high mineralization of the H bone could be an important determination of its high rigidity.

The contribution of collagen content and bone mineral crystals structure to bone strength is not yet well de?ned [22].The hydroxyapatite crystals of bone mineral con-tribute to the strength and rigidity of the collagen matrix. Collagen contributes to its?exibility,which allows it to absorb energy on loading[26].The role of collagen may be related either to the amount of collagen or its molecular stability and cross-linking.It has been proposed that the inter?brillar pyrrole of bone cross-links have a greater in?uence on the bending strength than the intra?brillar pyridoline cross-links.The reduction in collagen cross-links in rats severely affects the biomechanical properties of cortical bone.The de?ection capacity,the bending strength and elastic stiffness are reduced[30].In contrast, when numerous intermolecular cross-links are formed,they produce a stable,porous structure from which the bone,in part,derives its ultimate yield strength[31].It could be argued that the intermolecular collagen cross-links provide spacing for HAP mineral crystal nucleation and mineral enlargement.Martinez et al.[3]have found a greater amount of the stable nonreducible HP cross-links in the femur of pituitary-de?cient male rats which was attributed to a decrease of collagen turnover in cortical bone that was accompanied by a greater amount of the stable nonreduc-ible HP cross-links.The authors attributed these?ndings to the down-regulation of bone collagen turnover in response to hypophysectomy.These changes in the collagen matrix should be added to the high mineralization of the studied bone in the genesis of its increased stiffness and strength. Other factors are usually thought to affect bone material properties.They are tissue composition,the presence of microdamage,mineral composition,particle size,and dis-tribution.Their participation in the considerable increase in stiffness and strength found in the femoral cortical bone of the hypophysectomized rat is not known at present.

The observed changes in femoral material properties as the result of hypophysectomy could have been derived from the absence of one of all pituitary hormones.It is well established that growth hormone is a major regulator of bone growth and turnover and that administration of growth hormone to hypophysectomized rats can restore normal bone growth and increase turnover.Feldman et al.

[14]have shown that despite reduction in the cortical vBMD,hypophysectomy enhanced as much as70%the intrinsic bending stiffness(E)of cortical bone(in age-matched rats)and that treatment of hypophysectomized rats with increasing doses of rhGH improved the observed reduction of vBMD but did not affect the abnormally enhancement of E.Previously reported studies from this laboratory[32]might suggest that secondary hypothy-roidism induced by the lack of TSH could be at least partially responsible for the unusually large modulus of elasticity found in our hypophysectomized rats.In these studies,performed in young rats made hypothyroid by propylthiouracil,it was observed that the intrinsic mechanical quality of the hypothyroid bone tissue,esti-mated from the modulus of elasticity,was signi?cantly higher than the control bone30d after treatment.This was accompanied by a higher Ca content in femoral ashes. Thus,the femoral shafts of hypophysectomized rats and hypothyroid rats have in common an unusual increment of the intrinsic stiffness and elevated calcium content.In contrast,lack of other adenohypophyseal hormones has not reproduced the bone responses to hypophysectomy[33–35].The increased material stiffness found by Feldman et al.[14]in the femoral shaft of hypophysectomized rats occurred in animals that had been daily injected with 500l g of hydrocortisone,thus suggesting that the absence of ACTH in the hypophysectomized rat might not be responsible for the stiffening of its bone material.

In summary,the femur obtained from a middle-aged hypophysectomized rat was stronger and stiffer than the femur obtained from a young-adult normal rat,both spec-imens showing similar size and bone mass and almost equal geometric properties.The higher than normal struc-tural properties shown by the hypophysectomized femur were entirely due to the changes found in the intrinsic properties of the bone;the bone was thus stronger at the tissue level.This effect would not be the result of a failure of a bone regulatory mechanism operating under the pitu-itary control but the consequence of the lowering rate of physiological aspects of bone physiology.The change of the femoral bone tissue was associated with a high mineral

content and an unusual high modulus of elasticity and was probably due to a diminished bone and collagen turnover. Acknowledgments This investigation was supported by research grants from the University of Buenos Aires(UBACYT 20020100100389and20020100100067).RMA and CEB are Career Investigators from the National Council of Scienti?c and Technical Research(CONICET).

Con?ict of interest The authors declare that they have no con?ict of interest.

Ethical standards Authors declare that the experiments comply with the current laws of the country in which they were performed. References

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Excel函数怎么计算已知出生日期计算员工年龄

Excel函数怎么计算已知出生日期计算员 工年龄 如果老板给你一份关于所有员工的基本资料，里面有他们的出生日期，但是没有年龄，想让你计算出每一位员工的实际年龄，你会怎么做呢?借助Excel函数，可以很好的做到。以下是为您带来的关于Excel函数计算已知出生日期计算员工年龄，希望对您有所帮助。 Excel函数计算已知出生日期计算员工年龄 1、选中C2单元格，切换到“公式”选项卡，在“函数库”组中找

到日期和时间函数TODAY。 2、此时会弹出“函数参数”对话框，上面有对TODAY函数的介绍，说它是返回日期格式的当前日期，且不需要参数，直接确定即可。 3、现在C2单元格中会返回TODAY函数的值，我们双击C2单元格就可以进入编辑状态，然后在现有的公式后加上“-B2”即可。这是

我们一般理解的求年龄的方法，用现在的日期减去出生日期。 4、但是你会发现Excel算出来的结果是一个日期，这是比较容易理解的，因为一个日期减去另外一个日期嘛，结果当然也就是一个日期了，没关系，我们把这个日期换算成一个年份值就好了。Excel中正好有对应的函数，它的名字叫做YEAR。那现在只好委屈一下，让我们之前的那个公式成为YEAR函数的参数咯。

YEAR函数。

6、在弹出的YEAR函数参数对话框中，将之前剪切的内容粘贴到它的参数对应的文本框内，并确定。 7、当我们把日期值换算成一个年份值之后，你发现C2单元格显示的还是一个日期格式的值，那现在我们就要调整它的数字格式了。选

