Piezoelectric Effects of Materials on Biointerfaces - American

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Piezoelectric Effects of Materials on Biointerfaces Attilio Marino, Giada Graziana Genchi, Edoardo Sinibaldi, and Gianni Ciofani ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 09 May 2017 Downloaded from http://pubs.acs.org on May 9, 2017

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ACS Applied Materials & Interfaces

Piezoelectric Effects of Materials on Biointerfaces Attilio Marino,†,* Giada Graziana Genchi,†,* Edoardo Sinibaldi,‡, * Gianni Ciofani†,#,* †

Smart Bio-Interfaces, Istituto Italiano di Tecnologia, Viale Rinaldo Piaggio 34, 56025 Pontedera, Italy

‡

Center for Micro-BioRobotics @SSSA, Istituto Italiano di Tecnologia, Viale Rinaldo Piaggio 34, 56025 Pontedera, Italy

#

Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Corresponding Authors E-mail: [email protected]; [email protected]; [email protected]; [email protected]

KEYWORDS Piezoelectricity; wireless stimulation; excitable tissues; smart biointerfaces; modeling.

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ABSTRACT

Electrical stimulation of cells and tissues is an important approach of interaction with living matter, that has been traditionally exploited in the clinical practice for a wide range of pathological conditions, in particular related to excitable tissues. Standard methods of stimulation are however often invasive, being based on electrodes and wires used to carry current to the intended site. The possibility to achieve an indirect electrical stimulation, by means of piezoelectric materials, is therefore of outstanding interest for all the biomedical research, and emerged in the latest decade as a most promising tool in many bio-applications. In this paper, we summarize the most recent achievements obtained by our group and by others in the exploitation of piezoelectric nanoparticles and nanocomposites for cell stimulation, describing the important implications that these studies present in nanomedicine and tissue engineering. A particular attention will be also dedicated to the physical modeling, that can be extremely useful in the description of the complex mechanisms involved in the mechanical/electrical transduction, yet also to gain new insights at the base of the observed phenomena.

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1. Introduction The word “piezoelectricity” derives from the Greek “piezō” (πιέζω) and “ēlektron” (ήλεκτρον), and means “electricity resulting from pressure”. This property is exhibited by certain materials that therefore are termed as “piezoelectrics” as they are able to generate electricity when subjected to a mechanical stress. Specifically, piezoelectric material deformation induces an asymmetric shift of charges, which results into an electric polarization and in a consequent electricity generation. This phenomenon is known as direct piezoelectric effect. Viceversa, piezoelectric materials can undergo a strain in response to the application of an electric field: this mechanism is named reverse piezoelectric effect.1 Piezoelectricity was discovered in 1880 by Pierre and Jacques Curie,2 who also demonstrated the linear and reversible nature of this phenomenon. Piezoelectric devices are currently adopted as both actuators and sensors for a myriad of disparate applications, especially in automotive,3 biomedical4 and military5 fields, ranging from speakers and air-bag sensors to ultrasonic imaging systems. Recently, the piezoelectric properties of biocompatible ceramics and polymers have been exploited for the preparation of novel interfaces with biological systems (hereafter termed as “biointerfaces”) as, for instance, nanotransducers able to finely interact with intracellular compartments of living systems. In this context, piezoelectric biointerfaces are showing a great potential for the remote electrical stimulation of excitable tissues, such as nervous,6 bone,7,8 and muscle tissues.9 A mechanically-driven piezoelectric stimulation does not requires the installation of any implanted electrode: it can either be activated by mechanical forces to which the body is normally subjected (e.g., compressions, vibrations, sounds),10,11 or be externally triggered with a source of mechanical stimulation able to deeply penetrate biological tissues (e.g., ultrasound, US).12 Wireless stimulation of excitable tissues is of outstanding interest for the treatment of many pathological conditions13-15 and for tissue engineering/regenerative

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medicine applications, where electrical stimulation plays a fundamental role in the modulation of tissue functionality and maturation.16,17 Concerning the nervous system, pioneering work of Aebischer et al. was dedicated to the design of polymer-based peripheral nerve guidance channels in 1987.18 The positive effect of piezoelectric scaffolds on axonal outgrowth was independently confirmed by different groups with in vitro studies,6,19-23 and the modulation of the RhoA, Rac1 and Cdc42 biochemical pathways was then demonstrated to be involved in this process.24 For a comprehensive review of these investigations, the Reader is however referred elsewhere.25 Our group was the first one to exploit piezoelectric nanomaterials to deliver an indirect electrical stimulation to neurons in a wireless modality. In our seminal study, nanotransducers were remotely activated through US and were able to induce Ca2+ and Na+ transients in neurons by activating voltagegated membrane channels22 (for further details, please refer to Section 2.1). Collectively, all these findings open new perspectives in the stimulation of the central nervous system, which is typically characterized by restricted accessibility.26 Furthermore, the possibility to obtain in vitro neuronal constructs from human neural stem/progenitor cells by exploiting piezoelectric stimulations is of utmost interest in regenerative medicine and tissue engineering.21,27 Piezoelectric stimulation of neurons has been deeply investigated due to the high sensitivity of these cells to electrical stimuli. However, other excitable tissues are known to gain beneficial effects from electrical cues. Bone tissue, in particular, is itself a piezoelectric material, and its ability to remodel its architecture in response to mechanical stress is well known since the early studies of Julius Wolff in 1892.28 In addition to mechanical solicitation, several works reported the positive role of electrical stimulation in mediating bone regeneration.29,30 For these reasons, piezoelectric materials are particularly attracting also in the field of bone tissue engineering.31 Barium titanate (BT) ceramics were 4


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the first piezoelectric material adopted for bone regeneration applications.32 Other investigations in bone tissue engineering, also regarding other ceramic materials such as lithium sodium potassium niobate33 or polymers,34 included the use of piezoelectric materials as nanotransducers.35 Piezoelectric biointerfaces can be also integrated in more complex electronic systems, operating as biosensors and energy harvesters of bioelectromechanical sources.36 Concerning mechanical biosensors, piezoelectric nanoribbons of Pb(Zrx,Ti1-x)O3 (PZT) showed an extremely sensitive mechanosensory capability, allowing cell deformation monitoring at a nanometer scale (Figure 1).37 This approach offers a scalable platform for in vitro high-throughput investigations on cell mechanobiology, bypassing the limitations of atomic force microscopy (e.g., invasiveness and difficult multiplexing). Flexible piezoelectric films can also be used as energy harvesting components of biomedical self-powered systems:38 indeed, mechanical forces derived by the organ movements (e.g., heart contraction) represent a sustainable energy source that can be detected and converted in electric supply by piezoelectric biointerfaces.39-41 Piezoelectric biointerfaces characterized by different sizes (from nano- to micro-) and shape have been used for the piezoelectric stimulation/sensing of biological systems. 1D nanoparticles,42 2D films36 and 3D piezoelectric scaffolds8 are currently being investigated and their peculiarities have to be carefully considered before their exploitation in biomedicine. Obviously, the different dimensions of the piezoelectric interfaces allow for interactions at distinct scales of the biological systems: 1D piezoelectric nanoparticles can act at cellular/subcellular level by associating to cell membranes or organelles, while 2D and 3D piezoelectric devices can interface tissues and organs. Moreover, nanoparticles require efficient delivery, targeting and retention methods, while nanofilms and 3D scaffolds usually need a surgical intervention to be implanted and they necessitate strategies to prevent adverse reactions. Importantly, the piezoelectric transduction efficiency of nanostructures can be 5



