Immediate delivery of a second pulse of the opposite polarity in which the duration and amplitude were the same as the first pulse  or greater than the first pulse  had a stimulatory effect, evoking larger Ca2+ responses than the corresponding unipolar pulse. Progressively decreasing the amplitude of the opposite polarity pulse while also increasing its duration converted stimulation to attenuation, which reached a maximum of 43% when the positive phase was 150 ns at 3.1 kV/cm, and the negative phase was 800 ns at 0.2 kV/cm. When VGCCs were blocked, Ca2+ responses evoked by asymmetrical and even symmetrical bipolar pulses were significantly reduced relative to those evoked by the corresponding unipolar pulse under the same conditions, indicating that attenuation involved mainly the portion of Ca2+ influx attributable to membrane electropermeabilization. Thus, by tuning the shape of the bipolar pulse, Ca2+ entry into chromaffin cells through electropores could be attenuated while preserving Ca2+ influx through VGCCs.Exposing adrenal chromaffin cells to single 150 to 400 ns electric pulses triggers a rise in intracellular Ca In vivo, catecholamine secretion from chromaffin cells occurs when acetylcholine released from splanchnic nerve terminals stimulates nicotinic cholinergic receptors (nAChRs) that are ligand-gated Na+ channels. Na+ influx via nAChRs causes membrane depolarization leading to an elevation in intracellular Ca2+ concentration ([Ca2+]i) orchestrated by Ca2+ entry through several classes of voltage-gated Ca2+ channels 1. This sequence of events culminates in Ca2+-dependent exocytosis3.Neuroendocrine adrenal chromaffin cells are neural crest-derived excitable cells involved in the sympathetic discharge of the catecholamines epinephrine and norepinephrine into the vascular system during the “fight or flight” response. 4. Such short duration electric stimuli, particularly pulse durations that extend into the subnanosecond range, have the potential for remote, targeted delivery to tissues via antennas6, which could eliminate the need for invasive, contact electrodes. Moreover, the biophysical changes caused by nsPEF, one being the reversible formation of nanometer-diameter ion-conducting electropores  in the plasma membrane lipid bilayer11, may reveal novel mechanisms by which cell excitability can be altered. In adrenal chromaffin cells, as an example, we found that a single 5 ns, 5 MV/m pulse can stimulate these cells, producing an increase in [Ca2+]i followed by Ca2+-dependent catecholamine release that is triggered by a mechanism that bypassed nicotinic receptors but still involved Na+ influx, membrane depolarization and activation of VGCCs14. Because tetrotoxin failed to block the response4 ruled out voltage-sensitive Na+ channels as the pathway of Na+ influx and suggested instead that Na+ was most likely entering chromaffin cells via plasma membrane nanopores, causing membrane depolarization4. A similar mechanism of electroporation-induced depolarization may also be involved in the stimulation of rat hippocampal neurons by 200 ns pulses15. Convincing evidence in support of this mechanism of cell excitability in chromaffin cells has been provided by whole-cell patch clamp recordings of nsPEF-evoked inward Na+ currents16, leading us to conclude that nanopores could be subserving a function typically attributed to voltage-gated Na+ channels by causing membrane depolarization to a level that was sufficient to activate VGCCs4. Notably, Ca2+ does not also enter chromaffin cells via this plasma membrane pathway13, indicating that like stimulus-secretion coupling mediated by acetylcholine, activation of VGCCs is solely responsible for Ca2+ influx. Of note also is that nsPEF-evoked cell activation occurs without evidence of the plasma membrane perturbations that promote uptake of non-permeant dyes such as YO-PRO-114, release of Ca2+ from intracellular stores due to electroporation of membranes of Ca2+-storing organelles such the endoplasmic reticulum (ER)13, or adverse effects such as cell blebbing or cell swelling14. In addition to these findings from our group showing the potential for short duration nsPEF to be used for neurostimulation, Casciola et al. reported that 12 ns pulses applied to nerve fibers can elicit action potentials without causing nerve damage. Interestingly, the underlying mechanism of nsPEF-evoked excitability appears to be different in nerve than in chromaffin cells17.As modified post-ganglionic sympathetic neurons that are easy to isolate and maintain in culture, isolated chromaffin cells have played a major role in characterizing mechanisms underlying stimulus-secretion coupling. Accordingly, our group has been using bovine adrenal chromaffin cells as a model system to explore the potential for high intensity, nanosecond pulsed electric fields (nsPEF) to serve as a new modality for neurostimulation2+ responses also without evidence of cell swelling or cell blebbing, or uptake of YO-PRO-118. However, the more pronounced rise in [Ca2+]i evoked by these longer nsPEFs was found to be the result of Ca2+ entering the cells now by two pathways: (1) via VGCCs, which accounted for the bulk of Ca2+ influx (60–70%), and (2) Ca2+ influx through plasma membrane electropores18. Thus, the plasma membrane was no longer impermeable to Ca2+, coinciding with a similar finding of rapid influx of Ca2+ via nanopores in isolated rat hippocampal neurons exposed to 600 ns pulses19.While exploring other nsPEF parameters for stimulating chromaffin cells, a more recent study from our group revealed that exposing chromaffin cells to single longer duration nsPEF (≥150 ns) produced more robust and longer lasting Ca2+ influx through plasma membrane nanopores. In this new nsPEF paradigm, the application of a second pulse of opposite polarity and equivalent duration delivered immediately after the first pulse  could attenuate or even abolish the response produced by the first pulse, a process termed bipolar cancellation. This phenomenon was first described by Pakhomov et al.20 in non-excitable Chinese Hamster Ovary (CHO) cells exposed to single or multiple unipolar or bipolar nsPEF20. In these cells, a 60 ns unipolar pulse triggered a rise in [Ca2+]i that included nsPEF-induced Ca2+ influx from the outside the cell and Ca2+ efflux from the ER, attributed to a short-lived nanoelectroporation of the plasma membrane and ER membrane, respectively. At high stimulus intensities, Ca2+-induced calcium release (CICR) also contributed to the rise in [Ca2+]i20. When exposed to a symmetrical bipolar pulse (60 + 60 ns), CHO cells displayed much smaller Ca2+ transients than cells exposed to a 60 ns unipolar pulse, with each component that contributed to the Ca2+ response attenuated by the bipolar pulse. Bipolar cancellation was also demonstrated for longer duration pulses where a bipolar pulse (300 + 300 ns) was found to be less efficient for evoking increases in [Ca2+]i compared with the corresponding unipolar pulse (300 ns).Recently, a new modality of nsPEF stimulation has been reported that enables fine-tuning of cellular responses that include nsPEF-evoked Caet al.21 evaluated the effects of a single or multiple nanosecond electric field unipolar and bipolar oscillation (referred to as NEFO) on membrane electropermeabilization and changes in membrane conductance in CHO and GH3 cells. Relative to unipolar NEFO, bipolar NEFO yielded lower rates of uptake of YO-PRO-1 and, as determined by whole-cell patch clamp electrophysiology, a reduced membrane conductance21. These results and those of others reporting a similar reduction of electropermeabilization by bipolar pulses were attributed to the ability of these pulses to cause less plasma membrane perturbations24. In light of these results, we considered the possibility that in chromaffin cells exposed to nsPEF ≥ 150 ns, Ca2+ influx due to plasma membrane electroporation might be attenuated/cancelled by applying a bipolar pulse. This could potentially mean eliminating an undesirable effect of longer duration nsPEF while preserving the ability of the cells to be activated in a manner similar to that evoked by a short duration nsPEF. The primary objective of the present study was to evaluate whether bipolar cancellation could be detected in chromaffin cells for nsPEF ≥ 150 ns by exploring the effect of symmetrical bipolar pulses (same duration and peak amplitude for each phase) and asymmetrical bipolar pulses (duration and/or peak amplitude of the negative phase different than the positive phase) on [Ca2+]i. Our results show that depending on the pulse waveform, bipolar pulses could either enhance or attenuate Ca2+ influx evoked by a 150 ns unipolar pulse. Moreover, attenuation of Ca2+ entry by bipolar nsPEFs appeared to involve the portion of Ca2+ influx attributable to membrane electropermeabilization and not Ca2+ influx via VGCCs. Thus, tuning the shape of the bipolar pulse attenuated undesirable Ca2+ entry into chromaffin cells through electropores while maintaining Ca2+ influx through VGCCs. These results have implications for the future development of nsPEF stimulation approaches for modulating cell excitability non-deleteriously since the reduced electroporation efficiency of bipolar compared with unipolar pulses expands the range of nsPEF parameters that can be used for this purpose.In a subsequent report, Gianulis 2+ influx evoked by unipolar nsPEF could be “cancelled” by applying a second pulse of equivalent strength but opposite polarity and identical duration11. To determine whether bipolar cancellation of Ca2+ influx could be similarly achieved in excitable chromaffin cells, a systematic investigation of the impact of unipolar nsPEF on [Ca2+]i was first undertaken followed by an analysis of the effects of the corresponding bipolar nsPEF on [Ca2+]i. Cells were exposed to a single unipolar pulse of 150, 200, 300, 400 or 800 ns duration  and was not associated with adverse effects on cell morphology, such as cell swelling , they unequivocally demonstrate an absolute requirement for a Ca2+ entry pathway to trigger the response.Since VGCC activation is an all-or-none cellular process, symmetrical bipolar pulses were most likely enhancing Ca ns Fig. , ↑200 +  ns Fig.  or ↑400  ns Fig.  bipolar 2+ responses evoked by bipolar pulses, like single unipolar pulses18, increased in amplitude with pulse duration. For example, Ca2+ responses evoked by ↑200 + ↓200 ns or ↑400 + ↓400 ns bipolar pulses were 55% or 33% larger, respectively, than those produced by ↑150 + ↓150 ns bipolar pulses . Thus, the negative pulse phase acted as a 2nd stimulus regardless of pulse duration.The results of the experiments shown in Fig. ses Fig.  with the2+ influx induced by a bipolar pulse of ↑150 + ↓150 ns to a single unipolar pulse of 300 ns, which represents an equivalent amount of energy, the response elicited by the bipolar pulse was significantly smaller than that evoked by the unipolar pulse . Thus, even though the negative phase of the ↑150 + ↓150 bipolar pulse acted as a 2nd stimulus, Ca2+ influx was not comparable to that elicited by a single polarity 300 ns pulse. A possible explanation is that the positive phase of the bipolar pulse limited the extent to which the plasma membrane could be electropermeabilized by the negative phase of the pulse25. We also compared Ca2+ influx induced by a single bipolar pulse of ↑200 + ↓200 or ↑400 + ↓400 ns to a single unipolar pulse of 400 or 800 ns, which represents an equivalent amount of energy for each bipolar pulse, respectively. We found that the response triggered by a ↑200 + ↓200 ns vs a 400 ns pulse, or a ↑400 + ↓400 ns vs a 800 ns pulse was similar. Given the longer duration of these