中C2单元格，将其数字格式设置为“常规”。 8、好了，现在C2单元格中显示的是一个数值了，但还是不对，用脑子计算一下，你发现它多了1900年，这是因为Excel函数使用了1900年时间系统，YEAR函数返回的是一个1900至9999之间的值，所以我们自己在现有的公式后减去多出来的1900就好了。

Excel中常用函数及其使用方法简介

目录 一、IF函数——————————————————————————————————2 二、ASC函数—————————————————————————————————4 三、SEARCH函数——————————————————————————————4 四、CONCATENATE函数———————————————————————————4 五、EXACT函数———————————————————————————————5 六、find函数—————————————————————————————————5 七、PROPER函数——————————————————————————————7 八、LEFT函数————————————————————————————————7 九、LOWER函数———————————————————————————————7 十、MID函数————————————————————————————————8 十一、REPT函数———————————————————————————————8 十二、Replace函数——————————————————————————————9 十三、Right函数———————————————————————————————10 十四、UPPER函数——————————————————————————————10 十五、SUBSTITUTE函数———————————————————————————10 十六、VALUE函数——————————————————————————————12 十七、WIDECHAR函数———————————————————————————12 十八、AND函数———————————————————————————————12 十九、NOT函数———————————————————————————————13 二十、OR函数————————————————————————————————13 二十一、COUNT函数—————————————————————————————14 二十二、MAX函数——————————————————————————————15 二十三、MIN函数——————————————————————————————15 二十四、SUMIF函数—————————————————————————————16 二十五、OFFSET函数————————————————————————————17 二十六、ROW函数——————————————————————————————20 二十七、INDEX 函数————————————————————————————21 二十八、LARGE函数—————————————————————————————22 二十九、ADDRESS函数————————————————————————————23 三十、Choose函数——————————————————————————————24 三十一、HLOOKUP函数———————————————————————————24 三十二、VLOOKUP函数———————————————————————————26 三十三、LOOKUP函数————————————————————————————29 三十四、MATCH函数————————————————————————————29 三十五、HYPERLINK函数——————————————————————————30 三十六、ROUND函数————————————————————————————31 三十七、TREND函数—————————————————————————————32

Excel表格中的一些基本函数使用方法

Excel表格中的一些基本函数使用方法 一、输入三个“=”，回车，得到一条双直线； 二、输入三个“~”，回车，得到一条波浪线； 三、输入三个“*”或“-”或“#”，回车，惊喜多多； 在单元格内输入=now（）显示日期 在单元格内输入=CHOOSE(WEEKDAY(I3,2),"星期一","星期二","星期三","星期四","星期五","星期六","星期日") 显示星期几 Excel常用函数大全 1、ABS函数 函数名称：ABS 主要功能：求出相应数字的绝对值。 使用格式：ABS(number) 参数说明：number代表需要求绝对值的数值或引用的单元格。 应用举例：如果在B2单元格中输入公式：=ABS(A2)，则在A2单元格中无论输入正数（如100）还是负数（如-100），B2中均显示出正数（如100）。 特别提醒：如果number参数不是数值，而是一些字符（如A等），则B2中返回错误值“#VALUE！”。 2、AND函数 函数名称：AND 主要功能：返回逻辑值：如果所有参数值均为逻辑“真（TRUE）”，则返回逻辑“真（TRUE）”，反之返回逻辑“假（FALSE）”。

使用格式：AND(logical1,logical2, ...) 参数说明：Logical1,Logical2,Logical3……：表示待测试的条件值或表达式，最多这30个。 应用举例：在C5单元格输入公式：=AND(A5>=60,B5>=60)，确认。如果C5中返回TRUE，说明A5和B5中的数值均大于等于60，如果返回FALSE，说明A5和B5中的数值至少有一个小于60。 特别提醒：如果指定的逻辑条件参数中包含非逻辑值时，则函数返回错误值“#VALUE!”或“#NAME”。 3、AVERAGE函数 函数名称：AVERAGE 主要功能：求出所有参数的算术平均值。 使用格式：AVERAGE(number1,number2,……) 参数说明：number1,number2,……：需要求平均值的数值或引用单元格（区域），参数不超过30个。 应用举例：在B8单元格中输入公式： =AVERAGE(B7:D7,F7:H7,7,8)，确认后，即可求出B7至D7区域、F7至H7区域中的数值和7、8的平均值。 特别提醒：如果引用区域中包含“0”值单元格，则计算在内；如果引用区域中包含空白或字符单元格，则不计算在内。 4、COLUMN 函数 函数名称：COLUMN 主要功能：显示所引用单元格的列标号值。

“智慧课堂”平板电脑管理约定

沧江中学“智慧课堂”平板电脑管理约定 （试行） 信息技术素养是学生成长的核心素养之一。学校今年开始推行“智慧课堂”改革的目的是通过提升学生的信息技术素养，培养学生自主学习能力。让课堂从知识教育走向智慧教育，从培养“知识人”转为培养“智慧者”，用信息化手段来提升教育改革，引领教师和学生追求智慧，让智慧唤醒课堂，让智慧引领师生共同成长。由于信息化教学活动具体有特异性、多变性和不确定性，所以，为了让平板电脑更好辅助学习，规范平板电脑使用行为，特制订定本办法。 一、平板管理： 1、平板电脑必须统一张贴标签，写上班级、学号和姓名。 2、使用前，小组长提前5分钟从充电柜取出并分发组员。 3、使用后，由小组长回收并放充电柜保管。 4、逢周末放假，平板电脑须带回家，学校不作保管。 5、若不服从管理，出现平板电脑丢失或其它后果，责任自负。 6、学校仅提供保管服务，平板电脑质量问题，请自行解决。 二、使用范围： 1、使用时间： （1）课堂上：在老师指导下使用。 （2）晚自修：按老师要求，在规定时间内，使用平板电脑进行辅助学习，完成老师布置的学习任务单（坐班老师监管）。 （3）课堂外：禁止使用（周末放假在家长指导下使用）。 2、使用地点： 只能在教室使用。在宿舍、校园等老师无法监管的地方使用平板电脑，属违规行为。 三、学习行为：