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significantly higher compared to the respective bulk material.43 In this context, piezoelectric nanomaterials such as ceramics can be embedded in other materials (such as piezopolymers) to obtain composite materials with hybrid properties, and with exalted piezoelectric behavior.46, 44 Nanocomposites are also characterized by different mechanical (e.g., the Young's modulus E), topographical (e.g., roughness), and dielectrical properties with respect to the plain material, and this has to be taken into account when modeling and designing biointerfaces (please, also refer to Section 4).45 In this paper, the most exciting findings on piezoelectric nano- and micro- biointerfaces will be reviewed by focusing on fabrication methods, physicochemical properties, modifications for their exploitation in biological context (e.g., chemical functionalization), biocompatibility levels and main effects on living systems. We will provide an overview of innovative piezoelectric platforms, such as piezo-nanotransducers and 2D/3D piezoelectric biointerfaces, which are currently used for biomedical investigations/applications and that have a good potential for being exploited in designing of futuristic medical device solutions or in the clinical treatment of degenerative pathologies involving excitable tissues. Basic approaches to constitutive modeling will be also recalled, since it can be useful to describe both classical and bioorganic piezomaterials. 2. Piezo-nanotransducers The obtainment of biointerfaces able to remotely and non-invasively stimulate/recording the cell activity is a fundamental goal in biomedicine.46 The reversible nature of the piezoelectricity (i.e., the direct and indirect piezoelectric effects) potentially allows both the electrical/mechanical stimulation of living systems, sensing, and energy harvesting from different bio-electromechanical energy sources.47 Moreover, the miniaturization of piezoelectric materials at nanometric size remarkably reduces the invasiveness of biointerfaces, thus promising a broad spectrum of applications ranging from self6


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powered biorobotics to the remote treatment of degenerative diseases.25 As examined in detail in this section, piezoelectric nanotransducers can be grouped according to their chemical composition (e.g., boron nitride, bismuth ferrite, barium titanate, etc.) and shape (e.g., nanospheres, nanotubes, nanoribbons, etc.), and are characterized by remarkably different levels of biocompatibility, piezoelectric coefficients, and material purity. An accurate analysis of these properties is crucial for successfully interfacing nanotransducers with biologic systems. This Section is structured as follows: in Section 2.1 and Section 2.2 we focus on nanotransducers based on boron nitride nanotubes and barium titanate, respectively, while additional piezoelectric nanomaterials are considered in Section 2.3. 2.1 Boron nitride nanotubes Boron nitride nanotubes (BNNTs) are piezoelectric structural analogues of carbon nanotubes (CNTs), with boron and nitrogen atoms that substitute the carbon ones.48 BNNT piezoelectricity derives from the mechanical stress required to roll the hexagonal boron nitride plane into the tubular shape.49 Atomic arrangements in single-walled BNNTs (SW-BNNTs) can be zigzag, armchair, and chiral (Figure 2).50 Multi-walled BNNTs (MW-BNNTs) are rolls of stacked BN sheets and are easier to be produced with respect to SW-BNNTs. BNNTs can be synthesized by using several different routes, such as chemical vapor deposition, ball milling, laser-based techniques and plasma-based approaches, and different synthesis methods can produce BNNTs characterized by different morphologies.51 Interestingly, the morphology of BNNTs significantly affects their piezoelectricity: the diameter of the BNNT is known to be inversely proportional to its piezoelectric constant.49 For this reason, the preparation/obtaining of BNNTs characterized by a high level of purity and homogeneity is essential. BNNTs are currently distributed by a few companies with different grades of purity and dispersibility, and difficulties related to the lack of simple production process and to the lack of straightforward chemical 7



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functionalization approaches often limit a widespread exploitation/testing of BNNTs, thus slowing down the process toward a translational biomedical research.52 However, interests for BNNTs in biomedicine is extremely high, since these nanotransducers are characterized by physicochemical properties that are particularly interesting for biomedical applications. Firstly, BNNTs show a superior resistance to chemical and temperature oxidation with respect to their carbon counterparts.53 Moreover, the Young's modulus is particularly high (in the order of TPa), thus BNNTs can be used for the preparation of nanocomposites to reinforce polymeric or ceramic materials.54,55 Concerning electrical properties, BNNTs are insulators characterized by a uniform wide energy bandgap (about 5.5 eV),56 that reversibly switch to semiconductors under elastic bending deformation.57 Despite this difference with CNTs, which display either metallic or semiconducting behaviors, BNNTs can be functionalized with gold quantum dots and successfully used for the preparation of tunneling field effect transistors (FETs), thus envisaging futuristic applications as biological and chemical sensors.58 Because of their high hydrophobicity, BNNT dispersions in biological media need to be stabilized by nanotube functionalization/coating with different molecules, such as polyethyleneimine (PEI),59 poly-l-lysine (PLL),7,60 glycol-chitosan (GC),22,61 transferrin,62 gum Arabic63 and folic acid.64 Obviously, BNNT coating/functionalization also allows piezotransducer targeting to specific cell types. As an example, folic acid-functionalized BNNTs are up-taken with relatively high efficiency in tumor cells, which are known to over-express folic acid receptors.64 Good results in terms of biocompatibility were observed with both in vitro and in vivo models; however, BNNTs with different purity grades and dispersing agents were adopted for these studies, and their level of toxicity needs to be further clarified.65 BNNTs were the first piezoelectric nanotransducers used in the biomedical field for the excitation of neuron-like cells thanks to a pioneering work performed by our group in 2010 (Figure 3).22 In this 8


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work, neuron-like PC12 and SH-SY5Y cells were treated with GC-coated BNNTs and then chronically stimulated with US during neural differentiation. Interestingly, a significant enhancement of neurite outgrowth was demonstrated in response to the synergic stimulation (BNNTs + US) with respect to the other experimental conditions (BNNT-treated cultures without US, US-stimulated cultures without BNNTs, and both non-treated and non-stimulated cells) in both cell lines. Similarly to the electrical stimulation, the promotion of neurite outgrowth in response to the US-driven BNNT-assisted piezoelectric excitation was demonstrated to be a Ca2+-dependent phenomenon. In this work, US were used as mechanical energy source for remotely activating BNNTs. Since US can efficiently propagate in aqueous solution and deeply penetrate biological tissues, US-driven nanotransducer-assisted piezoelectric stimulation approach open new exciting perspectives for the wireless activation of the nervous system also in vivo. In the wake of this first positive result, BNNTs were also studied as piezo-nanotransducers for the USdriven stimulation of primary human osteoblast cells (hOBs) by Danti et al.7 In this work, hOBs internalized PLL-BNNTs in membrane vesicles, as demonstrated by transmission electron microscopy (TEM) analysis. Subsequently, chronic stimulations with low-frequency US were performed during in vitro osteoblast maturation. Similarly to the neural cells, the combined BNNTs + US stimulation was able to promote higher hOB functional maturation compared to the control cultures. Specifically, piezoelectric stimulation was able to up-regulate transcription of TGF-β1, a growth factor that is expressed in response to electrical stimulation, and the signaling of which is involved in bone formation.66 In addition, the highest levels of hOB maturation were obtained with the synergic BNNTs + US stimulation in terms of osteopontin expression, osteocalcin production, and Ca2+ secretion, thus demonstrating the great potential of BNNT-based nanotransducers also in the bone tissue engineering

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field. Futuristic applications regarding minimally invasive therapies to promote the regeneration of bone tissue are indeed envisaged. BNNTs can also act as efficient piezo-transducers in the context of muscle-like cells. In a work from Ricotti et al. US were applied in combination with BNNTs to perform the piezoelectric stimulation of co-culture of C2C12 muscle-like cells and fibroblasts growing on 2D micro-engineered hydrogels.9 Thanks to the synergic combination of stimuli (mechanical, topographical, chemical and piezoelectric), differentiation of C2C12 cells towards a mature muscle phenotype significantly improved with regard to actin and myosin expression and to electrical functionality. Concluding, BNNTs resulted to be efficient nanotransducers, able to remotely stimulate different cell types by virtue of their piezoelectricity. Thanks to their peculiar optical and physicochemical properties, BNNTs can be also exploited as nano-biointerfaces for further biomedical applications, such as, for example, drug delivery,67 neutron capture therapy for cancer,68,69 regenerative medicine,55 and biosensing.58 2.2 Barium titanate nanoparticles Barium titanate (BT) is a ceramic material based on perovskite-like oxides. BT is characterized by a high dielectric constant and is currently used for the preparation of various electrical and electronic devices. Furthermore, BT was the first ceramic material that was investigated for in vivo implants and demonstrated an excellent potential as bone-like graft.32,70 Nevertheless, only few investigations have been focused on the potential of BT nanoparticles (BTNPs) in nanomedicine. The first studies carried out with BTNPs are revealing a great potential of these nano-biointerfaces thanks to their excellent biocompatibility, piezoelectricity, and non-linear optical properties. Moreover, BTNPs are now