pulses relative to a ↑150 + ↓150 bipolar pulse or a unipolar 300 ns pulse, the Ca2+ indicator may have been saturated in each case, not allowing differences in [Ca2+]i to be detected among the groups.When we compared Ca2+ influx was not attenuated by symmetrical bipolar pulses. Instead, Ca2+ influx was enhanced. The next series of experiments investigated the effect of altering the shape of the bipolar pulse on Ca2+ influx by manipulating the parameters of the negative pulse phase.Taken as a whole, these results demonstrate that Ca2+ influx stimulated by single unipolar pulses increased in magnitude with pulse duration. Thus, increasing the duration of the negative phase of a bipolar pulse would presumably result in more electropermeabilization and hence more Ca2+ influx, resulting in even greater increases in [Ca2+]i when compared to that evoked by a symmetrical ↑150 + ↓150 bipolar pulse. To examine this possibility, the positive pulse phase was kept constant at 150 ns and the duration of the negative pulse phase was varied from 200 up to 800 ns, both phases set at an E-field of 3.1 kV/cm. The specific asymmetrical bipolar pulses used in the analysis were ↑150 + ↓200, ↑150 + ↓400 or ↑150 + ↓800 ns . These results are consistent with the demonstration in CHO cells that a ↑300 + ↓900 bipolar pulse caused more YO-PRO-1 uptake than a 300 ns unipolar pulse22. Table 2+ responses evoked by each asymmetrical bipolar pulse were also greater than those evoked by a symmetrical ↑150 + ↓150 bipolar pulse. Post hoc analysis revealed that Ca2+ responses elicited by ↑150 + ↓200 bipolar pulses were not significantly different from those produced by 150 ns unipolar pulses (p > 0.05) whereas responses to bipolar pulses of ↑150 + ↓400 and ↑150 + ↓800 were significantly different from those evoked by 150 ns unipolar pulses . Although the magnitude of the rise in [Ca2+]i tended to increase in a linear fashion with the duration of the negative phase  and ↑150 + ↓1000 ns at an E-field ≤ 0.4 kV/cm . Figure 2+ response elicited by the 150 ns unipolar pulse, not only was the magnitude of the rise in [Ca2+]i decreased but also [Ca2+]i returned to pre-stimulus levels during the 50-s post-pulse monitoring period. Indeed, the Ca2+ response triggered by these bipolar pulse waveforms now more closely resembled that evoked by the physiologic stimulus, activation of nicotinic cholinergic receptors26. Due to the technical limitations of our bipolar pulse exposure system, we could not determine if maximal cancellation of Ca2+ influx was achieved since this would require negative pulse phases of even lower E-field amplitude and/or longer duration, which are not possible with our setup.Consistent with the experiments described in the previous section, increasing the duration of the negative pulse phase led to enhanced stimulation, especially at higher E-fields  unipolar pulses is passing through VGCCs18, it is possible that bipolar pulses are unable or are less efficient at cancelling the Ca2+ influx component involving VGCCs, or that the Ca2+ that enters the cells via VGCCs affects how the cell responds to a bipolar pulse.As indicated previously, strong bipolar cancellation of Ca2+ influx by symmetrical bipolar pulses, as shown for cells that do not express VGCCs. For this determination, chromaffin cells were pre-treated with a combination (cocktail) of Ca2+ channel blockers and exposed to a ↑150 + ↓150 ns bipolar pulse. The cocktail of Ca2+ channel blockers comprised 100 nM ω-agatoxin GVIA (P/Q-type) + 20 nM ω-conotoxin (N-type) + 20 µM nitrendipine (L-type), which we previously determined was effective for blocking Ca2+ influx mediated by VGCCs in cells exposed to the pulse durations used in this study18. In other experiments, cells were pre-treated with dihydropyridines alone at high concentrations , which we previously also determined caused substantial inhibition of Ca2+ influx triggered by ≥150 ns pulses18. High concentrations of dihydropyridines ensured that both CaV1.2 and CaV1.3 isoforms of L-type channels, which are both expressed in bovine chromaffin cells27, were effectively inhibited since CaV1.3 channels are less sensitive to dihydropyridines than CaV1.228. That this treatment significantly inhibited Ca2+ influx10 most likely meant that the other types of VGCCs present in these cells were partially blocked29.To explore these possibilities, we determined whether conducting experiments under conditions that would eliminate the contribution of VGCCs to nsPEF-evoked responses would show cancellation of Ca2+]i that was larger by around 18% than that elicited by the corresponding 150 ns unipolar pulse. When cells were treated with the cocktail of VGCC blockers, Ca2+ influx elicited by a 150 ns pulse was inhibited by around 66%  reached statistical significance . These results are evidence that bipolar pulses were cancelling the portion of Ca2+ influx attributable to Ca2+ permeation mediated by electronanoporation and not Ca2+ influx via VGCCs. They also beg the question of why Ca2+ influx due to electronanoporation was now achievable when Ca2+ influx via VGCCs was suppressed. The answer to this question awaits future investigation30.Similar to the results shown in Fig. 66% Fig. , which i2+ influx was not achievable with the range of asymmetrical bipolar pulse waveforms available with our current exposure setup. It could also be because any depolarizing stimulus that causes Ca2+ entry via VGCCs in chromaffin cells, such as nicotinic receptor stimulation as well as nsPEF, may also trigger some CICR due to activation of ryanodine receptors33. Thus, blocking Ca2+ influx via VGCCs would also prevent CICR, causing an apparent enhanced cancellation effect relative to cells exposed to asymmetric bipolar pulses with VGCC responses intact. We did not test for the presence of CICR since it is a response that is secondary to Ca2+ influx via VGCCs and thus outside the scope of the present study, which was mainly focused on determining pulse parameters and conditions that would allow us to detect bipolar cancellation of Ca2+ influx.The levels of cancellation achieved by suppressing VGCCs were slightly greater than those achieved by asymmetrical bipolar pulses producing significant and optimal cancellation Table . This di2+ influx by symmetrical bipolar pulses was observed only when VGCCs were blocked, we explored how Ca2+ influx via VGCCs impacted the level of cancellation produced by an asymmetrical bipolar pulse having a long duration (1000 ns), low E-field amplitude (0.4 kV/cm) negative pulse phase. For these experiments, cells were exposed to a 150 ns unipolar pulse or to a ↑150 + ↓1000 ns bipolar pulse in the presence and absence of the VGCC blocker cocktail. As shown in Fig. 2+ influx by the asymmetrical bipolar pulse was significantly greater when VGCCs were blocked . These results again demonstrate that in chromaffin cells, bipolar pulses appear to be cancelling the portion of Ca2+ influx attributable to Ca2+ permeation mediated by electronanoporation. They also provide additional evidence that Ca2+ influx via VGCCs may impact cancellation efficiency.Since cancellation of Caduration 00 ns, loduration 000 ns, l2+ responses in excitable cells. Using neuroendocrine chromaffin cells isolated from the adrenal medulla as a cell model, we had previously reported10 and show here also that exposing these cells to unipolar pulses that are ≥150 ns in duration elicit an increase in [Ca2+]i that is mediated by Ca2+ influx via both VGCCs and putative plasma membrane nanopores, i.e. electropores. We now show that depending on the shape of the pulse waveform, exposing chromaffin cells instead to a bipolar pulse can partially cancel the portion of Ca2+ influx attributed to electropores, thereby attenuating an undesirable pathway of Ca2+ entry into the cells while leaving all-or-none VGCC activation intact. This finding, together with reports from other groups showing that bipolar pulses can cause less cell death of CHO, U937 and Jurkat cells than unipolar pulses24, provides incentive for continuing studies that explore the range of nsPEF parameters that can be used to drive neuromodulation safely and potentially non-invasively in the future.This study provides new insight into the potential application of bipolar pulses for modulating nsPEF-evoked Ca2+ influx, where the second phase of the bipolar pulse acts like a 2nd stimulus, most likely reflects an increase in the number of electropores. However, mechanisms underlying bipolar cancellation are not yet well defined and several have been proposed to explain the phenomenon. They include: (1) assisted membrane discharge20; (2) electropermeabilization of membranes as a two-step chemical process20; (3) reverse electrophoretic ion transfer34; (4) localized membrane charging and discharging22 and (5) nanopore occlusion35. Adding to the complexity of the bipolar cancellation phenomenon in chromaffin cells is the demonstration that for symmetrical bipolar pulses, Ca2+ influx via VGCCs can determine whether there is cancellation or stimulation. Future experiments will be carried out to test these various hypotheses.Regarding mechanisms, bipolar stimulation of Cain vivo.In conclusion, the demonstration in this study that the shape of bipolar nsPEFs could be altered in manner to allow for titrating the response of chromaffin cells may pave the way in the future for remote and non-invasive control of these and other types of excitable cells 2 as previously described36. Cells were used up until 2 weeks in culture. For nsPEF exposure, the large aggregates of cells that form in suspension culture were dissociated into single isolated cells with the protease dispase37 and plated onto fibronectin-coated 35 mm glass bottom dishes. Once attached, cells retained their spherical morphology and were used for a period not exceeding two days after attachment.Fresh bovine adrenal glands were obtained from a local slaughterhouse . After the outer adrenal cortex was removed by dissection, chromaffin cells were isolated by collagenase digestion of the adrenal medulla and maintained in suspension culture in Ham’s F-12 medium supplemented with 10% bovine calf serum, 100 U/ml penicillin, 100 µg/ml streptomycin, 0.25 µg/ml fungizone, and 6 µg/ml cytosine arabinoside at 36.5 °C under a humidified atmosphere of 5% CO2+]i were monitored in cells labeled with the Ca2+-sensitive fluorescent indicator, Calcium Green-1(Ex480 nm and Em535 nm) as previously described18. For dye loading, the cells were incubated with 1 µM Calcium Green-1 for 45 min at 37 °C in a balanced salt solution (BSS) containing 0.1% bovine serum albumin (BSA) and (in mM): 145 NaCl, 5 KCl, 1.2 NaH2PO4, 2 CaCl2, 1.3 MgCl2, 10 glucose, and 15 HEPES, pH 7.4. For fluorescence monitoring, cells were washed twice with dye-free BSS lacking BSA and placed on the stage of a Nikon TE2000 epifluorescence microscope equipped with a 100X objective. For Ca2+ free experiments cells were bathed in Ca2+-free BSS Ca2+ containing 1 mM EGTA. Fluorescence images of the cells were captured before, during and after application of a stimulus by an iXonEM + DU-897 EMCCD camera  using the open source microscopy software Micro-Manager . The exposure time of the camera was set to 100 ms and images were captured at a rate of 7.5 Hz. Bright field images were obtained at the start and end of an experiment, and all experiments were carried out at ambient room temperature.Changes in [Ca18 and complete fabrication details are given in Ryan et al.38. The unit has two independent circuits that deliver positive and negative pulses ranging from 150 to 1000 ns, with the ability to adjust the pulse widths and amplitudes of the positive and negative pulses