1、正确行为： 网班学习、查找学习资料（百度等）、英语听力（须佩戴耳机）、使用学习软件或APP（盒子鱼、猿题库、纳米盒、魔方格等）、主题学习网站（学科网、C20慕课联盟、微课网等）、看教师录制的微视频…… 说明：上课老师和座班老师应不定时检查学生的平板电脑使用行为，进行及时指导和监督。 2、禁止行为： QQ聊天、微信聊天、网络购物、玩游戏、看电影、听音乐、看小说、发微博、设置平板开机密码…… 说明：上课老师和座班老师发现以上不良行为的，应马上纠正并进行教育，同时将有关情况向班主任反馈。 四、其它说明： 1、使用平板电脑学习时，必须严格按要求进行学习，不得进行与学习无关的操作。 2、平板电脑在学校的唯一用途是学习，不能安装与学习无关的软件或下载、存储无关资料。 3、发现平板电脑违规行为的，德育量化考核扣5分/次，并写约800字保证书，严重者向家长通报。 佛山市高明区沧江中学 二〇一五年十月十日…………………………回执……………………………… 注：本回执请在周日晚交回班主任。

Excel如何根据身份证号码自动计算年龄

Excel如何根据身份证号码自动计算年龄方法1 1.打开要在excel中编辑的表格 2.如图所示，在身份证号后面的空格即年份一列第一格输入公式=MID(A2,7,4)，输入完成后按下enter键，A2指身份证号的单元格，数字7为数字开始位置，4为字符个数 3.按下enter键后，如图所示年份一栏已显示出出生年份 4.如图所示，选中已显示年份的一格，鼠标点击绿色框右下角的小方框并下拉至身份证号的最后一栏 5.如图所示，每个身份证号对应的年份都显示出来了 6.如图所示再在年龄一列第一格输入公式2018-MID（A2，7，4），按下enter键 7.即可看到年龄已被计算出来为21岁，如图所示鼠标点击绿色框右下角的小方框并下拉至身份证号的最后一栏 8.如图所示，用这种“自动填充”功能，就能让同类型单元格有同样的公式计算结果 方法2 1.打开要在excel中编辑的表格,并选中年龄那一列的第一格 2.点击公式 3.再点击插入函数 4.在弹出来的对话框中在选择函数那一栏点击全部 5.下拉右侧的滚动条找到MID函数点击它

6.点击右下角的确定 7.在弹出来的对话框中点击第一格 8.然后点击Excel文档中的A2单元格 9.在第二格中输入数字7，表示数字开始位置 10.在第三格中输入数字4，表示字符个数为四个 11.最后单击确定 12.即可看到该身份证号的年份已经算出来了 13.然后在该公示前输入2018-即公式2018-MID（A2，7，4）按下enter键 14.即可看到年龄计算出来为21岁，下拉该单元格右下角的小黑方使下面的单元格拥有同样的计算格式 15.最后即可看到所有的年龄就被计算出来了

Excel常用函数及使用方法

excel常用函数及使用方法 一、数字处理 （一）取绝对值：=ABS(数字) （二）数字取整：=INT(数字) （三）数字四舍五入：=ROUND(数字,小数位数) 二、判断公式 （一）把公式返回的错误值显示为空： 1、公式：C2=IFERROR(A2/B2,"") 2、说明：如果是错误值则显示为空，否则正常显示。 （二）IF的多条件判断 1、公式：C2=IF(AND(A2<500,B2="未到期"),"补款","") 2、说明：两个条件同时成立用AND,任一个成立用OR函数。 三、统计公式 （一）统计两表重复 1、公式:B2=COUNTIF(Sheet15!A:A,A2) 2、说明：如果返回值大于0说明在另一个表中存在，0则不存在。 （二）统计年龄在30~40之间的员工个数 公式=FREQUENCY(D2:D8,{40,29} （三）统计不重复的总人数 1、公式：C2=SUMPRODUCT(1/COUNTIF(A2:A8,A2:A8)) 2、说明：用COUNTIF统计出每人的出现次数，用1除的方式把出现次数变成分母，然后相加。

（四）按多条件统计平均值 =AVERAGEIFS(D:D,B:B,"财务",C:C,"大专") （五）中国式排名公式 =SUMPRODUCT(($D$4:$D$9>=D4)*(1/COUNTIF(D$4:D$9,D$4:D$9))) 四、求和公式 （一）隔列求和 1、公式：H3=SUMIF($A$2:$G$2,H$2,A3:G3) 或=SUMPRODUCT((MOD(COLUMN(B3:G3),2)=0)*B3:G3) 2、说明：如果标题行没有规则用第2个公式 （二）单条件求和 1、公式：F2=SUMIF(A:A,E2,C:C) 2、说明：SUMIF函数的基本用法 （三）单条件模糊求和 说明：如果需要进行模糊求和，就需要掌握通配符的使用，其中星号是表示任意多个字符，如"*A*"就表示a前和后有任意多个字符，即包含A。 （四）多条求模糊求和 1、公式：=SUMIFS(C2:C7,A2:A7,A11&"*",B2:B7,B11) 2、说明：在sumifs中可以使用通配符* （五）多表相同位置求和 1、公式：=SUM(Sheet1:Sheet19!B2) 2、说明：在表中间删除或添加表后，公式结果会自动更新。