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commercially available with a great level of purity and stringent control over nanoparticle size, shape and piezoelectric behavior.35 Similarly to BNNTs, BTNPs can be obtained by using different methods of synthesis (e.g., solvothermal,71 hydrothermal72 and sol-gel route73). Different fabrication methods can result into different BTNP size and crystal structure.74 For instance, the cubic crystal phase has a centrosymmetric arrangement of atoms and, for this reason, the resulting BT is non-piezoelectric. Conversely, tetragonal and orthorhombic configuration is non-centrosymmetric, thus conferring piezoelectricity to the material. BTNPs with non-centrosymmetric crystals are efficient piezoelectric nanotransducers characterized by relatively high piezoelectric coefficient (d33 of BTNPs fabricated with hydrothermal method and characterized by a tetragonal arrangement of the crystal lattice is about 30 pm/V).75 The non-centrosymmetric nature of piezoelectric BTNPs also confers them a peculiar optical property: specifically, piezoelectric BTNPs are optimal non-linear optical nanoprobes, characterized by a strong signal in second-harmonic imaging microscopy (SHIM).76,77 SHIM allows the analysis of cellular uptake and in vivo localization of BTNPs by overcoming several limitations of fluorescent probes, such as, for example, photobleaching, saturation, and blinking.78,79 Stability of BTNPs in solutions at pH < 12 is scarce and, similarly to BNNTs, BTNPs require surface functionalization/coating for avoiding precipitation. BTNPs have been thus modified with PLL,80 GC,81 gum Arabic,23 and β-cyclodextrin (β-CD)82 before assessing their biocompatibility both on in vitro and in vivo models, and resulted to be particularly harmless up to relatively high concentrations (about 100 µg/ml). The worst results in terms of biocompatibility were obtained with PLL-BTNPs, where a concentration of only 10 µg/ml induced a significant reduction of cell proliferation in H9c2 rat myoblasts.80 However, the toxicity was demonstrated to be caused by PLL, which was able to reduce

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the viability of cells also when administered alone. Notably, in vivo experiments showed as BTNPs are well tolerated by complex organisms, ranging from zebrafish embryos78 to adult mice.83 Our group successfully exploited for the first time BTNPs as US-sensitive nanotransducers for the stimulation of SH-SY5Y-derived neurons (Figure 4).23 In this work, the first direct biological proof of cell activation in response to the nanotransducer-assisted piezoelectric stimulation was additionally provided. BTNPs were stabilized with gum Arabic and, after a 24 h treatment, they were found strongly associated to the neuron membranes, both at the level of cell bodies and of their neurites. Then, the effects of acute US-driven piezoelectric stimulation on ion fluxes were investigated, demonstrating that the synergic US + BTNPs stimulation was able to evoke high-amplitude Ca2+ and Na+ peaks in SH-SY5Y-derived neurons. Ion transient amplitudes were modulated by tuning the power intensity of the US stimulus and were sensitive to both tetradotoxin (TTX) and Cd2+ blockers, thus indicating the involvement of voltage-gated ion channels in mediating the response to piezoelectric stimulation. Interestingly, US-driven stimulation with non-piezoelectric BTNPs, characterized by a centrosymmeric cubic configuration of the crystal lattice, was not able to elicit any significant cell response in terms of ion fluxes, thus highlighting the role of piezoelectricity in converting the pressure of US into electrical stimulation. The hypothesis of a US-driven BTNP-assisted piezoelectric stimulation was furthermore validated by an electroelastic mathematical model, according to which the voltage generated by BTNPs is able to activate voltage-sensitive channels (please refer to Section 4). Finally, BTNPs showed excellent potentials also in bone tissue engineering field, where osteogenesis can be even promoted by piezoelectricity without the application of an external source of mechanical stimulation.8 In summary, piezoelectric BTNPs are ceramic nanoparticles characterized by great biocompatibility, high piezoelectric coefficients, strong signal in SHIM and good commercial availability with high 12


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grade of material purity. Furthermore, the possibility to fabricate centrosymmetric non-piezoelectric BTNPs allows to perform negative controls in addition to the plain US treatment, thus allowing to properly demonstrate the role of piezoelectricity in triggering neuron responses upon US exposure. 2.3 Other piezo-nanotransducers Zinc oxide (ZnO) nanomaterials, such as nanowires and nanobelts, are also characterized by high piezoelectric coefficients.84 These elongated nanostructures can be folded so as to stretch at a surface and compress at the opposite one. This mechanical deformation generates an electric potential distribution across the width of the nanomaterial. The piezoelectric field consists in the displacements of the O2- anions from the Zn2+ cations, and the electric potential is maintained until the mechanical stress is released and the nanomaterial returns to its original resting position.85 The coupling of piezoelectric and semiconducting properties of ZnO nanowires and nanobelts has been successfully exploited for the fabrication of many electronic devices and components, such as FETs86 and diodes,87 paving the way for several applications in nanopiezotronics, especially focused on sensing and harvesting / recycling energy from biological and environmental sources. However, the biocompatibility of dispersed ZnO nanomaterial is quite poor, thus limiting their exploitation as in biointerfaces.88 Specifically, ZnO nanostructures are known to induce severe cytotoxicity, enhance the levels of reactive oxygen species, reduce the mitochondrial membrane potential, and induce the production of interleukin (IL)-8 in human A549 and BEAS-2B cells. However, possible modifications for stabilizing Zn-based nanomaterial (for example with stable carbon, silica or titanium oxide coatings) and preventing the release of Zn2+ and O2- will motivate the use of ZnO nanostructures for biomedical applications.89,90 Finally, future works will be dedicated to further explore the potential in nanomedicine of other piezoelectric nanostructures, such as the multiferroic ones composed by bismuth ferrite (BFO)91 and 13



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metal-based hybrid nanomaterials (e.g., piezoelectric gold-based nanocomposites).92 As an example, gold nanoshells with a piezoelectric BTNP core has already demonstrated first good results in the field of photothermal ablation therapy of cancer cells.93 3. Piezoelectric biointerfaces for tissue engineering Based on the relatively higher amount of related studies, in Section 3.1 we focus on piezoelectric biointerfaces for nervous tissue, while we consider other tissues in Section 3.2. 3.1 Nervous tissue engineering Development and functioning of biological tissues is mediated by an intricate interplay of chemical and physical stimuli. Several cells are in particular sensitive to electrical stimuli and major tissue functions are controlled by electrical signals. Neurons represent the paradigmatic example of how information can be processed by biological systems in the form of electrochemical signals. At molecular level, these cells express a complex set of voltage-sensitive ion channels that allow them to translate abovethreshold electrical stimulation into stereotypical electric potentials.94 Electric potentials are then transmitted along the neuronal axon up to electrical/chemical synapses, enabling neuron communication with other cells (i.e., neurons, muscle, and endocrine cells). During nervous system development, neurons that receive active electrical afferents signals survive and mature; conversely, neurons that do not receive electrochemical stimulation undergo programmed cell death (i.e., apoptosis). This selection mechanism also occurs at the neurite level: in this way, the nervous system develops and reshapes preserving only the active nodes and connections of the network.95 Electrical and chemical stimulations have therefore been used to promote the morphological and functional maturation of stem cells towards mature neuronal cells in vitro. The possibility to generate easily accessible in vitro models for a number of conditions additionally allows to study complex 14


