Flexoelectricity in Bones

Bones generate electricity under pressure, and this electromechanical behavior is thought to be essential for bone's self‐repair and remodeling properties. The origin of this response is attributed to the piezoelectricity of collagen, which is the main structural protein of bones. In theory, however, any material can also generate voltages in response to strain gradients, thanks to the property known as flexoelectricity. In this work, the flexoelectricity of bone and pure bone mineral (hydroxyapatite) are measured and found to be of the same order of magnitude; the quantitative similarity suggests that hydroxyapatite flexoelectricity is the main source of bending‐induced polarization in cortical bone. In addition, the measured flexoelectric coefficients are used to calculate the (flexo)electric fields generated by cracks in bone mineral. The results indicate that crack‐generated flexoelectricity is theoretically large enough to induce osteocyte apoptosis and thus initiate the crack‐healing process, suggesting a central role of flexoelectricity in bone repair and remodeling.

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adma.201705316.

DOI: 10.1002/adma.201705316
accumulation) has been observed near cracks at the surface of pure hydroxyapatite ceramics, where there is neither collagen nor streaming currents. [7] This result indicates that hydroxyapatite itself can also generate signals for the repairing cells. The nature and origin of such signals, however, is not known, and is one of the most intriguing and enduring problems in the field of osteogenesis. [8][9][10] One potential explanation is bone mineral piezoelectricity. Another possible culprit is flexoelectricity, which is a coupling between strain gradients and polarization allowed by symmetry in all materials, including non-piezoelectric ones. [11,12] Early studies suggested that hydroxyapatite is centrosymmetric and therefore not piezoelectric, [13] although more recent structural refinements [14] suggest that it might be. Meanwhile, functional measurements are ambiguous. Thin films yield substantial piezoelectric coefficients, [15] but thin films can easily become polarized by built-in fields, strain gradients, or defects. [16] Bulk ceramics, meanwhile, sometimes yield a small piezoelectricity [17] and sometimes no piezoelectricity at all. [2] These variations probably reflect differences in sample composition or morphology, making it difficult to make definite statements about intrinsic properties. Our own hydroxyapatite ceramic and commercially acquired ceramics from Berkeley Advanced Biomaterials, Inc., were measured by a direct load method, [16] yielding piezoelectric coefficients smaller than 0.001 pC N −1 . This is at least two orders of magnitude smaller than the piezoelectricity of bone, [7] and is comparable to the residual (defect-induced) piezoelectricity of SrTiO 3 , a reference nonpiezoelectric material used for comparison ( Figure S1, Supporting Information). Our bone ceramics are therefore not significantly piezoelectric, a result consistent with the lack of piezoelectricity in decollagenized bones. [2] Macroscopic measurements of course do not rule out the existence of piezoelectricity on a microscopic level: piezoelectric grains with different orientation can in theory average out their aggregate contribution; however, piezoresponse force microscopy ( Figures S2-S4, Supporting Information) showed no phase contrast between grains. If we discard piezoelectricity, however, how does hydroxyapatite direct the activity of osteoblasts towards damaged regions? [9] A plausible hypothesis is that bone mineral generates electromechanical signals due to flexoelectricity, which is a property of all dielectric (and even semiconductor [18] ) materials whereby they polarize in response to an inhomogeneous deformation such as bending. [19] The combination of built-in structural flexibility and mechanical texture at the microscale-the scale in which cells operate and build-is inherent to biological Bones generate electricity under pressure, and this electromechanical behavior is thought to be essential for bone's self-repair and remodeling properties. The origin of this response is attributed to the piezoelectricity of collagen, which is the main structural protein of bones. In theory, however, any material can also generate voltages in response to strain gradients, thanks to the property known as flexoelectricity. In this work, the flexoelectricity of bone and pure bone mineral (hydroxyapatite) are measured and found to be of the same order of magnitude; the quantitative similarity suggests that hydroxyapatite flexoelectricity is the main source of bendinginduced polarization in cortical bone. In addition, the measured flexoelectric coefficients are used to calculate the (flexo)electric fields generated by cracks in bone mineral. The results indicate that crack-generated flexoelectricity is theoretically large enough to induce osteocyte apoptosis and thus initiate the crack-healing process, suggesting a central role of flexoelectricity in bone repair and remodeling.