separately. For cell exposure, single unipolar and bipolar pulses were delivered to an attached cell via a pair of cylindrical tungsten rod electrodes (127 µm diameter) with their tips spaced 100 µm apart. The cell to be investigated was positioned at the center of the gap between the electrode tips, which were positioned 40 µm above the bottom of the dish using a motorized micromanipulator . A LabVIEW program (version 8.01) was used to control the delivery of pulses. Each cell was exposed to a single unipolar or bipolar pulse only once. As reported in Bagalkot et al.18, the E-field distribution in the vicinity and at the location of the target cell was computed using the commercially available Finite-Difference Time-Domain (FDTD) software package SEMCAD X . The simulations showed that the E-field at the location of the cell was essentially uniform and that minor differences in electrode placement among cells would have negligible impact on the E-field amplitude to which a cell was exposed18.The custom-designed high-voltage biphasic nanosecond pulse generator used to expose chromaffin cells to nsPEF has been previously describedhttps://imagej.nih.gov/ij/). Changes in cell fluorescence intensity (ΔF) were calculated by subtracting background fluorescence from the fluorescence of the cell (ΔF = Fcell − Fbackground). The values were then normalized to the fluorescence intensity value at the time when the pulse was applied (F0). All experiments were replicated using cells from different cell preparations and different days in culture. Results were expressed as the mean ± standard error of the mean (s.e.m.). Statistical analyses, which were performed using SigmaPlot 13 software , consisted of an unpaired two-tailed t-test when the means of two groups were compared, or a one-way ANOVA test followed by Tukey post hoc multiple range tests for multiple group comparisons. p < 0.05 was considered statistically significant.Fluorescence images for each cell were continuously recorded during a period spanning 10 s prior to nsPEF exposure to obtain baseline, and then for a period spanning 50 s after nsPEF exposure. Images were analyzed using the public domain image processing software ImageJ (


We expect this hybrid image-based modeling framework to be adaptable for the study of other tissues  and other vasculature-dependent diseases .There is a critical need for new tools to investigate the spatio-temporal heterogeneity and phenotypic alterations that arise in the tumor microenvironment. However, computational investigations of emergent inter- and intra-tumor angiogenic heterogeneity necessitate 3D microvascular data from ‘whole-tumors’ as well as “ensembles” of tumors. Until recently, technical limitations such as 3D imaging capabilities, computational power and cost precluded the incorporation of whole-tumor microvascular data in computational models. Here, we describe a novel computational approach based on multimodality, 3D whole-tumor imaging data acquired from eight orthotopic breast tumor xenografts (i.e. a tumor ‘ensemble’). We assessed the heterogeneous angiogenic landscape from the microvascular to tumor ensemble scale in terms of vascular morphology, emergent hemodynamics and intravascular oxygenation. We demonstrate how the abnormal organization and hemodynamics of the tumor microvasculature give rise to unique microvascular niches within the tumor and contribute to inter- and intra-tumor heterogeneity. These tumor ensemble-based simulations together with unique data visualization approaches establish the foundation of a novel ‘cancer atlas’ for investigators to develop their own  A major driver of inter- and intra-tumor heterogeneity is the underlying heterogeneity of the microvasculature, i.e. the irregular microvascular network and resultant abnormal hemodynamics that also pose a formidable hurdle for developing and delivering effective cancer therapies3. Therefore, there is a critical need for new computational tools that enable investigations of tumor vascular heterogeneity and the ‘emergent’ phenotypic alterations that result from changes in the tumor microenvironment4. However, in silico investigations of emergent inter- and intra-tumor angiogenic heterogeneity require that we have access to ‘whole-tumor’ 3D microvascular data as well as such data from ‘ensembles’ of tumors5. Until recently, technical limitations such as the lack of high-resolution 3D imaging techniques capable of whole-tumor coverage, insufficient computational power and cost presented major hurdles to such systems biology approaches. Here, we present a hybrid image-based modeling framework to demonstrate the feasibility of recapitulating inter- and intra-tumor heterogeneity of the breast cancer microenvironment in terms of vascular morphology, tumor hemodynamics and intravascular oxygenation.Clinical genotyping has recently demonstrated that subpopulations of cancer cells with unique genomes can exist in different regions or ‘microenvironments’ of a patient’s tumor and that these subpopulations can evolve over time11. Improvements in imaging resolution now permit acquisition of the 3D microvascular structure and quantification of the morphology of individual microvessel segments within solid tumors14 and other tissues16. Moreover, combinations of imaging and mathematical modeling now permit detailed vessel-by-vessel simulations of microvascular blood flow and oxygen transport18. These advances have been accompanied by the development of new computational approaches for modeling hemodynamics, the transport of oxygen and other molecules such as growth factors and nanoparticle-mediated drug transport in realistic tumor vasculatures19. However, traditional image-based computational frameworks are not well suited to modeling the emergent phenotypic heterogeneity that arises from the whole-tumor microvasculature because they are limited by the sparse spatial coverage of the underlying tumor microvascular network 18.The origins of microvascular heterogeneity in different organs have been investigated in numerous studies using experimental and computational approachesin vivo MRI, ex vivo micro-CT (μCT) and magnetic resonance microscopy (MRM)20 to generate an ensemble of high fidelity, high-resolution (~µm) whole-tumor microvascular networks (~GB size dataset) from eight orthotopic breast tumor xenografts. We developed computationally convenient approaches to model hemodynamics and intravascular oxygenation in these whole-tumor microvascular networks. This image-based computational framework made it possible to recapitulate whole-tumor angiogenic heterogeneity in terms of: (i) morphology of the tumor microvascular network; (ii) tumor hemodynamics; and (iii) intravascular oxygenation. We also present novel approaches for visualizing these parameters in 3D space to elucidate the spatial heterogeneity of the angiogenic phenotype within and between whole-tumor microvascular networks. Our tumor ensemble-based analyses of heterogeneity revealed larger dispersion in tumor hemodynamic indices than indices of microvascular morphology. We also discovered that heterogeneity of the angiogenic phenotype led to the emergence of distinct vascular niches within the tumor that uniquely shape its hemodynamic landscape. Finally, we characterized the emergent phenotype arising from these different tumor microenvironments based on their vascular morphology and hemodynamics for the entire tumor ensemble and discovered that hemodynamic parameters alone were insufficient for classifying these different tumor microenvironments. Nevertheless, one could exploit ‘ensemble-based’ metrics of tumor heterogeneity to classify these microenvironments and identify potential new biomarkers.To overcome these limitations, we developed an image-based modeling framework and specialized data visualization approaches that allowed us to incorporate 3D, high-resolution (~µm) whole-tumor microvascular images in models of inter- and intra-tumor phenotypic heterogeneity of the breast cancer microenvironment. We leveraged a multimodality imaging pipeline that exploits the strengths of complementary imaging modalities such as Day 21 or Day 35) wherein the tumor volumes ranged from 76–450 mm3. These unique 3D visualizations provide direct insight into the 3D heterogeneity of the angioarchitectural landscape within and between whole-tumors.Figure Day 21 and Day 35 tumors in terms of: distance to nearest vessel (Dv), vascular length density (Lv) and vascular surface area density (Sv), respectively. These quantitative maps illustrate the spatial heterogeneity of tumor vascular morphology and help identify unique regions within the tumor. For example, large avascular areas  were visible in the center of a Day 35 tumor  and high Lv and Sv  decreased with increase in tumor volume - from 0.86 in the smallest Day 21 tumor (76 mm3) to 0.36 in the largest Day 35 tumor (475 mm3). Figure Day 21 tumors had a greater percentage of small Dv values (10–60 µm) than advanced Day 35 tumors. The Day 21 group also exhibited a larger percentage of high Lv values (100–240 mm/mm3) and a higher median Lv of 40.7 mm/mm3 in contrast to 30 mm/mm3 for the Day 35 group. Pooled median Sv varied from 23.2 mm²/mm³ in Day 21 tumors to 22 mm²/mm³ in Day 35 tumors. Correspondingly, there were a greater number of dilated vessels in Day 35 tumors as indicated by the pooled median diameter of 13 µm versus 11 µm for Day 21 tumors.Figure mor Fig. , and are Dv Fig.  and high Sv Fig.  were visin vivo data as described in Pries et al.21. We observed excellent agreement between our simulated data and that from Pries et al.21, as indicated by R2 = 0.99 and 0.93 for blood flow rates and discharge hematocrit, respectively  and intravascular oxygenation PO2 (mmHg) computed for each whole-tumor microvascular network. We observed well-perfused and well-oxygenated vessels within the tumor rim of Day 21 samples  as well as under-oxygenated (0 ≤ PO2 ≤ 5 mmHg). This was also evident from the visualizations shown in Fig. Day 35 tumor vessels  exhibited high oxygenation values (60–87 mmHg), which resulted in the Day 35 PO2 distribution having a longer tail than the Day 21 distribution.Figure les Fig.  whereas les Fig. . Pooled Q ≥ 10−10 µl/s) demonstrated profound inter- and intra-tumor hemodynamic heterogeneity  for each tumor across different vascular parameters. These plots indicate that the distribution of blood flow rate , shear stress (τ), and velocity (Vel) exhibited CV values ranging from 2–8, i.e. were more heterogeneous. Moreover, we observed that the heterogeneity of some morphological variable pairs such as D and L, D and Sv, D and Dv, L and Sv was ‘coupled’ with each other for this tumor ensemble, as indicated by the significant (p < 0.05) positive correlation coefficients of 0.75, 0.89, 0.73 and 0.82, respectively ; Class 2 vessels ; Class 3 vessels . Functionally active vessels of Class 2 exhibited the greatest variation in hematocrit distribution  or D35 (i.e. Day 35 group). Figure Day 21 tumor  running parallelized MATLAB code. This simulation run-time could be dramatically reduced by switching to GPU-accelerated computing, an area we are currently exploring.Despite the advantages of this high-fidelity image-based computational framework, our approach did have some inherent limitations. For example, although we reconstructed more than 90% of vascular network nodes for all tumors to account for incomplete vascular filling of microvessels, we were unable to assess the effect of the remaining 10% of the nodes. Studies using percolation-based network models have shown that a significant fraction (>40%) of vessels needs to be excluded from the microvascular network before any