用Excel函数计算年龄几法

用Excel函数计算年龄几法 在Excel中利用系统时间和出生年月计算年龄是人事管理、工资统计中经常性遇到的工作，笔者由于工作关系对此有些研究，现将有关计算方法介绍如下，供读者朋友们参考： 一、利用DAYS360、CEILING和TRUNC函数 1.函数简介 ①DAYS360函数 它能按每年360天(每月30天)计算出两个日期间的天数，作为计算工龄的工具非常方便。它的语法为： DAYS360(Start_date，end_date，method) 其中，Start_date是计算时间段的起始日期，end_date是计算时间段的结束日期，method用来指定计算方法的逻辑值(取FALSE或忽略使用美国方法，取TRUE则使用欧洲方法)。 另外，不同地方计算工龄的规则不尽相同。有的按“虚工龄”计算，如1998年6月1日至2000年12月31日工龄为3年；而有的则按“实工龄”计算，1998年6月1日至2000年12月31日工龄为2年；对此可使用CEILING函数或TRUNC函数处理。 ②CEILING函数 它的语法为： CEILING(number，significance) 其中number为待计算的数值，significance确定取整计算的倍数；该函数可将number沿着绝对值增大的方向，计算出一个最接近(或最小倍数significance)的整数。 ③TRUNC函数 它的作用是将数字的指定部分截去，计算出一个最接近的整数或小数，语法为： TRUNC(number，num_digits) 其中number为待计算的数值，num_digits用于指定小数部分的截取精度，取0时不保留小数、取1时保留一位小数(依次类推)。 2.计算公式 ①“虚工龄” 根据计算要求和有关函数的特点，计算“虚工龄”的公式为：“=CEILING((DAYS360(A1，B1))/360，1)”。公式中的A1和B1分别存放工龄的起止日期，“DAYS360(A1，B1)”计算两个日期间的天数，(DAYS360(A1，B1))/360则按一年360天计算出工龄。由于工龄一般以年为单位，故用CEILING函数将上面的计算结果(沿绝对值增大的方向)取整，从而得出“虚工龄”。 ②“实工龄” 计算“实工龄”的公式为：“=TRUNC((DAYS360(A1，B1))/360，0)”，公式中计算工龄天数的方法与上面的相同。TRUNC函数将(DAYS360(A1，B1))/360的计算结果截去小数部分，从而得出“实工龄”。如果计算结果需要保留一位小数，只须将公式修改为“=TRUNC((DAYS360(A1，B1))/360，1)”即可。 二、YEAR和RIGHT函数 1.函数简介 ①YEAR函数 它可以计算出日期序列数(如两个日期相减的结果)所对应的年份数，其语法为：YEAR(Serial_ number)，其中Serial_ number为待计算的日期序列数，既可以是一个具体的数值，也可以是一个表达式。

Excel常用函数的使用方法

1、ABS函数 函数名称：ABS 主要功能：求出相应数字的绝对值。 使用格式：ABS(number) 参数说明：number代表需要求绝对值的数值或引用的单元格。 应用举例：如果在B2单元格中输入公式：=ABS(A2)，则在A2单元格中无论输入正数（如100）还是负数（如-100），B2中均显示出正数（如100）。 特别提醒：如果number参数不是数值，而是一些字符（如A等），则B2中返回错误值“#VALUE！”。 2、AND函数 函数名称：AND 主要功能：返回逻辑值：如果所有参数值均为逻辑“真（TRUE）”，则返回逻辑“真（TRUE）”，反之返回逻辑“假（FALSE）”。 使用格式：AND(logical1,logical2, ...) 参数说明：Logical1,Logical2,Logical3……：表示待测试的条件值或表达式，最多这30个。 应用举例：在C5单元格输入公式：=AND(A5>=60,B5>=60)，确认。如果C5中返回TRUE，说明A5和B5中的数值均大于等于60，如果返回FALSE，说明A5和B5中的数值至少有一个小于60。 特别提醒：如果指定的逻辑条件参数中包含非逻辑值时，则函数返回错误值“#VALUE!”或“#NAME”。 3、AVERAGE函数 函数名称：AVERAGE 主要功能：求出所有参数的算术平均值。 使用格式：AVERAGE(number1,number2,……) 参数说明：number1,number2,……：需要求平均值的数值或引用单元格（区域），参数不超过30个。

应用举例：在B8单元格中输入公式：=AVERAGE(B7:D7,F7:H7,7,8)，确认后，即可求出B7至D7区域、F7至H7区域中的数值和7、8的平均值。 特别提醒：如果引用区域中包含“0”值单元格，则计算在内；如果引用区域中包含空白或字符单元格，则不计算在内。 4、COLUMN 函数 函数名称：COLUMN 主要功能：显示所引用单元格的列标号值。 使用格式：COLUMN(reference) 参数说明：reference为引用的单元格。 应用举例：在C11单元格中输入公式：=COLUMN(B11)，确认后显示为2（即B列）。 特别提醒：如果在B11单元格中输入公式：=COLUMN()，也显示出2；与之相对应的还有一个返回行标号值的函数——ROW(reference)。 5、CONCATENATE函数 函数名称：CONCATENATE 主要功能：将多个字符文本或单元格中的数据连接在一起，显示在一个单元格中。 使用格式：CONCATENATE(Text1，Text……) 参数说明：Text1、Text2……为需要连接的字符文本或引用的单元格。 应用举例：在C14单元格中输入公式：=CONCATENATE(A14,"@",B14,".com")，确认后，即可将A14单元格中字符、@、B14单元格中的字符和.com连接成一个整体，显示在C14单元格中。 特别提醒：如果参数不是引用的单元格，且为文本格式的，请给参数加上英文状态下的双引号，如果将上述公式改为：=A14&"@"&B14&".com"，也能达到相同的目的。 6、COUNTIF函数 函数名称：COUNTIF 主要功能：统计某个单元格区域中符合指定条件的单元格数目。 使用格式：COUNTIF(Range,Criteria) 参数说明：Range代表要统计的单元格区域；Criteria表示指定的条件表达式。

excel中的vlookup函数的使用方法及注意事项

excel博大精深，其使用中有许多细节的地方需要注意。 vlookup函数的使用，其语法我就不解释了，百度很多，其实我自己也没看懂语法的解释，下面就按照我自己的理解来说说怎么用的。首先，这个函数是将一个表中的数据导入另一个表中，其中这两个表有一列数据是相同项，但是排列顺序不同。举例说明； 表1 表2 将表1中的face量一列导入表2中，但两表中的名称一列的排列顺序是不同的。此时需要使用vlookup函数。 下面介绍vlookup的使用方法。