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neuronal features96 and to carry out high-throughput investigations on drugs in a simplified and controlled manner.97 Furthermore, in vitro differentiated neurons can potentially be transplanted in order to innervate a host brain, and replace injured or even dead cells in the context of neurodegenerative diseases.98 For all of these reasons, the fabrication of biointerfaces (e.g., piezoelectric thin films) able to successfully tune cell behavior and inducing the in vitro differentiation/maturation of a high number of neuronal cells is of extreme interest in the fields of tissue engineering and regenerative medicine. Piezoelectric films can be composed by inorganic ceramics such as BaTiO3,99 PZT,38,41 and (1x)Pb(Mg1/3Nb2/3)O3 – xPbTiO3 (PMN-PT),40 which allow enough flexibility for implantable electronic applications, although with different extent of biocompatibility: in particular, lead oxide in PZT and PMN-PT can result into toxic effects when released in biological context.100 Furthermore, flat substrates and thin films of piezoelectric polymers as poly(vinylidene fluoride) (PVDF) and poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) can be successfully used for cell culturing.6,34 In this context, piezoelectric flat substrates composed of micron-sized aligned PVDF-TrFE fibers efficiently promoted the in vitro neural differentiation of human neural stem/progenitor cells in terms of morphological maturation of neurites and expression of a peculiar neuron marker, β3-tubulin.21 Moreover, a decreased expression of nestin, typical marker of neural stem cells, was observed on these piezoelectric substrates, further indicating the promotion of cell differentiation. Interestingly, the piezoelectric-mediated enhancement of neural differentiation was observed even in the lack of inductive biochemical factors. The Authors suggested that the direct piezoelectric effect was generated through minute deformations of the fibers due to cell adhesion and migration. Cell response was modulated based on the extent of the substrate piezoelectric coefficient: indeed, the best results of 15



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neural differentiation were observed by growing stem/progenitor cells on annealed PVDF-TrFE fibers, which are characterized by a significantly higher piezoelectric coefficient compared to the native ones.21 A good example of piezoelectric material application to neuronal stimulation can be found in a work from Inaoka and co-workers, dealing with cochlear prosthetics. In this work, a piezoelectric device was fabricated based on P(VDF-TrFE) films and a silicone frame aiming at restoring hearing in the case of hair cell loss. Congenital or acquired hair cell deficiency (also termed sensorineural hearing loss) determines a missing transduction of sounds (mechanical stimulation) into electrical stimulation of the auditory nerves in the cochlea. For this reason, P(VDF-TrFE) films were tested for compensating missing hair cell function through direct piezoelectric effect both in vivo and ex-vivo. In vivo experiments demonstrated that a 1000-fold amplification of the electrical signals generated by the films in response to sound stimuli (over 100 dB) was necessary to obtain auditory brain-stem responses after delivery to the cochlea of deafened guinea pigs. Ex-vivo experiments conducted with piezoelectric films positioned at the basal turn of the scala timpani of whole excised cochleas clarified that the voltage generated by the films after sound stimulation in a broad range of frequencies was not sufficient to stimulating auditory neurons.11 Improvements in terms of material choice and manipulation should therefore be done to make piezoelectric films reliable biointerfaces for auditory neuron stimulations. Aiming at merging the excellent mechanical properties of the piezopolymers with the higher piezoelectric properties of certain nanoceramics, our group recently proposed composite P(VDF-TrFE) films loaded with tetragonal BTNPs for neuron-like cell culturing and stimulation (Figure 5). Our work represented a first attempt at developing a single-unit prosthetic device for sensorineural hearing loss treatment. The piezoelectric behavior of P(VDF-TrFE) films loaded with BTNPs was characterized at a 16


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surface and at a bulk level, demonstrating improved piezoelectric responses of the composite films compared to plain polymeric ones. Specifically, the piezoelectric coefficient d31 of the nanocomposites was significantly higher with respect to the plain polymeric P(VDF-TrFE) substrates. Furthermore, the dielectric constant εd of the nanocomposite substrates resulted about 1.5-folds higher compared to the P(VDF-TrFE) films. An increase of the β-phase percentage of the crystalline component of P(VDFTrFE) was found after BTNP loading (53% in the composite against 32% in the plain copolymer), which concurs to the observed improvement of piezoelectric behavior of the composite film. An external mechanical source of US was applied for the stimulation of SH-SY5Y neuron-like cells through direct piezoelectric effect. During US stimulation, intracellular Ca2+ transients were elicited on piezoelectric surfaces, thus indicating a US-mediated piezoelectric activation of neuron-like cells. The amplitude of these transients was increased by the higher piezoelectric properties of the composite films. Moreover, chronic US treatments during in vitro differentiation determined an increased expression of β3-tubulin and an enhanced axonal outgrowth on piezoelectric substrates with respect to non-piezoelectric control surfaces. The best results of differentiation were observed on composite substrates. P(VDF-TrFE)/BTNP films were thus able to influence neuron-like cell behavior by promoting differentiation in vitro, promising applicability in the treatment of hearing impairments.6 Very recently, fibrous piezoelectric scaffolds were fabricated by Lee et al. for the elaboration of innovative spinal cord conduits. Hollow P(VDF-TrFE) guides were thus prepared aiming at supporting spinal cord regeneration. Conduits were seeded with Schwann cells (SCs), known to play an essential role in axonal regeneration of the peripheral nerves and also to improve functional recovery in rat spinal cords. Piezoelectric P(VDF-TrFE) fibers were electrospun in aligned or in randomly-oriented configuration, thus modulating the surface topography of the piezoelectric biointerface. Both types of scaffold well supported the regeneration of sensory and brainstem axons, the outgrowth of astrocytic 17



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processes and blood vessels maturation after 3 weeks from conduit implantation. Thanks to their anisotropic surface topography, aligned P(VDF-TrFE) fibers also allowed a better regeneration of noradrenergic fibers and astrocytic processes into the transplant bridging spinal cord stumps of a completely transected adult rat with respect to randomly oriented fibers conduits.101 3.2 Other tissues Electric signals do not only affect intercellular communication of neural cells. Rather, they modulate a plethora of different biological phenomena both at cell and tissue levels, such as, for example, cell migration,102 embryogenesis,103 osteogenesis,104 ligament healing,105 myogenesis,106 and muscle regeneration.107 In addition, piezoelectricity was found on different biological structures of the human body, such as tendons,108 bone,109 dentin110 and cartilage.111 Even complex biomolecules like deoxyribonucleic acids (DNA), polysaccharides, and proteins (e.g., collagen) displays significant piezoelectric features. For this reason, the possibility to design smart biointerfaces able to actively interact with living systems by mimicking the characteristic of biological piezoelectric structures is of great interest for the entire field of tissue engineering. As concerns bone tissue engineering, very few examples can be found on the exploitation of direct piezoelectric effect for addressing cell behavior. In a work performed by Ribeiro and co-workers, PVDF films were prepared by casting, poled by corona discharge and used for human adipose stem cell culture. Notably, poled PVDF films supported higher osteodifferentiation of stem cells in terms of alkaline phosphatase activity compared to unpoled films, and when the cultures were exposed to vibrational stimulation, they promoted an even higher osteodifferentiation.112 Our group also explored direct piezoelectric effect for promoting differentiation of osteoblast-like cells. Three-dimensional scaffolds reproducing trabecular bone structure were fabricated by two photon 18