observable impact on network connectivity or simulated blood flow distribution55, the current computational algorithm did not incorporate this diversity in cellular composition. We have utilized tumor data from two imaging time points (Day 21 and Day 35), however, our computational framework can also be used to study earlier stage tumors or tumors following therapy, as long as each tumor exhibits a patent microvascular network that that can be perfused with a contrast agent that is visible using 3D imaging approaches . Finally, the current blood flow simulations were conducted for steady-state conditions and therefore do not recapitulate the temporal aspects of hemodynamic heterogeneity known to exist within tumors56, which is an ongoing area of future development.Since it is challenging to perform 3D reaction-diffusion-convection simulations for the whole-tumor volume, the current formulation for oxygen transport did not include the 3D extravascular diffusion of oxygen in the tissue. Although intratumoral blood flow can be influenced by other factors such as physical stress and the interaction between tumor cells and stromal components57. Due to these limitations, our analysis of tumor vascular heterogeneity may not recapitulate every aspect of phenotypic heterogeneity observed in breast cancer patients. However, that was not the primary goal of the current study and our approach did recapitulate salient features of the breast tumor microenvironment such as hypoxia, physiologically anomalous blood flow and the emergence of distinct microvascular niches3. We expect future computational applications to be based on images derived from syngeneic tumor models or patient derived xenografts (PDX) in immunocompetent animals. A potential avenue for computationally modeling cancer heterogeneity in patients would be to employ vascular data directly derived from in vivo breast cancer angiography or resected breast cancer tissue in which the vasculature has been labeled by some means. This approach seems feasible owing to recent advances in optical clearing methods in conjunction with novel optical imaging techniques such as light-sheet microscopy. For example, recently a fixed human brain tissue sample (3 × 3 × 1 cm3) was optically cleared to acquire high-resolution images of the brain microvasculature58. We are hopeful that these techniques would soon be available for optical clearing of patient derived tumor tissue.It is worth mentioning that our computational approach was based on tumor microvasculature derived from an orthotopic xenograft model of human breast cancer. Since most tumor xenografts only proliferate in immune compromised animals, their microenvironments lack the immune components exhibited by human tumors. Additionally, tumor xenografts do not recapitulate all the genetic diversity observed in primary human tumors56 in response to antiangiogenic therapies, and other treatments that target the vasculature55. Multiparametric datasets generated using this platform could also be useful for future clinical investigations. For example, when high-resolution measurements of tumor vasculature in patients become clinically available using in vivo CT angiography59, personalized simulations could predict the tumor’s angiogenic status and drug distribution levels. Physician-researcher partnerships49 could facilitate such efforts, since not all clinical settings may have the state-of-the-art computational resources necessary for simulating tumor hemodynamics. As a potential clinical application of this approach, in silico phenotypic data of metastatic breast cancer patients could be combined with their genetic and metabolic profiles to develop patient-specific data-libraries49 that could be shared widely and be used for predicting metastatic risk or stratifying patient treatment.The image-based platform we developed here would be ideal for preclinical investigations of drug development applications, such as studying vascular phenomena at the whole-tumor scale including vessel adaptation and remodelingin silico applications; (ii) a computational model of antiangiogenic resistance that facilitates discovery of translational biomarkers for identifying patients who would benefit most from antiangiogenic agents; (iii) an in silico platform for testing novel therapeutics that can circumvent antiangiogenic resistance in breast cancer. We expect this image-based computational framework to be adaptable to other vasculature-dependent diseases such as stroke60 and myocardial infarction61.In conclusion, we believe that the development of an integrated imaging and computational platform based on high-fidelity tumor ensemble data will help establish: (i) a freely downloadable, multimodality atlas for cancer systems biology investigators and novel 20, 3 × 106 triple-negative human breast cancer (MDA-MB-231) cells were inoculated orthotopically into the mammary fat pad of eight female Ncr-nu/nu mice. The animals were perfused with Microfil  a radio-opaque vascular filling agent, on Day 21 or 35 post inoculation. Ex vivo μCT imaging was performed at Numira Biosciences  on a high-resolution (8 μm) scanner . The following parameters were used: 55 kVp, 300 ms exposure time, 2000 views and 5 frames per view. Since tumors were perfusion-fixed prior to perfusing with Microfill and imaging was conducted ex vivo20, cellular damage from X-ray exposure was not a concern. Ex vivo MRM images were acquired on a vertical bore Bruker 9.4 T spectrometer using a 10 mm volume RF coil  and a T2*w MGE sequence with the following parameters: TE = 4.9/9.7/14.5/19.3/24.0/28.8 ms, TR = 150 ms, θ = 30°, NA = 14, resolution = 40 × 40 × 40 μm3. 3D visualization of whole tumors . All animal experiments were conducted in accordance with an approved Johns Hopkins University Animal Care and Use Committee (JHU ACUC) protocol. The Johns Hopkins University animal facility is accredited by the American Association for the Accreditation of Laboratory Animal Care and meets National Institute of Health standards as set forth in the “Guide for the Care and Use of Laboratory Animals”.According to the experimental protocol40. The one-dimensional blood flow model40 encompassed the generalized 1D Poiseuille law, mass conservation at vessel junctions and the nonlinear rheological effects of blood flow  that are known to be significant in the microcirculation62. An optimization algorithm, that was based in part on a prior study63, monitored the vessel segments that feed and drain blood from the network, and optimized the boundary pressures to ensure mass conservation. Using these optimized pressures as boundary conditions, a system of linear equations was solved to obtain pressure distribution at the vessel junctions40. For a microvascular network for which complete boundary data is available , our blood flow model can be run without implementing the optimization algorithm.To perform hemodynamic simulations, we reconstructed the topology of whole-tumor microvascular networks from 3D µCT images using a bioinformatics-based algorithm we recently reported54. The current implementation is a highly simplified model and does not consider the three-dimensional extravascular diffusion of oxygen in the tissue because it is very challenging to perform 3D reaction-diffusion-convection simulations for the whole-tumor volume. As an approximation, the tumor volume was divided into multiple tissue domains whose volumes are proportional to corresponding vessel segment lengths, Lij. The total flux from the vessel segment is then proportional to tumor oxygen consumption rate; we utilized the rates determined experimentally for breast cancer xenografts by Vaupel et al.35. Therefore, this approach is equivalent to a generalized Krogh Cylinder Model, but without the geometric representation; thus, the tissue oxygen distribution cannot be calculated from Krogh-type approximation.We employed the oxygen model introduced by Goldman and Popel with appropriate boundary conditions to estimate intravascular oxygen distribution within each whole tumorij of length Lij (where i and j represent branching or boundary nodes) are estimated from the blood flow model. Pij is the oxygen tension in the blood; Cbind and Lij; Mc is the oxygen consumption rate for breast cancer xenografts derived from Vaupel et al.35, mtissue is the tissue mass; nhill is the Hill coefficient for hemoglobin binding cooperativity (2.7)64, P50 is the constant for 50% hemoglobin oxygen saturation (37 mmHg)64 and αpl is the oxygen solubility in plasma (2.82 × 10−5 ml O2/ml tissue/mmHg)64.The governing equations for the individual segments can be described as follows:Dint and Sint are the sparse matrices containing the transport coefficients for dissolved and bound oxygen derived from Equation Pint is the oxygen tension vector for branching nodes; Dbound and Sbound are the vectors of intravascular transport coefficients for boundary segments; Pbound is the oxygen partial pressure vector for boundary segments. This system is solved for oxygen tension (Pint) at all branching nodes and then SHb values are updated based on Equation Equation mentclass2pt{minimHD > 0.01 and vascular segment transit time, vstt < 25 s. In a more stringent approach, the local flux per unit length is determined by matching the intravascular and extravascular transport64; nevertheless, the approximation of a constant flux used here provides useful indices of intravascular oxygenation.Since the oxygen flux per unit length entclass1pt{minima21. We implemented our blood transport model for this public dataset as described in Pries et al.65. The boundary conditions for these simulations consisted of measured blood flow and discharge hematocrit values at all inlets (n = 31), and measured blood flow values at all outlets (n = 5), except the main venular outlet node that was maintained at constant pressure21. In addition, we compared the results of hemodynamic simulations based on our tumor ensemble data with experimental and simulated data from the extant literature33.To validate the predictions from our image-based computational framework, we employed a widely used and publicly available dataset derived from a 546 segment rat mesentery microvascular network3 voxel) maps of distance to nearest blood vessel from the reconstructed whole-tumor microvasculature images in Amira  using the Distance Map Module. The value assigned to each voxel was its 3D Euclidian distance to nearest blood vessel. We generated 3D maps of vascular length density and surface area density from the reconstructed skeletonized vasculature using custom Matlab code . First, every vascular pixel was assigned an effective vascular length (and surface area) based on its position along the vessel. Next, the resulting data was convolved with a 20 × 20 × 20 kernel to estimate average vascular length density, Lv (mm/mm3) or surface area density, Sv (mm2/mm3) in a tumor sub-volume VROI = 160 × 160 × 160 µm3. To render 3D visualizations of spatial distributions of blood flow and intravascular oxygenation, we used the spatial graph visualization module in Amira® wherein each vessel was scaled by its mean diameter and color-coded by the functional parameter being displayed.To quantify heterogeneity of the tumor vascular morphology, we generated 3D high-resolution  and oxygenation (10 mmHg) based on tumor hemodynamics definitions in the extant literatureCV) (i.e. the ratio of the standard deviation to the mean) for each parameter distribution as a normalized measure of its heterogeneity. To determine the strength of the association between the heterogeneity of different parameters, we computed the Pearson correlation coefficient between every parameter