将鼠标放到表2中的D2单元格上，点击fx,会出现一个对话框，里面有vlookup函数。若在常用函数里面没有，下拉找“查找与引用”，里面有此函数。点确定。表示此函数是在表2中的D2单元格中应用。 此时出现对话框： 在第个格里输入B2，直接用鼠标在表2中点击B2单元格即可。表示需要在查找的对象是表2中的B2单元格中的内容。

然后是第二个格，点表1，用鼠标选择整个表的所有数据。表示要在表1中的B1—C14区域查找表2中的B2单元格中的内容。

第三个格里输入在表2中要导入的列数在表1中的列数的数字。在此例中为C列，其列数数字为2.表示将表1中（B1—C14）区域中查找到的单元格里的内容相对应的列（第2列）中的单元格中的内容（face量列中的数据）导入表2中相应的单元格（D2）。 最后一个格中输入“0”。表示查找不到就出现#N/A。点确定，即出现相应数据，然后下拉复制格式。

当下拉出现这种情况的时候： 其实是其查找区域在下拉过程中随着行的改变而改变了。需要对查找区域做一下固定。其方法为，在选择区域后，在区域前面加“$”号（$B$1：$C$14）。

平板电脑优学派

平板电脑优学派 平板电脑优学派如何，平板电脑优学派了解，今天就来细说平板电脑优学派，自平板电脑优学派上市以来，颇受学生及家长们的好评。那么平台电脑优学派究竟有啥特别之处？下面小编来简单分析一下。 2011年，诺亚舟推出震撼中国教育界、对教育信息化发展有突破性贡献的“云学习”平台，它以“云思想”来构建知识系统，以学习者为中心，以互动探究为特色，提供量身定制的个性化精准学习内容与服务，在此基础上，诺亚舟延伸出了“优学派”。 平板电脑优学派系列产品理念： 平板电脑优学派是“云学习”的承载终端，通过它，学习者可在“云引擎”强大动力支持下，对云学习平台上的内容实现随时随地、即需即学的互动探究式学习。 开放：让你不再受封闭学习环境的限制，同步共享云学习平台上的海量知识宝库！ 便捷：让你随时获取新鲜、源源不断的优质资源，不再担心机器内存容量不够！ 人性化：只根据你的需求推送精准个性化学习内容，你的学习轨迹自己掌控！ 自主性：让你可以根据自己的学习轨迹，自由下载、卸载机器里的功能，很酷！ 平板电脑优学派系列产品特色： 基于引领全球教育发展方向的U-learning泛在学习理念 U-learning倡导通过智能化的学习环境和工具，让学习者无论在何时何地都能进行主动高效的学习，与传统的狭窄学习模式有很大的差异。 基于创新科技的知识云服务 知识云的强大在于：通过云计算把百万网民贡献的各种百科知识，整合成一个脉络清晰、互相关联的宝藏群，供所有用户共享，彻底改变了封闭、孤立、简单堆积的知识呈现。 基于诺亚舟十年电教行业精髓沉淀

十四年教育行业的深耕细作让诺亚舟积累了大量宝贵的教育资源和经验，“优学派”是诺亚舟所有精髓的完美呈现。 基于全球领先的“互动U学”学习平台 “互动U学”平台的出现将彻底颠覆被动、孤立、封闭的学习环境和模式，在中国教育史上的有着划时代的里程碑意义。

EXCEL中常用函数及使用方法

EXCEL中常用函数及使用方法 Excel函数一共有11类：数据库函数、日期与时间函数、工程函数、财务函数、信息函数、逻辑函数、查询和引用函数、数学和三角函数、统计函数、文本函数以及用户自定义函数。 1.数据库函数 当需要分析数据清单中的数值是否符合特定条件时，可以使用数据库工作表函数。例如，在一个包含销售信息的数据清单中，可以计算出所有销售数值大于1,000 且小于2,500 的行或记录的总数。Microsoft Excel 共有12 个工作表函数用于对存储在数据清单或数据库中的数据进行分析，这些函数的统一名称为Dfunctions，也称为D 函数，每个函数均有三个相同的参数：database、field 和criteria。这些参数指向数据库函数所使用的工作表区域。其中参数database 为工作表上包含数据清单的区域。参数field 为需要汇总的列的标志。参数criteria 为工作表上包含指定条件的区域。 2.日期与时间函数 通过日期与时间函数，可以在公式中分析和处理日期值和时间值。 3.工程函数 工程工作表函数用于工程分析。这类函数中的大多数可分为三种类型：对复数进行处理的函数、在不同的数字系统（如十进制系统、十六进制系统、八进制系统和二进制系统）间进行数值转换的函数、在不同的度量系统中进行数值转换的函数。 4.财务函数 财务函数可以进行一般的财务计算，如确定贷款的支付额、投资的未来值或净现值，以及债券或息票的价值。财务函数中常见的参数： 未来值(fv)--在所有付款发生后的投资或贷款的价值。 期间数(nper)--投资的总支付期间数。 付款(pmt)--对于一项投资或贷款的定期支付数额。 现值(pv)--在投资期初的投资或贷款的价值。例如，贷款的现值为所借入的本金数额。 利率(rate)--投资或贷款的利率或贴现率。 类型(type)--付款期间内进行支付的间隔，如在月初或月末。 5.信息函数 可以使用信息工作表函数确定存储在单元格中的数据的类型。信息函数包含一组称为IS 的工作表函数，在单元格满足条件时返回TRUE。例如，如果单元格包含一个偶数值，ISEVEN 工作表函数返回TRUE。如果需要确定某个单元格区域中是否存在空白单元格，可以使用COUNTBLANK 工作表函数对单元格区域中的空白单元格进行计数，或者使用ISBLANK 工作表函数确定区域中的某个单元格是否为空。 6.逻辑函数 使用逻辑函数可以进行真假值判断，或者进行复合检验。例如，可以使用IF 函数确定条件为真还是假，并由此返回不同的数值。