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lithography. The fabrication procedure enabled the dispersion of BTNPs in a ceramic-like photoresist (Ormocomp), that thus gained piezoelectric properties. The resulting scaffolds were defined “OsteoPrints”. The piezoelectric coefficient d33 of BTNP-loaded Osteo-Prints was much higher (~8x) than that one of the unloaded scaffolds. Osteo-Prints were used as active biointerfaces for SaOS-2 osteoblast-like cell culture, and promoted exit from cell cycle, up-regulation of bone differentiation marker genes, and mineralization increment compared to traditional glass substrates. Interestingly, BTNP-loaded OsteoPrints that were exposed to US induced higher osteodifferentiation compared to unloaded Osteo-Prints, and to BTNP-loaded Osteo-Prints not exposed to US. Osteoblast-like cell cultures performed on BTNP-loaded Osteo-Prints and stimulated with US exhibited a lower expression of Ki-67 (a nuclear marker of proliferation), and a 2-fold higher secretion of collagen (a marker of differentiation) compared to cells on the unloaded substrates, irrespectively of US exposure or not. They also showed a 6-fold higher hydroxyapatite deposition than on the unloaded Osteo-Prints not stimulated with US, providing preliminary evidences on the suitability of the Osteo-Print hybrid biointerface to bone tissue engineering.8 In summary, different piezoelectric materials have therefore been exploited for the fabrication of biointerfaces as substrates capable of stimulating cells by direct piezoelectric effect with various applications, ranging from single-component cochlear implants, conduits for peripheral nerve and spinal cord repair, and platforms for promoting the in vitro differentiation of stem cells and progenitors towards a mature phenotype. Furthermore, the advent of nanocomposite biointerfaces characterized by higher piezoelectric coefficients and dielectric constants provides encouraging results concerning a significant improvement of the sensitiveness and the performances of piezoelectric devices. Table 1 summarizes the main applications, properties, functionalizations, and other important information of the different piezomaterials considered in this report. 19



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Table 1. Piezoelectric materials for biointerfaces: properties and applications Piezomaterial

Applications

Other information

Cell stimulation: • • •

H9c2

Crystal structure:74

80

SaOS-2

• 8

SH-SY5Y

• 23

Cubic non-piezoelectric Non-centrosymmetric piezoelectric Surface coating/ functionalization:

Barium titanate nanoparticles

Optical probe

•

Au nanoshell93

•

β-cyclodextrin82

•

PLL coating80

•

glycol chitosan coating81

•

gum Arabic coating23

76,77

Biosensing58

Boron neutron capture therapy64,68 Boron nitride nanotubes

Surface coating/ functionalization: •

Au quantum dots58

•

folic acid coating64,68

•

glycol chitosan coating22,61

•

gum Arabic coating63

•

PEI coating59

•

PLL coating7,60

•

transferrin coating62

Cell stimulation: •

C2C12 and fibroblast9

•

High chemical stability58

•

hOBs7

•

High Young's modulus54,55

•

PC12 and SH-SY5Y22

•

Insulators56

•

Semiconductors (reversibly)57

Regenerative medicine55 Poly(vinylidene difluoride)

Physico-chemical properties:

Cell stimulation of

20


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human adipose stem cells112 Cell stimulation: •

Auditory neurons11

•

SH-SY5Y6

Poly(vinylidene difluoridetrifluoroethylene)

Regenerative medicine: •

neural differentiation21

•

neural regeneration101

Lithium sodium potassium niobate

Bone tissue engineering33

Pb(Zrx,Ti1-x)O3 (PZT)

Biosensing/energy harvesting37,41

(1-x)Pb(Mg1/3Nb2/3)O3 – xPbTiO3 (PMN-PT)

Biosensing/energy harvesting40

ZnO nanostructures

Nanopiezotronics85

4. Piezoelectric material modeling with application to cell stimulation Let us consider a piezoelectric material in contact with a living cell (hereafter assumed as reference bioorganic material, for ease of presentation), the former to be activated to stimulate the latter. To frame our discussion, let us consider a “classical” piezoelectric crystal (indeed, 20 of the 32 crystal classes exhibit piezoelectric behavior, namely those non-centrosymmetric).113 Piezoelectricity is commonly defined through a linear coupling between applied mechanical stress and induced polarization (direct effect), or between applied electric field and induced strain (converse effect). Differently, the electromechanical coupling exhibited by many bioorganic materials cannot be described by simple constitutive relations. The cell membrane, for instance, contains electrical charges and dipoles, and non-trivial conformational changes of membrane proteins transport both intrinsic charged residues and extrinsic ions, as made available by the heterogeneous biological medium.114 Moreover, stress-/strain-induced conformational changes in proteins affect gating currents, and

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mechanosensitive channels can be (de)activated or switched through mechanisms that still need to be fully elucidated.115 At present, we are not able to model this realm of biophysical effects. Experimentally, we know that 19 of the 20 known aminoacids have non-centrosymmetric crystal structures, thus paving the way for interpreting electromechanical coupling in many fibrous, globular and transmembrane proteins.116,117 Moreover, chirality (also featured by aminoacids) was invoked to interpret electromechanical coupling in DNA and phospholipids,116 also using liquid crystals theory.118 Furthermore, temperature affects electromechanical coupling in biological membranes, which obey the Curie-Weiss law for ferroelectrics.119 In this regard, polarization hysteresis is typically used to indicate ferroelectric-like behavior in bioorganic materials, and molecular modeling (quantum-chemical computations) was recently introduced to better understand these effects for glycine (the simplest aminoacid).119 Based on the complexity of the underlying mechanisms, electromechanical coupling in cells cannot be exhaustively modeled by merely recalling the methods introduced, e.g., for crystalline materials (to emphasize this aspect, electromechanical coupling, rather than piezoelectricity, was precisely addressed in the present discussion). Indeed, besides the difficulty in identifying the role of specific biological units at the nanoscale, additional physical phenomena are expected to play a role, including surface effects114 and flexoelectric effects (which can appear when also considering centrosymmetric charge distributions, and the relative importance of which increases at smaller length-scales).115,120 Recent celllevel modeling efforts are incrementally being backed by experimental findings. For instance, with regard to electromechanical coupling (also called electromotility) in outer hair cells, the identification of the key role played by the transmembrane protein prestin121 motivated the introduction of finer-level models of charge transfer through the cell membrane, e.g., based on the Fokker-Planck equation122 up to including time-rate (viscoelastic) effects115 in idealized cell geometries. The lack of conclusive experimental data, however, does not allow for a complete understanding of the related transduction 22


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mechanisms,114,115,117 and finer-level models can currently complement, rather than replace, phenomenological approaches.123,124 Hence, we can currently model the response of the activated piezoelectric material more reliably/accurately than the induced cell response. Nevertheless, modeling the piezoelectric material per se is very important, since it permits to potentially compensate for experimental conditions hard to measure/characterize, to organize the experimental results, and to design further experiments. Moreover, all of the previously mentioned assets can be achieved, in principle, at a relatively contained cost. In addition, modeling the piezoelectric material per se also enables better interpretation of the cell response, e.g., through quantitative estimates, or by reducing the uncertainty intrinsically associated with experiments. We thus recall in Section 4.1 a continuum modeling framework for piezoelectric materials, namely a thermodynamics-based formulation that can be used to define both linear and nonlinear constitutive relations. We deliberately pursue such a general approach because the same framework can also be used for deriving phenomenological constitutive relations able to describe electromechanical coupling effects in cells. Indeed, model development must be based on a careful consideration of the final objectives and implementation constraints, including any limitations on the reliability/accuracy with which we can calibrate the involved parameters. Based on the available experimental data, a reasonably developed/calibrated continuum model can thus increase/refine our knowledge on the biological system by describing its behavior more accurately than, to say, a finer-level yet poorly calibrated approach. As a matter of fact, the considered modeling framework supports applications at large. The rest of the section is structured as follows. As anticipated, in Section 4.1 we present the general constitutive framework, with some emphasis on alternative formulations that can be selected based on the available data and specific application. In Section 4.2 we recall one-dimensional linear constitutive relations, since they are commonly used in applications. Section 4.3 then reports the application of 23