Bone Flexoelectricity
All animals-including of course humans-require electricity to perform functions as basic as muscle contraction or nervous impulse sensing and transmission. In the case of vertebrates, bones are also known to generate electricity, [1,2] and this is considered essential for bone regeneration. [3,4] One way to generate electricity is through piezoelectricity, which in bones can be provided by collagen. [2,5] In addition, ionic streaming potentials [6] also contribute to the electromechanical properties of wet bones. Intriguingly, however, bone-repair functionality (osteoblast www.advmat.de www.advancedsciencenews.com tissues, and constitutes an optimal environment for flexoelectricity. For example, flexoelectricity has already been identified in stereocillia (inner ear microhairs), as an important ingredient of mammalian hearing. [20] The highly textured and inhomogeneous structure of bones, with radial porosity gradients and curved walls, also lends itself to flexoelectric phenomena. Already in 1975 Williams and Breger [21] claimed that some electromechanical properties of bones could perhaps be explained by "gradient polarization" or inhomogeneous piezoelectricity. Around the same time, Lakes also performed a theoretical analysis of the potential role of gradients in bones, which could not be substantiated due to lack of quantitative knowledge of their flexoelectric coefficients. [22] Later, Fu reported in a conference the existence of bending-induced polarization in bones, [23] wrongly attributing this flexoelectric-like response to collagen. Though these antecedents are few and scattered, together they provide tantalizing evidence that there may be an important role for flexoelectricity in bones.
In this paper, we have quantified the flexoelectricity of hydroxyapatite and its participation in the electromechanical response of bones. The results indicate that most of the electromechanical response of a bone to bending comes from the flexoelectricity of bone mineral rather than from collagen. We have then used our measured flexoelectric coefficient of hydroxyapatite to calculate the flexoelectricity generated by cracks in bone mineral (see Figure 1). The calculated intensity exceeds 5 kV m −1 within a perimeter of 40 µm around the crack tip, and it therefore can provide a powerful electrical signal from the center of damage to stimulate bone repair.
Fresh bovine femurs were cut in beams oriented parallel to the bone axis and electroded for measuring flexoelectricity. The same femurs were also ground to powder, calcined, and sintered into ceramic pellets (see Experimental Section). We used a dynamic mechanical analyzer to deliver an oscillatory bending and a lock-in amplifier to detect the bending-induced polarization (see Experimental Section). The bending-induced polarization of bone, natural hydroxyapatite, and commercially acquired synthetic hydroxyapatite are shown in Figure 2. The effective flexoelectric coefficients µ eff are extracted from the slopes of the linear fits of the polarization as a function of bending (see Experimental Section).
Bones and hydroxyapatite presented some variation from sample to sample. The dispersion of the flexoelectric coefficient for each material is presented as the shadowed area: red for hydroxyapatite and blue for bones. The effective flexoelectric coefficients are between 0.2 and 2.3 nC m −1 for bone, and between 0.7 and 1.6 nC m −1 for hydroxyapatite. Collagen increases the mechanical toughness of bones, allowing them to withstand bigger bending than brittle hydroxyapatite ceramics; but, for any given curvature, hydroxyapatite flexoelectricity is comparable to the flexoelectricity of bones. Hydroxyapatite flexoelectricity can by itself account for most of the bendinginduced polarization of bones without needing to invoke collagen piezoelectricity.
The next important question is: considering that bones already generate electromechanical voltages from streaming potentials and collagen piezoelectricity, what (if any) is the additional benefit of having a flexoelectric contribution from bone mineral? The answer appears to be related to the multiscale functional   www.advmat.de www.advancedsciencenews.com architecture of bones. Strain gradients grow in inverse proportion to feature size. [19,24] This means that although at macroscopic scales the average strain (and thus piezoelectricity) can dictate the global response, at small scales the strain gradient, and thus flexoelectricity, can be much larger and dominate the local electromechanical response. [23] A dramatic manifestation of this principle takes place at the apex of cracks, which concentrate in a very small volume (a crack junction is atomically sharp) the maximum stress that a material can withstand before rupture; according to theoretical calculations, the flexoelectric polarization near a crack apex can exceed the piezoelectric polarization for even the best piezoelectric materials. [25] In the context of bones, microcracks are common flaws formed due to cyclically applied stress, but they usually represent no risk for the integrity of the bone thanks to the process of remodeling. [11,26] As our calculations show, crack-generated flexoelectricity is capable of triggering the process of damage repair and remodeling.
The critical intensity factor K C , which in bones is in the order of 3 MPa m 1 2 ; [27] this is the stress concentration at which cracks propagate through bone. Using our measured flexoelectric coefficients, we have calculated the flexoelectric field (Figure 3) around a microcrack under critical load (see Experimental Section). The flexoelectric field is biggest at the crack tip and decays progressively away, being bigger than 10 3 V m −1 up to a distance 50 µm around the crack apex. These numbers are significant because pulsed electric fields of 5 kV m −1 are known to induce apoptosis in bone cells, [28] osteocyte apoptosis being the first step of bone regeneration; when dead, osteocytes release chemical triggers that signal the osteoclasts to initiate the repair by cleaning the damaged region, followed by osteoblasts that segregate new bone mineral. [10,23] Electric fields also attract screening ions creating electrochemical gradients that assist osteogenesis, [29] thus further increasing the velocity of reparation of the damaged region. [30] Osteoblast tends to attach near by the tip of cracks in pure bone mineral, [9] suggesting that osteoblasts do indeed detect a crack tip as the center of damage. Moreover, the apex is itself a movable entity: as the crack is healed, its apex will recede, continually pointing to the osteoclasts and osteoblasts the new position of the region to repair. [10] Flexoelectricity is strong enough to act as the beacon in this process, suggesting a new line of inquiry for tissue regeneration where stress-gradient engineering may be used as an additional degree of freedom in bone-forming prosthetic designs.