学习平板电脑学习机营销把握几个关键点

3、采取合理的渠道政策：渠道政策有两类，一类是控制性政策，另一类是支持性政策，两类政策相辅相成，缺一不可。控制性政策主要是对渠道成员的资金能力、资源能力、市场能力、管理能力、信誉能力、销售政策、回款政策等的约束规定;支持性政策主要是形象支持、价格支持、广告支持、促销支持、公关支持、培训支持等激励措施。厂商在选择渠道成员时，应综合考虑自身的优劣势、市场地位、竞争能力、市场目标等，量体裁衣，注意适度。不同的渠道成员有着不同的需求侧重，厂商可以因地制宜，灵活制定合作政策，但一定要注意不失“平等”。 4、采取有效的招商方式：对于资金实力雄厚的企业，可以通过广告进行招商。对于资金短缺的企业，也可以通过销售人员进行招商，如：通过查询资料电话联络渠道成员，或到各销售终端寻找渠道成员等。 四、品牌传播层面： 说到品牌，诸如“候博士”、“文曲星”、“好记星”、“太奇奇记本”等，这些名字不得不令人叫好。说到品牌传播，学习机产品正处于教育市场阶段，产品广告占主流(品牌广告一般在产品认知宣传完成以后进行)，一些小品牌甚至没有广告。现阶段，学习机产品在品牌传播方面应该注意以下几点： 1、广告诉求不但要说功能，更要讲利益。大卫·奥格威曾经说过：顾客买的不是“钻子”，而是“钻子”钻的洞。对于学习产品，具有某种功能，是为了帮助消费者解决某方面的需求。正如“好记星”的广告：它具有XXX几大功能，它可以帮助孩子们解决XXX 几大难题。在进行广告诉求时，一定要把产品利益和消费者需求结合起来。 2、导入品牌形象，创造品牌差异化优势。“好记星”的广告虽然一直在讲产品的功能和利益，但“外教老师”的鼎立推荐却不离其中。学习机产品虽然出世不久，但市场却处于高速发展状态，市场很快就会进入成熟阶段，产品的“同质化”程度也会越来越高，竞争将由产品竞争转入品牌竞争，产品功能以外的其它影响因素将越来越重要，消费者也将通过品牌的各种识别元素来寻找自我。所以，利用形象代言人、个性化视觉符号等建立差异化品牌优势势在必行。 3、注意品牌背后的支撑点。品牌背后的组织是一群什么样的人，跟我有什么关系?他们有实力吗?等，对消费者的情绪都有极大的影响。所以，组织的教育权威性、与世界接轨性、与课堂的关联性等问题将越来越受消费者的关注。学习机厂商必须学会“虚拟经营”，创造权威性和可信度。 4、有效选择品牌与消费的接触点。电视广告既可以针对渠道成员，也可以针对家长、老师，还可以针对学生，其宣传面广。学习类的杂志广告可谓是最好的“终端媒体”，它可以使产品(品牌)与消费者亲密接触。另外，厂商还可以考虑与学校联合搞各种形式

Excel中最精确的计算年龄的公式

Excel中最精确的计算年龄的公式( 网上搜到的共式大概有这么几种： 1、计算出生日期到某一指定日期（一般选用某年的最后一天入2006年12月31日）的的天数，然后除以360 ，得到一个数值，然后用 int()函数取整，得出需要的年龄。一般使用的公式如下： =IF(C12="","",INT(DAYS360(C12,"2006-12-31")/360)) 聪明一点的人知道使用这个公式， =IF(C12="","",INT(DAYS360(C12,TODAY())/360)) 这个方法，这个公式的弊端在于，一、将每个月默认为30天去计算两个日期之间的天数，二、将每年默认为360天去计算年龄。这种方法显然不精确。 2、年份直接相减 计算周岁 =YEAR(NOW())-YEAR(C12) 计算虚岁 =YEAR(NOW())-YEAR(C12)+1 这种算法的精确程度显而易见，粗略估算还算可以。 3、使用DATEDIF函数 这种方法与第一种方法采用了相同的思路，但是其的精确程度显然比第一种方法要高，这取决于DATEDIF函数本身的精确性。 =IF(C12="","",INT(DATEDIF(C12,"1983-3-20","D")/365)) 或者， =IF(C12="","",INT(DATEDIF(C12,now(),"D")/365)) 但是这种方法强行将一年固定为365天，我们知道通常情况每个四年就有一年是366天所以这种算法也不是很精确。 通过认真分析，我觉得只有结合我们计算年龄的实际方法，才能编制出准确无误的公式。首先分析人们计算年龄的方法，例如，笔者系1983年3月20日生人，如果要在2007年3月23日这天计算他的年龄，通常采用这样的方法。首先，人们会用2007减去1983得出的年龄为24岁，然后再看看他“满没满”24岁，就是看看出生的月份和日期比今天早还是晚，如果出生日期晚于今天则表示没有满，那么他的年龄就应该是2007-1983-1=23岁。如果出生日期早于今天或者就是今天，就说明他已经满了24岁或者正好满24岁，则他的年龄就是 2007-1983=24岁。分析清楚了计算年龄的过程我们再根据这个过程编写公式就很容易了。 综上，我编写了如下公式，在实际应用中将公式中所有的C12替换为，你的所使用的出生日期所在的表格行号列号组合即可。如（A1，B2等等） =IF(MONTH(NOW())MONTH(C12),YEAR(NOW())-YEAR(C12),IF(DAY(NOW())>=DAY(C12),YEAR(N OW())-YEAR(C12),YEAR(NOW())-YEAR(C12)-1))) 公式说明