pair.Substantial variations in tumor vascular morphology and hemodynamics make it challenging to compare the heterogeneity of one vascular parameter with another. Therefore, to quantify inter- and intra-tumor heterogeneity within the tumor ensemble, we estimated the coefficient of variation (Day 21 and Day 35) in terms of median morphological properties such as distance to nearest vessel, vascular length and diameter, as well as median hemodynamic properties such as vascular segment transit time and oxygenation. To ensure valid clustering results, Cophenetic correlation coefficients were computed using the NCSS statistics package  and values greater than 0.8 deemed significant for hierarchical clustering.Two-tailed Mann-Whitney U test (α = 0.05) was performed using the NCSS statistical software  to determine whether there was a significant difference between the two tumor groups (i.e. D21 (i.e. Day 21 group) or D35 (i.e. Day 35 group), we implemented the unweighted pair-group method of hierarchical clustering in NCSS on the median values of vascular parameters. These included tumor volume, Vol (mm3); vascular morphological parameters such as length, L (mm); vascular length density, Lv (mm/mm3); surface area density, Sv (mm2/mm3); distance to nearest vessel Dv (µm); and the following vascular functional parameters: blood flow rate, Q (ml/s), flow velocity, u (mm/s); wall shear stress, τ (dyne/cm2); and vascular segment transit time, vstt (s)40, and intravascular oxygen tension, PO2 (mmHg)Dij is the segment diameter; μij is the segment apparent viscosity; and Qij is the simulated segment blood flow rate. The mean path length, MPL (µm) for each tumor was computed as:To classify the emergent angiogenic phenotype as belonging to Supplementary Material


Microfracture does not lead to complete healing of full-thickness cartilage defects. The aim of this study was to evaluate the effect of modifying Wnt/β-catenin signaling following microfracture, on the restoration of a full-thickness cartilage defect in a rabbit model. The modification of the canonical Wnt pathway was achieved through per os administration of lithium carbonate, which is an intracellular inhibitor of glycogen synthase kinase 3-β (Gsk3-β) and therefore induces Wnt/β-catenin signaling.n = 6) based on post-surgery treatment differences, as follows: microfracture only (group 1), microfracture plus lithium carbonate 7 mM in the drinking water for 1 week (group 2), microfracture plus lithium carbonate 7 mM in the drinking water for 4 weeks (group 3). All animals were sacrificed 9 weeks after surgery. The outcome was assessed histologically, by using the International Cartilage Repair Society (ICRS) visual histological scale. Immunohistochemistry for type II collagen was also conducted.Full-thickness cartilage defects of 4 mm in diameter were created in the patellar groove of the right femurs of 18 male New Zealand white rabbits. The rabbits were divided into three groups of six (Statistical analysis of the histological ICRS scores showed that group 3 was significantly superior to group 1 in four out of six ICRS categories, while group 2 was superior to 1 in only two out of six.The combination of microfracture and systematic administration of lithium carbonate 7 mM for 4 weeks shows statistically significant superiority in four out of six ICRS categories compared with microfracture only for the treatment of full-thickness cartilage defects in a rabbit experimental model. In these procedures, perforation to the subchondral bone allows blood and marrow-derived cells to fill the defect and a blood clot is formed. The subsequent wound repair cascade finally leads to the formation of vascularized granulation tissue and the proliferation of pluripotent mesenchymal progenitor cells with a capacity to differentiate into multiple mesenchymal cell types [Articular cartilage has a low intrinsic reparative capacity . Marrow-ll types –5.Cartilage formation is the desirable outcome in osteochondral lesions, but it is quite unwelcome as a final result of the fracture healing process. An important observation made in fracture nonunion is the presence of cartilage between the bone ends, associated with the formation of fibrous tissue and minimal bone regeneration –8. DurinThese findings imply that, if microfracture regenerative procedure was considered as a special case of fracture repair, several pathways could be targeted in an attempt to promote the recruitment of progenitor cells towards the chondroblast instead of osteoblast lineage during endochondral ossification. Both fracture healing and endochondral bone formation are directly regulated by BMPs , 13, fibKey regulator of the canonical Wnt pathway is glycogen synthase kinase 3-β (Gsk3-β). In the absence of appropriate Wnt ligands, a destruction complex comprising Axin and adenomatous polyposis coli (APC) mediates the phosphorylation of β-catenin by Gsk3-β, which leads cytosolic β-catenin to degradation by the proteasome. The presence of certain agents such as lithium (Li) has been shown to induce the phosphorylation of Gsk3-β, rendering the kinase inactive. This is followed by the reduction of Gsk3-β activity and accumulation of cytoplasmic β-catenin, which will function as a co-factor of TCF/LEF transcription factors to induce expression of Wnt target genes. Gsk3-β activity is required for both chondrocyte and osteoblast differentiation . ActivatΤhe aim of this study was to evaluate the effect of modifying Wnt/β-catenin signaling following microfracture, on the restoration of a full-thickness cartilage defect in a rabbit model. The modification was achieved through per os administration of lithium carbonate, which is an intracellular inhibitor of Gsk3-β and therefore induces Wnt/β-catenin signaling. Finally, Gsk3-β inhibition causes β-catenin accumulation inside the nucleus of cells, where the transcription of target genes is triggered .Cartilage defects were experimentally created in the right trochlear groove of 18 male New Zealand white rabbits, weighing between 3.0 and 3.6 kg and 16 weeks of age. All animal procedures were approved by the Veterinary Policy Committee of the prefecture of Attica Greece and the Scientific Council of KAT General Hospital Kifissia Greece. All procedures were conducted in the experimental surgery of the Laboratory for the Research of Musculoskeletal Disorders, Medical School, National and Kapodistrian University of Athens, Greece.Each rabbit was anesthetized with an intramuscular injection of Midazolam 2 mg/kg (Dormicum) and Ketamine 30 mg/kg . In addition, anesthesia was maintained by slowly administering 30 mg/kg Thiopental through an auricular vein. The rabbit was placed in the supine position, and a medial parapatellar approach was used to operate on the right knee joint. Then, the patella was dislocated laterally to expose the articular surface. A full-thickness chondral defect (4 mm in diameter) was generated at the center of the trochlear groove by using an osteochondral transplantation system. The defect was completely debrided of its calcified cartilage layer. Then microfracture was performed with a 1.0-mm Kirschner wire with a stopper at 2 mm from the tip, in order to control the penetration depth. Within the chondral defect, 4 microfracture perforations were created, at a distance of 1.0–1.5 mm from each other , microfracture plus lithium carbonate of 7 mM in the drinking water for 1 week (group 2), microfracture plus lithium carbonate of 7 mM in the drinking water for 4 weeks (group 3). Lithium carbonate was administered orally by adjusting the drinking water to a concentration of 7 mM. We obtained blood specimens from an auricular vein at weeks 1 and 4 and measured lithium concentrations. This treatment protocol resulted in serum lithium concentrations of 0.40 ± 0.20 mM/L (mean ± SEM) which were relatively stable at weeks 1 and 4. These serum levels are slightly lower than the range of 0.6–1.2 mM/L, concentrations achieved and maintained during lithium therapy in human subjects . All rabThe specimens were fixed in 10% neutral w/v phosphate buffer 0.05 M and decalcified in 2% nitric acid and afterward 4% formic acid. Afterward, they were dehydrated with serial ethanol, embedded in paraffin, and cut into 3-μm sections. . The sections were stained with toluidine blue, hematoxylin–eosin and Weigert–Van Gieson stains and viewed under a light microscope. They were blindly scored by two different investigators according to the International Cartilage Repair Society (ICRS) visual histological scale. Immunohistochemistry for collagen type II was performed in all groups, using the EnVision Flex kit and the Autostainer Link (DAKO).Data were expressed as median (IQR) for quantitative variables and as percentages for qualitative variables.The comparison of variables between 3 groups was performed using the Kruskal–Wallis test. Pairwise comparisons were performed using the Dunn adjusted by the Benjamini–Hochberg FDR test.p < 0.05. All analyses were performed using the statistical package SPSS vr 21.00 .All tests were two-sided, and statistical significance was set at The histological sections of group 1were characterized by an irregular surface of the newly formed tissue, the cell distribution was disorganized and they presented a fibrocartilage matrix Fig. a, d. Grop = 0.028), matrix (p = 0.022), cell distribution (p = 0.029), and subchondral bone (p = 0.004) compared with the control group. Group 2 (lithium intake for 1 week) presented statistically significant higher values of surface (p = 0.028) and subchondral bone (p = 0.050) compared with the control group  presented statistically significant higher values of surface  to optimize the environment of the clot created for the proliferation of the marrow-derived mesenchymal stem cells (MSCs), this being achieved through the use of membranes or scaffolds that cover the clot and therefore protect the cells contained within , 24, (b)One of the morphogenetic pathways regulating fracture and consequently microfracture healing is the Wnt/β-catenin. The interplay between several components of the pathway causes β-catenin accumulation inside the nucleus of cells, where the transcription of target genes is triggered. The Wnt/β-catenin pathway is also involved in both pre-natal and adulthood skeletal development, so several studies have investigated the potential of Gsk3-β inhibition upon chondrogenic differentiation . The finIn an animal experimental model, intra-articular injection of GIN, a Gsk3-β inhibitor in rat knee joints induced nuclear accumulation of β-catenin in chondrocytes and was associated with surface fibrillation, a decrease in glycosaminoglycan expression and chondrocyte hypocellularity. These results suggest that, by downregulating β-catenin, Gsk3-β preserves the chondrocytic phenotype and is involved in the maintenance of the cartilage extracellular matrix. Short term β-catenin upregulation in cartilage secondary to Gsk3-β inhibition may be sufficient to induce osteoarthritis-like features in vivo .On the contrary, Gsk3-β inhibitors appeared to significantly enhance cartilage matrix production in chondrogenic cultures. In this in vitro study, MSCs were derived from human marrow aspirates, centrifuged into small aggregates, and provided with a chondrogenic medium supplemented with either lithium or SB216763, which is another Gsk3-β inhibitor. The addition of either SB216763 or lithium to cultures significantly enhanced matrix glycosaminoglycan concentrations .Additionally, in an in vitro pellet culture model, a binary SiO2–Li2O solution gel–derived glass was utilized for the controlled delivery of lithium. Dissolution products that contained 5 mM lithium and 3.5 