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linear constitutive models in the context of neuronal and osteoblast-like cells stimulation, respectively. In both cases, modeling permitted to quantitatively corroborate the hypothesis of piezoelectric cell stimulation. 4.1 Thermodynamics-based constitutive framework Let us consider thermodynamically-reversible changes of a generic (non-magnetic) material. By applying the first and the second law of thermodynamics to a unit volume, the infinitesimal change in its internal energy reads:113 dU = σ ij d ε ij + Ei dDi + TdS ,

(1)

where σij and εij respectively denote stress and strain (tensors), Ei and Di respectively denote electric field and electric displacement (vectors), T and S respectively denote temperature and entropy (scalars), and the summation over repeated indexes is hereafter understood. It is well known that dU is a perfect differential, whereas its work (σij dεij + Ei dDi) and heat (T dS) components are not, and therefore

  ∂U  σ ij :=     ∂ε ij  D , S   ∂U    Ei :=   ,  ∂Di ε , S    T :=  ∂U    ∂S ε , D 

(2)

where differentiation with respect to each tensor/vector component is carried out by also keeping all of the other components constant. By specifying the internal energy

U = U ( ε , D, S ) ,

(3)

which also implies the definition of a reference condition since Eq. 1 only involves differentials, one immediately obtains the following constitutive relations for the considered material from Eq. 2:

24


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σ ij = σ ij ( ε , D, S )   Ei = Ei ( ε , D, S ) ,  T = T ( ε , D, S ) 

(4)

which will be, in general, nonlinear. The differentials of σij, Ei and T then read:

 ∂σ ∂σ ∂σ dσ ij =  ij  d ε kl +  ij  dDk +  ij  dS   ∂S ε , D  ∂ε kl  D , S  ∂Dk ε , S   ∂Ei   ∂E    ∂E   d ε jk +  i  dD j +  i  dS ,  dEi =   ∂S ε , D   ∂ε jk  D , S  ∂D j ε , S   ∂T   ∂T    ∂T  dT d ε ij +  dDi +  =     dS   ∂ε ij  D S ∂ ∂   ε ,D i     ε , S  D,S

(5)

where each of the six “off-diagonal” partial derivative terms clearly represents a coupling amongst mechanic, electric and thermal effects. Finally, being U a potential, the following thermodynamic constraints on the partial derivative terms hold:

 ∂σ   ∂ 2U   ∂Ek   ij  =   =   ∂Dk ε , S  ∂Dk ∂ε ij  S  ∂ε ij  D ,S    ∂Ei   ∂ 2U   ∂T  =     =  ,  ∂ S ∂ S ∂ D   , D i ε  ε  ∂Di ε , S   2   ∂σ ij  =  ∂ U  =  ∂T       ∂S   ∂S ∂ε  ∂ε ij    ij  D , D ε   D,S 

(6)

which state that, for any couplings, a “direct” effect is (quantitatively) equal to the corresponding “converse” one (conjugate variables, i.e., temperature/entropy, stress/strain, and electric field/displacement, appear in the considered thermodynamic constraints). The previous derivation applies to any thermodynamic potentials, since we only exploited the first two principles of thermodynamics. Alternative (equivalent) formulations, e.g., in terms of Helmholtz free energy F = F (ε,D,T) or Gibbs free energy G = G (σ,E,T), can thus be obtained by a classical

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Legendre transform.125,126 They are summarized in Table 2 for conciseness. In practical applications, the choice of a specific formulation depends on the available experimental data: typically, researchers aim to explicitly define the corresponding potential based on the variables that they directly control through measurements. This approach is completely general, and it was also applied to define phenomenological models of bioorganic materials, including nonlinear models of the outer hair cell based on the (electric) Gibbs free energy.123,124

Table 2. Equivalent formulations based on thermodynamic potentials Thermodynamic potential

Legendre transform# from U

Independent variables and differential form

U: Internal energy

-

U = U (ε, D, S) dU = σij dεij + Ei dDi + T dS

F: Helmholtz free energy

F := U[S] = U – T S

F = F (ε, D, T) dF = σij dεij + Ei dDi - S dT

G: Gibbs free energy

G := U[ε,D,S] = U - σij εij - Ei Di - T S

G = G (σ, E, T) dG = - εij dσij - Di dEi - S dT

G1: Elastic Gibbs energy

G1 := U[ε,S] = U - σij εij - T S

G1 = G1 (σ, D, T) dG1 = - εij dσij + Ei dDi - S dT

G2: Electric Gibbs energy

G2 := U[D,S] = U - Ei Di - T S

G2 = G2 (ε, E, T) dG2 = σij dεij - Di dEi - S dT

H: Enthalpy

H := U[ε,D] = U - σij εij - Ei Di

H = H (σ, E, S) dH = - εij dσij - Di dEi + T dS

H1: Elastic enthalpy

H1 := U[ε] = U - σij εij

H1 = H1 (σ, D, S) dH1 = - εij dσij + Ei dDi + T dS

H2: Electric enthalpy

H2 := U[D] = U - Ei Di

H2 = H2 (ε, E, S) dH2 = σij dεij - Di dEi + T dS

#

Given a function f(x,y), f[x] := f – (∂f/∂x) x. The generalization to the case of more variables is understood.

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Linear constitutive laws are classically introduced starting from differential relations like those in Eq. 5. Assuming relatively small variations of the independent variables around a reference state, the differentials are replaced by finite variations and the partial derivative terms are consistently replaced by constant coefficients. Working with the Gibbs free energy, for instance, the linear constitutive relations are typically written as follows:113   ε = s E ,T σ + d T E + α E ∆T ijkl kl kij k ij  ij T σ ,T σ  Di = d ijkσ ij + κ ij E j + pi ∆T ,  σ ,E ∆S = α ijEσ ij + piσ Ei + C ∆T  T

(7)

where sijkl, κij and C represent elastic compliance, electric permittivity and heat capacity, respectively, whereas subscripts and superscripts respectively indicate fixed variables and tensor indexes. The constraints previously illustrated through Eq. 6 are already implemented in Eq. 7, since: dijk denotes direct and converse piezoelectricity; αij denotes thermal expansion and its converse (piezocaloric) effect; pi denotes pyroelectricity and its converse (electrocaloric) effect. Moreover, using the wellknown Voigt notation (and by leveraging mild assumptions on some coefficients, such as hyperelasticity for the purely elastic behavior127), it is possible to recast Eq. 7 in a compact matrix notation functional to practical computations (the sparsity pattern of the involved matrices is well defined, e.g., for crystalline materials).113 An additional simplification can be achieved by neglecting the ∆S equation and the ∆T terms in Eq. 7, based on estimates of the relatively lower importance of thermal effects or, as in many practical applications, due to the lack of proper measurements. These constitutive laws were used for the finiteelement simulation of piezoelectric nanogenerators (cantilever beams with regular cross-section), and permitted to obtain analytical solutions by neglecting charge transport in the material. 4.2 One-dimensional linear constitutive relations

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In this section we deliberately overwrite some of the symbols introduced in Section 4.1 to comply with the notation most widely adopted in the literature when presenting one-dimensional constitutive laws for piezoelectricity. This abuse of notation is confined to the present section. Let us adopt the following symbols: S (strain), T (stress), E (electric field), D (electric displacement). The one-dimensional linear constitutive relations in the absence of thermal/entropy effects are summarized in Table 3, where: s and c denote elastic compliance and stiffness, respectively; d, e, g and h denote piezoelectric coefficients; є denotes electric permittivity. Moreover, superscripts

are understood as above, and thermodynamic constraints are already implemented (so that, e.g., the direct/converse piezoelectric effects are associated with the same symbol, up to sign). In Table 3 we also show the (quadratic) potential corresponding to each formulation, to parallel Table 2 (up to notation). To disambiguate the potential definition, we tacitly assume temperature as a fixed independent variable, to be consistent with literature126 and experimental practice while neglecting thermal/entropy effects.