Excel中函数的使用方法

各函数使用方法大全 Excel函数使用方法 1、ABS函数 主要功能：求出相应数字的绝对值。 使用格式：ABS(number) 参数说明：number代表需要求绝对值的数值或引用的单元格。 应用举例：如果在B2单元格中输入公式：=ABS(A2)，则在A2单元格中无论输入正数（如100）还是负数（如-100），B2中均显示出正数（如100）。 特别提醒：如果number参数不是数值，而是一些字符（如A等），则B2中返回错误值“#VALUE！”。 2、AND函数 主要功能：返回逻辑值：如果所有参数值均为逻辑“真（TRUE）”，则返回逻辑“真（TRUE）”，反之返回逻辑“假（FALSE）”。 使用格式：AND(logical1,logical2, ...) 参数说明：Logical1,Logical2,Logical3……：表示待测试的条件值或表达式，最多这30个。 应用举例：在C5单元格输入公式：=AND(A5>=60,B5>=60)，确认。如果C5中返回TRUE，说明A5和B5中的数值均大于等于60，如果返回FALSE，说明A5和B5中的数值至少有一个小于60。 特别提醒：如果指定的逻辑条件参数中包含非逻辑值时，则函数返回错误值“#VALUE!”或“#NAME”。 3、AVERAGE函数 主要功能：求出所有参数的算术平均值。 使用格式：AVERAGE(number1,number2,……) 参数说明：number1,number2,……：需要求平均值的数值或引用单元格（区域），参数不超过30个。 应用举例：在B8单元格中输入公式：=AVERAGE(B7：D7,F7：H7,7,8)，确认后，即可求出B7至D7区域、F7至H7区域中的数值和7、8的平均值。 特别提醒：如果引用区域中包含“0”值单元格，则计算在内；如果引用区域中包含空白或字符单元格，则不计算在内。 4、COLUMN 函数 主要功能：显示所引用单元格的列标号值。 使用格式：COLUMN(reference) 参数说明：reference为引用的单元格。

EXCEL利用身份证号码计算年龄以及年龄分段的技巧

在EXCEL中如何利用身份证号码计算出生年月年龄及性别 1、身份证号码简介（18位）： 1～6位为地区代码；7～10位为出生年份；11～12位为出生月份；13～14位为出生日期；15～17位为顺序号，并能够判断性别，奇数为男，偶数为男；第18位为校验码。 2、确定“出生日期”： 18位身份证号码中的生日是从第7位开始至第14位结束。提取出来后为了计算“年龄”应该将“年”“月”“日”数据中添加一个“/”或“-”分隔符。 ①正确输入了身份证号码。(假设在D2单元格中) ②将光标定位在“出生日期”单元格(E2)中，然后在单元格中输入函数公式 “=MID(D2,7,4)&"-"&MID(D2,11,2)&"-"&MID(D2,13,2)”即可计算出“出生日期”。 关于这个函数公式的具体说明：MID函数用于从数据中间提取字符，它的格式是:MID （text,starl_num,num_chars）。 Text是指要提取字符的文本或单元格地址（上列公式中的D2单元格）。 starl_num是指要提取的第一个字符的位置（上列公式中依次为7、11、13）。 num_chars指定要由MID所提取的字符个数(上述公式中，提取年份为4，月份和日期为2）。 多个函数中的“&”起到的作用是将提取出的“年”“月”“日”信息合并到一起，“/”或“-” 分隔符则是在提取出的“年”“月”“日”数据之间添加的一个标记，这样的数据以后就可以作为日期类型进行年龄计算。操作效果如下图：

3、确定“年龄”： “出生日期”确定后，年龄则可以利用一个简单的函数公式计算出来了：将光标定位在“年龄”单元格中，然后在单元格中输入函数公式“=INT((TODAY()-E2)/365)”即可计算出“年龄”。 关于这个函数公式的具体说明： ①TODAY函数用于计算当前系统日期。只要计算机的系统日期准确，就能立即计算出当前的日期，它无需参数。操作格式是TODAY（）。 ②用TODAY（）-E2，也就是用当前日期减去出生日期，就可以计算出这个人的出生天数。 ③再除以“365”减得到这个人的年龄。 ④计算以后可能有多位小数，可以用【减少小数位数】按钮，将年龄的数值变成“整数”，也可在公式= (TODAY()-E2)/365中再嵌套一个“INT”函数取整数，即 “ =INT((TODAY()-E2)/365)”，这样就会自动将后面的小数去掉，只保留整数部分。操作效果如下图： 还有一种函数（datedif）可以解决这个问题：这个函数用于计算两个日期之间的天数、月数或年数。 语法：DATEDIF(start_date,end_date,unit) start_date为一个日期，它代表时间段内的第一个日期或起始日期。 end_date为一个日期，它代表时间段内的最后一个日期或结束日期。

教师信息技术培训资料28862学习资料

教师信息技术培训资料2015-2016学年度 第二学期 东风小学 2016年3月1日

教师信息技术培训目录 一、培训计划 二、培训教案 三、活动记录 四、培训总结

学校教师信息技术培训计划 2015-2016学年度 第二学期 一、指导思想 为加快我校教育信息化进程，提高全校教师信息技术运用能力，经研究决定，对全校教师进行信息技术提高培训。 二、目的要求 1、、能使用电子信箱、进入百度云平台。 2、微课制作和智慧课课堂平台使用。 3、完善自己账号国家教育的资源库。 三、培训教师和地点： 蔡静玲计算机多媒体教室 四、培训时间： 从2016年3月1日开始每月一次，时间为周三下午。3月份班任学习月份科任学习。 五、参加对象： 全员教师培训 六、培训内容： 主要包括以下二个方面的内容： 1、微课宝使用 2、智慧课堂平台使用 七、培训方式：