mM silicon induced chondrogenic differentiation and hyaline cartilaginous matrix formation without the presence of growth factors such as TGF-β .The main findings of our study are the following: (1) Induction of the Wnt/β-catenin signaling pathway for 4 weeks after application of microfracture results in significantly statistical superiority in four out of six histological ICRS categories. (2) Immunohistochemistry in group 3 is consistent with orderly oriented collagen type II fibers, while in group 2 they would follow an amorphous entangled pattern. (3) Induction of the pathway during only the first week post microfracture was not sufficient to exert the beneficial effect of the 4-week treatment upon the histological properties of the repair tissue. On the other hand, it demonstrated statistically significant higher ICRS values of surface and subchondral bone compared with the control group.In the present study, the chondrogenic differentiation effect of lithium as a Gsk3-β inhibitor revealed by culture studies was exerted on the microfracture clot. The wound repair cascade initiated in the clot and the proliferation of pluripotent mesenchymal progenitor cells with a capacity to differentiate into multiple mesenchymal cell types offer a substrate with healing potential. In the case of intra-articular injection of GIN in rat knees, given the low intrinsic cartilage reparative capacity, there is a lack of substrate for the chondrogenic differentiation effect of lithium. The aforementioned combination of healing potential through microfracture and chondrogenic differentiation through lithium may justify the results of our study.The tissue produced in articular lesions after microfracture presents good short term clinical results. However, fibrocartilage is mechanically weaker than hyaline cartilage and degenerates easily. Deterioration tends to occur beyond 2 years as the fibrocartilage breaks down . A limitRegarding other limitations of the study, it is clear that lithium administration requires monitoring of the blood levels, as is routinely practiced for patients who receive it as bipolar disorder treatment. Ensuring lithium concentration that does not exceed therapeutical levels is of key importance, as it minimizes side effects. Notably, in our study, no adverse events due to lithium treatment were noted. Additionally, lithium is widely known as a mental disorder medicine, a fact that might compromise patient compliance, where they intended to receive it for another purpose. Such problems could be overcome by the utilization of an anti-sclerostin antibody as Wnt/β-catenin signaling enhancer.On the other hand, lithium is an inexpensive and rather safe medication well studied for many years. Additionally, systemic administration ensures that, through blood flow, lithium is transported inside the forming clot itself and therefore exerts its action effectively, while a reagent that would require intra-articular injection would form an interface with the surface of the clot only.2 cartilage defect, which is 25% of the area. According to the literature, the percentage found in clinical practice is 20–40% [2 human lesion the scaling factor of 3 for linear dimensions was applied to choose the proper tool. Finally, the tool used was 1 mm in diameter while the clinical tool is 3 mm.Considerations regarding the design of our experimental model include the dimensions of the full-thickness cartilage defect, as well as the tools used to generate microfractures. In order to simulate clinical practice, we created four holes of 1 mm diameter in a 12.56-mms 20–40% . AdditioBased on the findings of the present study, the induction of the Wnt/β-catenin signaling pathway may augment the microfracture derived repair tissue when treating full-thickness cartilage defects. Certain limitations must be dealt with in order to utilize this combined, one stage treatment at the clinical level. More experimental studies are required in order to determine the optimal interaction between the microfracture regenerative procedure and the intrinsic induction of the Wnt/β-catenin pathway. Other canonical Wnt signaling participating molecules may be targeted, but finally, the conclusion of the present experimental study is that inducing the pathway after microfracture may be an effective adjuvant therapy for treating full-thickness cartilage defects.


Nonunions of the subtrochanteric region of the femur after previous intramedullary nailing can be difficult to address. Implant failure and bone defects around the implant significantly complicate the therapy, and complex surgical procedures with implant removal, extensive debridement of the nonunion site, bone grafting and reosteosynthesis usually become necessary. The purpose of this study was to evaluate the records of a series of patients with subtrochanteric femoral nonunions who were treated with dynamic condylar screws (DCS) regarding their healing rate, subsequent revision surgeries and implant-related complications.We conducted a retrospective chart review of patients with aseptic femoral subtrochanteric nonunions after failed intramedullary nailing. Nonunion treatment consisted of nail removal, debridement of the nonunion, and restoration of the neck shaft angle (CCD), followed by DCS plating. Supplemental bone grafting was performed in all atrophic nonunions. All patients were followed for at least six months after DCS plating.Between 2002 and 2017, we identified 40 patients with a mean age of 65.4 years (range 34–91 years) who met the inclusion criteria. At a mean follow-up period of 26.3 months (range 6–173), 37 of the 40 (92.5%) nonunions healed successfully (secondary procedures included). The mean healing time of the 37 patients was 11.63 months (± 12.4 months). A total of 13 of the 40 (32.5%) patients needed a secondary revision surgery; one patient had a persistent nonunion, nine patients had persistent nonunions leading to hardware failure, two patients had deep infections requiring revision surgery, and one patient had a peri-implant fracture due to low-energy trauma four days after the index surgery.The results indicate that revision surgery of subtrochanteric femoral nonunions after intramedullary nailing with dynamic condylar screws is a reliable treatment option overall. However, secondary revision surgery may be indicated before final healing of the nonunion. Subtrochanteric femoral fractures account for approximately 25% of all hip fractures and have a bimodal age and sex distribution . The subThe electronic medical database at the authors’ institution was searched for patients 18 years of age or older with aseptic subtrochanteric femoral nonunions after failed IMN and DCS treatment at our institution Fig.  26]. Al. Al26]. The 40 included patients had been referred to our hospital for nonunion treatment. Additional information about each patient was gathered, including demographics, comorbidities and trauma mechanism. The fractures were classified according to the Seinsheimer classification and the Orthopaedic Trauma Association (OTA) classification system as well . To condEighteen different surgeons performed the index procedures. Cefazolin (two grams intravenously) was administered for perioperative antibiotic prophylaxis 30 min before the skin incision. The patient was placed in a supine position on a radiolucent table. Radiographic examinations were used to guide the osteotomy and the positioning of the implant. The initial approach was incorporated and extended distally into the lateral approach, with the fracture site fully exposed. The nail was removed and extensive debridement of the fracture site and nonunion site, including removing fibrotic tissue and necrotic bone, was performed until the bleeding bone was exposed. A collection of tissue samples was collected for microbiological analysis. After the screw insertion into the femoral neck, the DCS plate was then inserted over the lag screw. The plate length was selected according to the surgeon’s preference (9–22 holes). The CCD angle was restored by reduction of the shaft to the plate and was maintained with a reduction clamp. The degree of valgus correction depended on the preoperative measured neck shaft angle. To allow proper valgus correction, the plate may have been precontoured using plate benders before plate application Figs. . An artip-value of 0.05 or less was considered statistically significant. In the case of missing data due to the retrospective design of the study, the specific missing information was marked and explained. If further calculation was performed with an incomplete dataset, listwise deletion was used. Data were analyzed using SPSS Statistics version 23 and Microsoft Excel version 14.5.9.Patient characteristics were described by their mean and standard deviation, as well as their minimum and maximum values. Normality of variables was tested with the Shapiro-Wilk test. Significance was calculated using a t-test, Wilcoxon-Mann-Whitney test, contingency tables and Fischer’s exact test. A Between January 2002 and July 2017, 40 patients fulfilled the inclusion criteria and were included in the study. The average length of the follow-up period was 26.3 months (range 6–173 months), with a median of twelve months. The mean age of the 24 women and 16 men upon admittance to our clinic was 65.4 years (range 34–91 years). Regarding clinical constellations, initial fractures were treated with a gamma nail (fa. Stryker) in 17 patients, and a proximal femoral nail  was used in eight patients. Fifteen fractures were treated by Targon-, Sirius-, Trigen-, Vero-, Friedel or Orthofix intramedullary nails. Among these cases, ten of the 40 patients (23.3%) had already undergone revision surgery after nailing, including for dynamization of the nail, bone grafting, additional augmentation plate insertion or exchange nailing  and a median of nine months after the initial nailing. The mean operation time was 154.25 min (range 70–265 min). In 18 patients (45%), an additional LCDCP was used. With the exception of ten patients, an autologous cancellous bone graft taken from the anterior iliac crest was used. In five patients, a demineralized bone matrix was applied instead of an autologous bone graft. The remaining five patients without additional bone grafting had hypertrophic nonunions. The preoperative CCD of the 40 patients prior to the index procedure was 118° (range 101° – 131°). The mean postoperative CCD was calculated to be 128° (range 114° – 142°) with a mean valgus correction of ten degrees. The mean length of the hospital stay was 15.08 days (range 6–40 days). On average, three units of red blood cells were transfused during the hospital stays (range 0–12 units).p = 0.03; healing time p = 0.01).Bony union was achieved in 27 of the 40 nonunions (67.5%) after the index procedure. A total of 13 of the 40 (32.5%) patients needed secondary revision surgery, including one persistent nonunion (2.5%), nine persistent nonunions leading to hardware failure (22.5%), two deep infections requiring revision (5%) and one peri-implantary fracture (2.5%) due to low-energy trauma four days after index surgery (Table n = 9), removal of the plate and a revision procedure using the same implant again or a double plate construct  and iliac bone crafting was performed after a mean of 5.9 months (range 1–15 months). In one case, a patient developed a femoral head necrosis with screw cut-out and was treated with THR. In the case of a persistent nonunion without implant failure (n = 1), further revision with additional anterior plating using LCDCP and iliac bone crafting was performed. Due to infections (n = 2), local surgical debridement was performed leaving the