Experimental Section
Sample Preparation and Characterization: Freshly cut (less than 48 h from slaughter) bovine femurs were obtained from a butcher's shop and stored in a physiological solution. Pieces of compact bone (porosity < 15%) were then cut using a diamond wire at low speed in order to avoid damage to the tissue. The samples were cut in consideration of the orientation of the collagen inside the bone; in this case, all the samples were longitudinal to the long axis of the bone. The samples were polished up to 0.1 µm grain size disk with an Allied precision polishing system at low velocity to minimize damage to the samples.
Hydroxyapatite compact disks were commercially obtained from Clarkson Chromatography Products, INC., with certified purity greater than 95%. Also hydroxyapatite was produced from bovine bones following the procedure of Ooi et al. [31] The commercially acquired hydroxyapatite samples had a porosity between 8% and 13%, and natural hydroxyapatite samples that were prepared by grounding, firing and sintering bone had a porosity smaller than 7%. In order to do the compact disks, the hydroxyapatite was milled and the powder was sieved to 125 µm particle size. Then, the powder was uniaxially pressed into pellets of 22.58 mm of diameter with 25 metric tons. Finally the pellets were air sintered at 1360 °C during 4 h. Samples were cut and polished using the same procedure as for the bones. Platinum electrodes were deposited using pulsed laser deposition. Special care was taken to have low resistance across the electrode (<100 Ω). The quality if the electrodes were checked by measuring the capacitance and dielectric losses, being 0.2 for the latest.
Polarization was induced by a DMA8000 dynamic mechanical analyzer (DMA) of Perkin-Elmer and was measured using the method described by Zubko et al. [32] The DMA was used to apply a periodic three-point bending stress at room temperature. This periodic signal was used as a reference for a lock-in amplifier, model 830 of Stanford Research Instruments, while the signal obtained from the electrodes fed the measurement channel of the lock-in amplifier, which recorded the bending-induced displacement currents. The current was converted into polarization using P vA , where v is the frequency of the bending force and A is the area of the electrodes. The polarization measured by the lock-in is related to the effective flexoelectric coefficient µ eff by where L is the separation between the standing points of the sample, a is the half-length of the electrodes, and z 0 is the maximum vertical  Measurements were taken after all samples had been dried in an oven at a temperature of 90 °C for 7 h. All the results presented in this paper were obtained by measurements at 13 Hz, which in the range of frequencies that covers the characteristic timescales of the periodic loads in vivo. [33] We also measured for some samples at 1.3, 23, 31, 37 and 43 Hz to ensure the results. Flexoelectric measurements are not affected by variations in the frequency. Although lower frequencies are particularly relevant because it is the characteristic timescale of periodic mechanical loads such as walking, a compromise between noise (noise scales as f −1 ) and relevant frequencies was made to obtain lower dispersion.
Data Analysis: From Equation (1), the effective flexoelectric coefficient is defined as the relation between the polarization and the stress gradient. For more accuracy, several strain gradients were applied to each sample and the flexoelectric coefficient was extracted from the slope of the plots of polarization as a function of strain gradient, [19] as can be seen in Figure 4.
Calculation of Flexoelectric Field: From the equations of strain around a crack mode 1 [34] ε υ σ υ σ δ = where Y is the Young's modulus, ε is the Poisson's ratio, and σ ij is the stress applied to the crack in each direction where K I is the intensity factor taken as 3MPam 1 and f ij is the flexocoupling tensor. The flexocoupling tensor was calculated with the effective flexoelectric coefficient µ eff and the dielectric susceptibility χ eff e ff χ µ = f (9) For this calculation, f 11 = f 22 = f 12 = f 21 = f eff = 10 V and the shear component was taken as null. We used 10 V as a general case since we measured several samples and all the flexocoupling values ranged from 9.3 to 11.8 V. Same happened with the relative dielectric constant, all the samples showed different values ranging from 10 to 15.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author. Because bones are more flexible than hydroxyapatite, it could withstand much larger curvatures, but the slope was still almost the same as for pure hydroxyapatite. Inset: sketch of the measurement apparatus.