Table 3. Equivalent one-dimensional linear constitutive laws (neglecting thermal/entropy effects) Independent variables#

Constitutive relations

and thermodynamic potential S = sE T + d E,

D = d T + єT E

G = G (T, E) G := - (1/2) sE T2 - d T E - (1/2) єT E2

S = sD T + g D,

E = - g T + (1/єT) D

G1 = G1 (T, D) G1 := - (1/2) sD T2 - g T D + (1/(2 єT)) D2

T = cE S - e E,

D = e S + єS E

G2 = G2 (S, E) G2 := (1/2) cE S2 - e S E - (1/2) єS E2

T = cD S - h D,

E = - h S + (1/єS) D

F = F (S, D) F := (1/2) cD S2 - h S D + (1/(2 єS)) D2

#

Temperature is tacitly assumed to be fixed (corresponding expressions in Table 2 are paralleled, up to notation).

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Let us remark that the 22 formulations in Table 3 are equivalent to one another (like the 23 formulations in Table 2, where we also considered temperature/entropy effects), and therefore any 3 parameters featuring in a chosen formulation must be suitable for recasting the remaining 7. Table 4 then shows a representation of such 7 independent constraints that, while being obtainable through simple algebraic manipulations, can be also discussed in terms of thermodynamic arguments.113

Table 4. Constraints on the constitutive parameters appearing in Table 3 Constitutive parameter

Units (SI)

Constraint(s)

d

[C/N]=[m/V]

d = єT g = sE e

e

[ C / m2 ] = [ N / (V m) ]

e = є S h = cE d

g

[ m2 / C ] = [ (V m) / N ]

g = sD h

h

[N/C]=[V/m]

h = cD g

єT

[-]

єT = єS + d e

In spite of the underlying simplifications, constitutive laws such as those in Table 3 were also used to derive equivalent-circuit models of, e.g., outer hair cells electromotility,128 which can be extended by considering viscoelastic effects.115 However, model calibration is not trivial at the nanoscale, not even for classical crystalline materials, and bulk properties are commonly used in the absence of specific measures or estimates based on atomistic computations.129 4.3 Applications: Piezoelectric stimulation of neuronal and osteoblast-like cells

We originally took a quantitative step for the study of piezoelectric nanoparticle-assisted neuronal stimulation.23 In particular, we considered tetragonal barium titanate nanoparticles (BTNPs) located at the neural plasma membrane and subjected to ultrasound (Figure 6a). Based on the involved lengthand time-scales, such nanoparticles underwent a quasi-static deformation driven by the ultrasound pressure pUS, so that we aimed at estimating the corresponding voltage variation φR (Figure 6b). Its 29



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experimental measure was beyond the current possibilities, and therefore we proposed a simplified modeling approach (based on spherical symmetry) to obtain explicit analytical solutions highlighting the role of the involved physical phenomena. We modeled a single BTNP as a sphere with radius R, considering its material as homogeneous, isotropic, and linearly-elastic. Using spherical coordinates (r, θ and ϕ), its mechanical equilibrium was given by the following problem:

σ r − σθ  =0 σ r′ + 2 r  , σ r ( r = R ) = − pUS 

(8)

where σr and σθ are the stress tensor components and prime hereafter denotes differentiation with respect to r. Moreover, the only component Dr of the electric displacement was null because it was divergence-free and to avoid singularities at the BTNP center. The considered constitutive relations were formulated as follows (cf. the G2-formulation in Table 3, up to notation):

u   σ r = crr u ′ + 2crθ r + errϕ ′  u  σ θ = crθ u ′ + ( cθθ + cθφ ) + erθ ϕ ′ , r  u   Dr = err u ′ + 2erθ r − є rrϕ ′ 

(9)

where u denotes the radial displacement and φ indicates the electric potential, so that the relevant deformation tensor components (u', u/r) and the electric field component (-φ') in Eq. 9 are easily identified. After obtaining φ' in terms of u and u' (using Dr = 0) and by substituting σr and σθ from Eq. 9, we obtained from Eq. 8 an ordinary differential equation for u leading to the following solution: s

u ϕ r = =  , uR ϕR  R 

(10)

where, in particular,

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ϕ R := −


R ( s err + 2 erθ )  pUS    s є rr s γ +2 α 

(11)

and uR := - R pUS / (s γ+2 α), s := ((1 – 4 λ)1/2 - 1) / 2, λ := 2 (α - β) / γ, α := crθ + (err erθ) / є rr , β := cθθ + cθϕ + (2 erθ2) / є rr and γ := crr + (err2) / є rr . Moreover, we expressed the elastic coefficients in terms of the Young modulus (E) and Poisson ratio (ν), namely crr = cθθ = E (1 - ν) / ((1 + ν) (1 - 2ν)) and crθ = cθϕ = E ν / ((1 + ν) (1 - 2ν)). Let us remark that the obtained solution reduces to the classical one when considering the purely elastic case.130 Based on the selected BTNPs, we adopted the following parameter values:23 R = 150 nm, E = 70 GPa, ν = 1/3, err = 10 C/m2, erθ = -1 C/m2 and є rr / є0 = 102 ( є0 being vacuum electric permittivity). Moreover, we estimated pUS by exploiting a classical plane-wave approximation: pUS = (2 IUS Zw)1/2, where Zw is the water impedance and IUS denotes ultrasound intensity, which was directly controlled during the experiments. In particular, we stimulated with IUS = 0.1 and 0.8 W/cm2, thus inducing φR = 0.3 and 0.8 mV, respectively, based on Eq. 11. These estimates suggested that, when using 0.8 W/cm2, an induced voltage of a few mV could locally affect channel open probability (by also considering superposition where BTNPs clustered, as observed by confocal microscopy) and enhance the voltage sensitivity of the voltage-gated channels. Differently, channel activation was more difficult when using 0.1 W/cm2. Model predictions were in full agreement with the indirect experimental observations on biological models, and they quantitatively supported the hypothesis of BTNP-mediated, piezoelectric neuron stimulation (for the first time in literature, to the best of our knowledge). More recently, we considered piezoelectric film-assisted stimulation of osteoblast-like cells (data to be published). In particular, we considered both plain P(VDF-TrFE) films (which are piezoelectric per se) and composite films made by loading P(VDF-TrFE) with piezoelectric boron nitride nanotubes 31



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(BNNTs), for osteoblast-like cell culturing once fixed in a Petri dish through a thin adhesive poly(dimethylsiloxane) (PDMS) layer. During cell culture, the films were subjected to ultrasound (Figure 6c). Neither direct measurements of the induced potential nor extensive quantitative control of all working parameters were trivial; hence, we introduced a numerical model to support the interpretation of the stimulation experiments in terms of piezoelectric effects. In light of the modest film thickness (tf = 50 µm) compared to the characteristic length-scale of the experimental setup (order of cm), a simplified two-step approach was implemented: the ultrasound-induced pressure field was first computed by neglecting the film; the voltage was then derived based on the computed pressure at the film site. We modeled the inner volume of the Petri dish as a cylindrical domain Ω partitioned into three layers: PDMS, water and air (Figure 6c). In Ω we considered the classical linear acoustic equation in the frequency domain,131 looking for a pressure field of the form p exp(j ω t), where ω := 2π fUS and fUS is the chosen ultrasound frequency, t denotes time and the unknown p only depends on space. Being the ultrasound transducer suitably coupled with the Petri, we assumed a harmonic displacement dUS exp(j ω t) and we enforced the corresponding acceleration on the boundary ∂Ω (Figure 6d), besides assuming pressure continuity at each material interface. Thus, we numerically solved the following problem:

  1  ω2 p = 0 in Ω  ∇ ⋅  − ∇p  − 2   ρ0  ρ 0c0  . 2  n ⋅  − 1 ∇p  = n ⋅ d on ∂Ω  US ( jω ) z   ρ 0   

(

(12)

)

where ρ0 and c0 represent medium density and sound speed in unperturbed conditions, respectively, n and z denote unit vectors normal to ∂Ω and aligned with the cylinder axis, respectively, and classical differential operators are understood. Once fixed fUS = 1.089 MHz and dUS = 1.3 nm (based on 32


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vibrometry measurements), we obtained a pressure pf = 2-6 kPa on the piezofilm by also considering uncertainty on the sound speed within PDMS, as well as sensitivity to dUS (Figure 6e). We then obtained the voltage ∆Vf induced on the piezofilm by using a simple one-dimensional approximation commonly used in literature, namely (cf. the G1-formulation in Table 3 with D = 0 and up to notation): ∆V f = E t f = g33 p f t f .