plate in situ with subsequent antibiotic therapy. Implant removal was performed in seven patients after a mean follow-up period of 14 months (range 6–24 months) due to a planned foreign body removal or local pain sensation. Of the 13 patients, a subcategory of eight patients (20%) needed a second additional surgery. Second revisions were performed a mean of two months (range 6 days – 8 months) after the first revision. Second revision surgeries were necessary due to implant failure (n = 4), persisting nonunion without implant failure (n = 1) and a deep infection requiring surgical debridement (n = 3). In the case of a hardware failure, the same revision procedure with double plating was repeated. In the three patients with infections, debridement was repeated in two patients. In one case, resection arthroplasty resulting in a Girdlestone situation was performed. The nonunion without implant failure was treated with an iliac bone graft and demineralized bone matrix. A total of three of the 13 patients (7.5%) patients needed one or more additional surgeries, leading to two cases of osseous consolidation and one case of persisting nonunion.Revision surgery was performed at a mean of 4.9 months after the index procedure (range 4 days – 12 months). In cases of a persistent nonunion with hardware failure  hips. The other 30 hips (75%) had a limited range of motion, with a minimum of 90° of hip flexion. A total of 15 patients (37.5%) could walk without any walking aids, nine patients (22.5%) walked with forearm crutches and eight patients (20%) walked with a walking frame. Two patients used a wheelchair (5%). One patient was bedridden (2.5%). In five patients, postoperative mobility could not be evaluated due to a lack of data.The purpose of this study was to evaluate a series of DCS treatments of subtrochanteric femoral nonunions following IMN regarding the healing rate and implant-related complications. To the best of our knowledge, our patient series of 40 subtrochanteric femoral nonunions represents the largest study reporting on a standardized salvage DCS procedure after failed intramedullary nailing.n = 9 after nailing; n = 20 after open reduction and internal fixation (ORIF) with blade plate, dynamic compression plate or DCS), open correction osteotomy if needed (n = 3), secondary osteosynthesis with a gamma nail (overreaming to provide biologic augmentation) and bone grafting in case of loss of bone substance (n = 5) [n = 11) or IMN  [n = 32) [Nonunions of the subtrochanteric region of the femur are uncommon; however, they are difficult to treat. In addition to general risk factors , mechano (n = 5) . Of thes (n = 5) . Wu trea (n = 5) . The pat (n = 5) , 44, but (n = 5)  showed t (n = 5) . In cont (n = 5) ), Gianno (n = 5)  presente, n = 3) . In tota[n = 32) . The ave[n = 32) , ten patAccording to the current literature, there is no strong evidence to support the use of either IMN or extramedullary devices in the revision of subtrochanteric nonunions. Despite the development of new implants and increasing knowledge of nonunion, the treatment of postoperative complications and persisting nonunion still presents a challenge. To date, no prospective randomized study has been published; therefore, level IV studies are currently the best available evidence . We presn = 6) occurred in patients older than 74 years [Our data series has a relatively high number of postoperative complications leading to revision surgery (13/40). Rosso et al.  and Kulk74 years . Our stu74 years . Cement-74 years , 58. Hip74 years , 60. TheWe acknowledge the limitations of the study. First, only retrospective data gathered from a local electronic database without a defined follow-up protocol is presented. Second, there is a heterogeneity of the study cohort. We included all participants with subtrochanteric nonunions following IMN regardless of the type of initial trauma, type of nonunion and the number of prior revisions. Although there was no significant impact on bony healing in any of these categories, in our cohort group that might be a result of subgroup analysis with small group samples. Third, the index procedure was performed over the course of 15 years observational time by 18 different surgeons with varying levels of experience. Fourth, the 40 included patients had been referred to our hospital for nonunion treatment. Additional information about inital fracture treatment was limited and the rate of nonunion after fracture treatment was not available.This study shows that treatment of subtrochanteric nonunions is still a challenge. Despite high overall healing rates, a significant number of patients needed secondary surgical revisions, especially among elderly patients.


Generation of coherent light with desirable amplitude and phase profiles throughout the optical spectrum is a key issue in optical technologies. Nonlinear wavefront shaping offers an exceptional way to achieve this goal by converting an incident light beam into the beam (or beams) of different frequency with spatially modulated amplitude and phase. The realization of such frequency conversion and shaping processes critically depends on the matching of phase velocities of interacting waves, for which nonlinear photonic crystals (NPCs) with spatially modulated quadratic nonlinearity have shown great potential. Here, we present the first experimental demonstration of nonlinear wavefront shaping with three-dimensional (3D) NPCs formed by ultrafast-light-induced ferroelectric domain inversion approach. Compared with those previously used low-dimensional structures, 3D NPCs provide all spatial degrees of freedom for the compensation of phase mismatch in nonlinear interactions and thereby constitute an unprecedented system for the generation and control of coherent light at new frequencies. Generation of light with desirable amplitude and phase profiles with nonlinear wavefront shaping is important for optical technologies. Here, the authors demonstrate nonlinear wavefront shaping with three-dimensional nonlinear photonic crystals formed by ultrafast-light-induced ferroelectric domain inversion approach. Compared with traditional beam shaping processes based on linear optical elements such as spatial light modulators, the added functionality of nonlinear frequency conversion allows manipulation and structuring of coherent light at new frequencies, which opens up exciting new possibilities for important applications including all-optical self-routing1, volume nonlinear holography2, generation of entangled states3, and ultrafast laser technology8. Furthermore, the nonlinear wavefront shaping based on alternative approach of structuring the input beam first and then converting it into different frequency, usually does not work due to the difficulty of satisfying the phase-matching requirements with non-Gaussian beams.Recently, generation of spatially modulated wavefronts via optical frequency conversion, i.e., nonlinear wavefront shaping, has attracted a great deal of research interest11 and nonlinear metamaterials5, have proved to be excellent candidates for nonlinear wave shaping. In particular, the NPC comprises a nonlinear optical medium with spatially modulated quadratic χ(2) nonlinearity, which ensures the high efficiency of nonlinear optical interactions via the so-called quasi-phase matching (QPM)14. Depending on the geometry of interaction, the QPM can be implemented through the schemes of nonlinear Bragg diffraction15, Čerenkov-type16 emission and nonlinear Raman-Nath diffractions17. In these NPCs the wavefront shaping often relies on transversely patterned nonlinearity, i.e., χ(2) varies spatially  | and −| χ(2) |) in a plane perpendicular to the propagation direction of the incident beam20. In this respect, the transverse χ(2) modulation plays a role analogous to that of spatial variation of refractive index in linear optical media. However, while the index pattern imposes just desired amplitude and phase profile on diffracted incident wave, in nonlinear media the spatial χ(2) pattern leads to frequency conversion with simultaneous amplitude and phase structuring of the emitted new frequencies. Because of analogy with linear diffraction this nonlinear process is called nonlinear diffraction17. It has been already demonstrated that appropriately designed χ(2) patterns provide new functionalities including second harmonic (SH) beam-focusing and splitting, as well as the generation of spatially complex optical frequency converted wavefronts such as Bessel, Airy, Semi-Gaussian, and vortex sum frequency beams21. As an example, Fig. 19, i.e. lSH = 2lFB + mlc, where lSH and lFB represent the OAM of the SH and fundamental beams, respectively , lc is the topological charge of the fork structure, and m is the nonlinear diffraction order of the SH wave.Nonlinear optical microstructured materials, such as nonlinear photonic crystals (NPCs) 22. In this process strong electric field applied to the crystal via patterned electrodes reverses locally direction of spontaneous polarization which amounts to the sign reversal of χ(2). However, in this traditional approach for the formation of NPCs the nonlinearity modulation is restricted to a single transverse plane. The ability to modulate χ(2) along the third orthogonal direction is highly sought after and it has been theoretically shown the a 3D modulation would greatly enhance the role of NPCs in many applications including wavefront shaping28. As displayed in Fig. χ(2) nonlinearity modulation structures to generate multiple second harmonics with different wavefronts. This is a unique capability that cannot be accomplished with a single low-dimensional nonlinear photonic crystal.The most common technique used to fabricate NPCs is the electrical poling of ferroelectric crystals30. As the amorphisation decreases the strength of the nonlinearity, one can, in principle, realize arbitrary spatial modulation of χ(2). However, this process introduces significant scattering losses30 for interacting beams and hence has limited practical applicability.The 3D spatial nonlinearity modulation can be achieved, e.g., by selective amorphisation of crystalline structure of the nonlinear medium, with tightly focused femtosecond pulses, as demonstrated recently31. The technique utilizes nonlinear absorption of light in the optical beam’s focal volume. That, in turn, induces a high-temperature gradient and appearance of a thermoelectric field that allows for precise inversion of spontaneous polarization and, consequently, the sign of χ(2) nonlinearity33. By carefully controlling the infrared radiation inside a transparent Ba0.77Ca0.23TiO3 ferroelectric crystal, we have realized the first monolithic 3D NPCs and demonstrated their application in nonlinear frequency conversion. As the inversion of ferroelectric domains does not induce optical loss, this infrared beam method offers an exceptionally efficient way to fabricate 3D NPCs.We have very recently introduced a breakthrough technique for fabrication of 3D NPCs via ultrafast infrared light induced ferroelectric domain inversion0.28Ba0.72Nb2O6 (CBN) crystal and employ them for parallel three-dimensional nonlinear wave shaping in quasi-phase matched second harmonic generation. By using transversely overlapping fork, grating, and homocentric ring domain patterns localized at various depths inside a single CBN crystal, we demonstrate the simultaneous conversion of a Gaussian fundamental beam into three pairs of second harmonics with helical, Gaussian, and conical wavefronts, respectively. Furthermore, by making use of longitudinal separation of structures we achieved the first real dynamic control of nonlinear wavefront shaping in 3D