1、示范讲授与动手操练相结合。 2、集中培训与分散练习相结合。 3、自主探索与协作研讨相结合。 八、培训要求与考核办法 1、严格考勤制度。参训教师按时参加培训，不得无故缺席。 2、辅导教师认真备课，耐心辅导。 3、每一位老师结合自己的教学实际设计制作一节微课和平台习题内容。 4、完善自己账号国家教育的资源库。

微课培训教案 培训教师：蔡静玲 微课视频制作培训方案 1 什么是微课？ “微课”是指为使学习者自主学习获得最佳效果，经过精心的信息化教学设计，以视频形式展示的围绕某个知识点或教学环节开展的简短、完整的教学活动。精美的视频配上悦耳的音乐，达到学习知识的目的，并引发学生更深入的思考。它的形式是自主学习，通过内容的可视化及精美的制作，目的是最佳效果，内容是某个知识点或教学环节，时间是简短的，本质是完整的教学活动。因此，对于老师而言，最关键的是要从学生的角度去制作微课，而不是在教师的角度去制作，要体现以学生为本的教学思想。 2 微课的主要特点 微课只讲授一两个知识点，没有复杂的课程体系，也没有众多的教学目标与教学对象，看似没有系统性和全面性，许多人称之为“碎片化”。但是微课是针对特定的目标人群、传递特定的知识内容的，一个微课自身仍然需要系统性，一组微课所表达的知识仍然需要全面性。 3 微课的特征有： （1）主持人讲授性。主持人可以出镜，可以话外音。 （2）流媒体播放性。可以视频、动画等基于网络流媒体播放。 （3）教学时间较短。5-10分钟为宜，最少的1-2分钟，最长不宜超过20分钟。 （4）教学内容较少。突出某个学科知识点或技能点。 （5）资源容量较小。适于基于移动设备的移动学习。 （6）精致教学设计。完全的、精心的信息化教学设计。 （7）经典示范案例。真实的、具体的、典型案例化的教与学情景。 （8）自主学习为主。供学习者自主学习的课程，是一对一的学习。 （9）制作简便实用。多种途径和设备制作，以实用为宗旨。 （10）配套相关材料。微课需要配套相关的练习、资源及评价方法。 4 微课的表现形式 微课可以是一种策略课程，但是小策略，解决教学大问题；或是一种反思课程，通过小的细节，引发对问题的深度思考；或是一个故事课程，小故事中启迪教育实践；或是电影课程，从视听盛宴中了解世界；或是经典阅读，从经典故事中启迪大智慧；或是学科课程，让课堂增加视听元素；或是学生课程，让学生参与经典享受；或是家长课程，让家长吸纳高端教育。 5 微课的分类 （1）按照课堂教学方法来分。微课划分为11类，分别为讲授类、问答类、启发类、讨论类、演示类、练习类、实验类、表演类、自主学习类、合作学习类、探究学习类。 （2）按课堂教学主要环节分类。微课类型可分为课前复习类、新课导入类、知识理解类、练习巩固类、小结拓展类。其它与教育教学相关的微课类型有：说课类、班会课类、实践课类、活动类等。 6 微课制作标准 （1）微课功能理解透彻：解惑而非授业。 （2）时间不超过十分钟。

2016新编Excel中根据出生日期计算年龄的公式

2016新编Excel中根据出生日期计算年龄的公式 1、“出生日期”单元格格式全部设置为“日期”(如输入< xmlnamespace prefix ="st1" ns ="urn:schemas-microsoft-com:office:smarttags" />1965年3月28日，在键盘录入时应输入为1965-3-28)< xmlnamespace prefix ="o" ns ="urn:schemas-microsoft-com:office:office" /> 2、年龄单元格格式设置为“常规” 根据出生日期计算年龄的公式=YEAR(NOW())－YEAR(出生日期单元格)，计算出一个单元格后用填充柄向下填充。(此公式在年龄单元格内输入) 注意：此公式是当前日期减出生日期，每过一年计算出的年龄将自动增加。应注意把计算机的日期校准。 但是我们会发现以上公式有时并不能完全满足我们的要求。 比如说：计算学生从出生年月到统计年月（如2010年8月31日）的周岁，忽略了月份。如2003年5月和2003年10月出生的两个学生，分别是7岁和6岁，而使用上面的计算方法计算出来的结果都是7岁。 如何解决这个问题呢？我们可以采取以下方法。 首先，要求保持“出生年月”、“统计年月”单元格的“日历”属性，以方便其他数据库软件的调用，如2003年5月21日，在数据输入时要采用Excel认可的日期格式（如2003-5-21），而不能为了计算方便输入成2003.5。（当然，如果日期格式没有正确输入当然也有解决的方法，在此暂且不作详细说明。） 然后我们可以进行以下几个步骤的操作： 1. 在Excel中打开“全校学生花名册”文件（此文件已在开学初完成，其中含全校学生的姓名（A列）、性别（B列）、出生年月（C 列）等信息）。 2. 在数据库文件中新建一列（D列），并命名为“统计年月”，在D2中（第一个学生对应的单元格）输入“2010-8-31”，然后将鼠标移到此单元格的右下角，光标变成“+”后，按住[Ctrl]键（切记），此时光标会变成两个“+”，向下拖动复制单元格，快速完成每个学生“统计年月”的输入。 3. 再在文件中新建一列（E列），并命名为“年龄”，鼠标点击表头上的E，选中此列，单击菜单[格式]→[单元格]→[数字]，选择“数值”，并将“小数位数”设为0。在E2（第一个学生对应的单元格）