(13)

Assuming g33 = 0.2 Vm/N for the P(VDF-TrFE) films, we obtained ∆Vf = 20-60 mV (Figure 6f), which is high enough to effectively elicit cell response.132 Let us finally remark that we deliberately introduced simplified models, commensurate in particular with the available data, by focusing our modeling efforts either on the ultrasound stimulus (when the piezoresponse was more easily obtainable, as for the BNNT-loaded piezofilms) or on the piezoelectric response itself (when it was less straightforward, up to accepting further simplifications on the ultrasound stimulus). We demonstrated piezoelectric cell stimulation by also exploring in silico some model uncertainties, thus quantitatively supporting the study of biointerfaces based on piezoelectric nanomaterials.

5. Conclusion The history and origin of electrical stimulation for medical purposes, also commonly known as electrotherapy, is very peculiar and originates as early as 400 B.C. when torpedo fishes, taken live from lakes and streams and placed on a painful area of the body, were exploited to produce series of electric shocks (of about 100-150 V) that were considered useful in reducing or control the pain. With the advancement of knowledge and with the ability to store electricity into batteries, electrical stimulation of tissues for various biological applications gained popularity in the 1800s, however a general

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skepticism soon hindered its wide spreading until 1965, when the gate control theory of pain was introduced.133 Nowadays, it is well known that cells and tissues are highly responsive to electrical cues, and the possibility to achieve an indirect stimulation, even inside cells, thanks to piezoelectric nanostructures is therefore extremely exciting, opening a wide spectrum of applications in the clinical practice. Nanostructured piezoelectric interfaces own the actual potential to offer beneficial environments for cell and tissue stimulation, and, at the same time, they introduce new scenarios into nanomedicine, where nanomaterials, owing to their “smart” properties, are exploited as active devices rather than as passive structural units or carriers for medications.134 Future applications of piezoelectric nanomaterials range from self-powered artificial cardiac pacemakers, artificial cochlear epithelium and nano-piezotransducers for non-invasive deep brain stimulation, peripheral nerve regeneration and bone tissue engineering. Despite the impressive potential of piezoelectric nanostructures in biomedical field, further research efforts are still necessary for the evaluation of the nanomaterial biocompatibility, retention, degradability, accumulation in complex in

vivo systems before actual exploitation in clinical context. These investigations can be focused on a huge variety piezoelectric nanostructures characterized by peculiar chemical/physical properties and will allow for the identification of a “golden standard” nanotechnology-based device/treatment to be adopted for the human healthcare.

Acknowledgements This work has been partially supported by the Italian Ministry of Health, Grant Number RF-201102350464 and by Fondazione Umberto Veronesi.

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Figure 1. Biointerfacing piezoelectric nanoribbons to single cells (a, b) and tissues (c-j). (a) The scheme depicts the sensor device with suspended piezoelectric nanoribbons and cultured PC12 cells. The mechanical deflection of the cells are induced by a glass pipette (PPT). Cell deflections are detected and transduced to electric signals by the PZT nanoribbons. Electric signals are then collected 35



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by indium tin oxide (ITO) electrodes, which are electrically isolated thanks to SiNx coating. (b) Scanning electron microscopy (SEM) imaging of a PC12 neural-like cell interfaced with PZT nanoribbons (scale bar: 15 µm). (c) SEM scan of piezoelectric nanoribbons integrated onto a flexible PDMS substrate (scale bar: 15 µm). (d) Optical microscopy shows the inter-digitated gold electrodes (horizontal yellow lines) and the PZT nanoribbons (vertical dark lines, scale bar: 50 µm). (e) Photograph reveals the flexibility of the PDMS chip with nanoribbons, once interfaced with bovine lung tissue (f) to detect the mechanical deformations associated to the different phases of respiration: in (g) and (h) the chip is respectively in rest and strained state (scale bars of e-h photographs: 1 cm). The graphs in (i) and (j) show the voltage (V) and the current (nA) recorded by the chip of PZT nanoribbons during the respiration, respectively; the oscillatory electric signal reveals the repeated deformation of the cow lung. Adapted with permission from [37]. Copyright 2012 Macmillan Publishers Limited.

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Figure 2. Atom arrangements in (a) boron nitride nanosheets (BNNSs) and in boron nitride nanotubes (BNNTs) characterized by (b) zigzag (10,0), (c) armchair (6,6), and (d) chiral (7,5) configurations. Adapted with permission from [50]. Copyright 2009 Springer.

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Figure 3. Chronic piezoelectric stimulation with boron nitride nanotubes (BNNTs) and ultrasound (US) promoted neurite elongation in PC12 neural-like cells. PC12 cells were treated with BNNTs at different concentrations (0-10 µg/ml) and then stimulated with US (w US). The neurite length of PC12 cells was then compared with non-stimulated controls (w/o US). (a) PC12 cells of the different experimental conditions are labeled with calcein. (b) The neurite lengths measured during in vitro neural differentiation are reported in graphs. Adapted with permission from [22]. Copyright 2010 American Chemical Society.

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Figure 4. Piezoelectric stimulation of SH-SY5Y neuron-like cells by exploiting piezoelectric barium titanate nanoparticles (BTNPs) in combination with an external source of ultrasound (US). (a) SEM and (b) TEM images of piezoelectric tetragonal BTNPs. (c) 3D rendering of confocal laser scanning showing BTNPs (in red) associated to the membranes of SH-SY5Y cells (in green). Ca2+ imaging experiments of cells stimulated with US only (d), with US + piezoelectric BTNPs (e), and with US + non-piezoelectric BTNPs (characterized by cubic crystalline structure). Graphs showed the activation of high-amplitude Ca2+ peaks only when neurons are synergistically stimulated with US and tetragonal BTNPs. Adapted with permission from [23]. Copyright 2015 American Chemical Society.

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Figure 5. Nanocomposite films prepared by P(VDF-TrFE) and tetragonal BTNPs supported proliferation and differentiation of SH-SY5Y neuron-like cells. SEM images of plain polymeric (a) and composite films (b) after cryosection. Piezoresponse force microscopy maps of P(VDF-TrFE) (c) and P(VDF-TrFE)/BTNP films (d), showing enhanced piezoactivity of composite substrates. Confocal fluorescence microscopy of cells at the end of a differentiation process conducted in the presence or absence of ultrasound: β3-tubulin in green and nuclei in blue (e). Quantification of cell differentiation (f) and of neurite length (g) in the different experimental classes (* p < 0.05). Adapted with permission from [6]. Copyright 2016 Wiley.

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Figure 6. (a) Schematic of a piezoelectric nanoparticle on the neural plasma membrane, subjected to ultrasound. (b) Voltage φR induced by ultrasound pressure pUS. (c) Schematic of piezoelectric films (supporting osteoblast-like cells) fixed in a Petri dish and subjected to ultrasound. (d) Computational domain (cross-section) with ultrasound-driven boundary vibration (amplitude dUS, frequency fUS). (e) Pressure at the piezofilm site as a function of dUS and cPDMS (sound speed within PDMS). (f) Voltage

∆Vf induced by ultrasound as a function of cPDMS. Uncertainty on cPDMS was accounted for in silico, through the parameter sweeps in (e) and (f).

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