NPC. We show that by just shifting longitudinally the focal position of the fundamental beam inside the crystal, we can vary the spatial structure of the emitted SH. Our results clearly show that 3D NPCs represent a major advancement compared to the low-dimensional geometries, opening possibilities for versatile control of nonlinear optical interactions and will contribute significantly to development of structured light sources at new frequencies.In this letter, we present the first experimental demonstration of novel functionalities of 3D NPCs which are inaccessible in traditional lower-dimensional systems. In particular, we fabricate a number of optically induced nonlinearity patterns in ferroelectric Ca34. The domain engineering process relies on nonlinear absorption of light in the optical beam’s focal volume, which induces a high-temperature gradient and appearance of a thermoelectric field that forces the spontaneous polarization of the crystal to align along the same direction31. The use of infrared femtosecond pulses allowed us to focus the light deep inside the transparent CBN and, consequently, to form various 3D ferroelectric domain structures (See the Methods). In Fig. χ(2) nonlinearity patterns comprising fork grating, regular one-dimensional grating, as well as circular grating. Figure 35. Furthermore, we used the piezoresponse force microscopy (PFM)36 to confirm that the structures formed in this way are indeed ferroelectric domain patterns and not material modifications such as an optical damage or refractive index change  gratings with charge lc = 2 fork-type dislocation, oriented at 0°, 60°, and 120° with respect to horizontal direction  gratings were fabricated to have a periodicity of Λ = 2 or 3 μm and the inverted domain structures were uniform across the whole written area of 60 × 60 μm2.In more details, the pattern 1 contains three periodic ion Fig. . The graing Fig. . Finallylc = 2 and periodicity Λ = 2 μm. One can clearly identify the six vortex beams emitted from the three fork patterns. These vortices represent first-order nonlinear Raman-Nath diffraction patterns. The measured emission angle is 23.9° outside the crystal, agreeing well with the theoretical value of 23.6° (see Method). In fact the higher order nonlinear diffraction patterns are also emitted in the process but they are much weaker compared to the first order. As the fork dislocation is of the second order, the emitted SH vortices carry the topological charge lSH = ±2. We confirmed the charge by using astigmatic transformation introduced by placing a cylindrical lens in the paths of emitted beams. The resulting intensity distribution . One can clearly identify two donut beams along the vertical and two localized intensity peaks along horizontal directions, respectively. They all lay on a circle representing conical SH beam emitted by circular domain pattern. The graph in Fig. Figure 37. In Fig. 39. Interestingly, the vortices observed in experiment did not split displaying well-defined dark core. The most likely reason of experimentally observed robustness of charge 2 vortices is that we use short (200 fs) pulses not cw in fundamental beam. The broader spectrum of the pump leads to smearing of the vortices making them effectively insensitive to small scale variations of the nonlinearity pattern.Simultaneous appearance of multiple SH patterns of almost equal intensity generated in the volume of 3D NPC results from the fact that the fundamental beam is not being depleted in the interaction process. Therefore, this beam experiences nonlinear diffraction on each of the embedded nonlinear holograms with almost constant power. Furthermore, since the input beam consists of train of pulses, the SH emission from these two or three holograms (nonlinearity patterns) is completely independent as their separation exceeds the pulse length. This, in turn, gives rise to the total intensity pattern as an incoherent superposition of contributions from each of the layer separately. In fact, this process can be analyzed theoretically by employing simple model for second harmonic generation in the undepleted pump regime. In this, low conversion efficiency regime, the far-field emitted SH is expressed by the Fourier transform of the nonlinearity modulation40 such that even for nominal focusing of the beam at the first structure, the periphery of the focus still partially overlaps with the second structure generating the spurious  SH signal. To the best of our knowledge this is the first time to obtain dynamic nonlinear wavefront shaping41 with 3D nonlinear photonic crystals. Thereby, this work represents a significant progress that may open new possibilities in many fields such as laser display, optical trapping, and imaging.To better demonstrate the multilayer character of ferroelectric domain pattern in wavefront shaping we optically wrote two planar nonlinearity structures containing mutually orthogonal  fork-type grating and simple linear grating with the same periodicities. The structures were laser-induced inside the CBN sample and were separated in longitudinal direction such that could be independently accessed with tightly focused beam. The focusing position of the fundamental beam was fixed and then the sample was moved along the beam direction (z-axis) such that the light focal spot was translated through the sample. Figure 0.28Ba0.72Nb2O6 ferroelectrics, and have demonstrated unprecedented control over the nonlinear wave emissions from these crystals thanks to the full flexibility of 3D nonlinearity modulation. Using a three-layer nonlinear photonic structure comprising fork grating, regular 1D grating, as well as circular grating embedded inside the crystal, we demonstrated a simultaneous conversion of a fundamental Gaussian beam into second harmonic vortex, Gaussian, and conical beams. In addition, thanks to the longitudinal separation between layers of domain patterns, we demonstrated the first dynamic control over the nonlinear interactions in 3D nonlinear photonic crystals. In fact, as ferroelectric domains can be imprinted independently to form various patterns at different depths, the 3D nonlinear photonic crystals pave the way for manipulating target-specific features of nonlinear interactions without affecting the others. Thus, the results reported here constitute an important contribution towards development of advanced coherent light sources at new spectral range, which are at the core of many optics-related fundamental research and industrial applications. In order to exploit further all advantages of 3D character of nonlinearity modulation enabling quasi-phase matched interaction in arbitrary direction, our future efforts will be directed towards realization of complex nonlinearity structures with continuous spatial modulation of the nonlinearity along propagation direction, such as the previously proposed twisted nonlinear photonic crystals28. Structures of such complexity are beyond reach of traditional techniques and can only be fabricated by employing our optical domain reversal method.We fabricated 3D nonlinear photonic crystals by using our femtosecond-laser domain inversion approach in Ca34.We used a z-cut as-grown sample of calcium barium niobate crystal. As the crystal was unpoled it exhibited a random spatial distribution of antiparallel ferroelectric domains. The multi-domain character was confirmed by strong conical (Čerenkov) emission of second harmonic signal upon the propagation of fundamental beam propagating along the crystal z-axis. Based on our earlier works with the samples from the same crystal boule, the random domains are mostly on the submicron scaleThe infrared writing optical beam originated from a femtosecond oscillator  operating at 800 nm (short enough to excite the two-photon process), with a pulse duration of 180 fs and a repetition rate of 76 MHz. The optical beam was focused by a 50× microscope objective (NA = 0.65) into the sample with an estimated beam diameter of ~1 μm. The illumination of tightly focused femtosecond laser leads to the alignment of the originally random domains along the same direction within the focus area. To this end the CBN sample was mounted on a translational stage that could be positioned in three orthogonal directions with a resolution of 100 nm. The power of the incoming laser beam could be continuously varied by using a half wave plate followed by a polarizer.z = 115, 69, and 23 μm below the surface, respectively. The influence of laser power on the resulting domain patterns was discussed in our earlier work31.The multilayer ferroelectric domain patterns were written layer by layer and from bottom to top. For domain inversion in each layer, the sample was translated against the beam propagation direction so that the position of the focal region of the writing beam moved at an average speed of 10 μm/s over a distance of 20 μm. After that a shutter blocked the beam and the sample was transversely translated to the next location where the process was repeated. In order to produce stripe-like areas of inverted domain, the distance between the neighboring domain spots was kept small (~0.5 or 1 μm) causing them to merge. The average power of the writing beam was selected to be slightly lower than the optical damage threshold, and was 505 mW, 370 mW, and 280 mW for the three layers located at 2 in the transverse plane (XY in our case). The length of inverted domains in  each layer is ~30 μm, measured by using the Čerenkov second harmonic microscopy. The maximal writing depths that could be reached from one side of the sample was ~150 μm, and was restricted mainly by the maximal laser power available in the experiment. Furthermore, the focusing condition of the femtosecond laser beam gets worse with the depth due to aberrations, which also makes it difficult to write deep inside materials with high refractive indices. In order to create domain layers that are sufficiently far from each other for dynamic nonlinear wave shaping, we wrote a layer of domains from one side of the sample, and then wrote the other layer from the other side. To simplify localization of nonlinearity structures and their alignment in our experiment, rectangular frames made of optically damaged spots were created surrounding the laser-written ferroelectric domain patterns. The frames also served as alignment markers to facilitate precise spatial overlap of the two or three layers in the transverse plane.The typical sizes of the laser-written domain area are 60 × 60 μmz-axis of the sample and was linearly polarized to generate the second harmonic via nonlinear coefficient d31. The beam was loosely focused into the NPCs and the beam size was slightly exceeding 70 μm in diameter, to ensure the illumination of the whole area of nonlinearity modulation (60 × 60 μm2). A short-pass filter was used to block the fundamental beam. The emitted second harmonic signal was projected on to a screen placed behind the sample and then recorded by a CCD camera. The SH images shown in Fig. The incident laser beam was derived from the Coherent Chameleon + Chameleon OPO system delivering 200 fs pulses at 80 MHz repetition rate with the wavelength being tunable between 800 and 1600 nm. The beam propagated along the k2sin θ = mG, where k2 is the wave vector of the SH beam, θ is internal emission angle, m is an integer denoting the order of nonlinear diffraction, and G is reciprocal lattice vector corresponding to the χ(2) modulation pattern. Taking Snell’s law into account, we obtain the external emission angle of the first-order nonlinear Raman-Nath diffraction α = sin−1(mλ2/Λ), where λ2 is the wavelength of the second harmonic and Λ is the period of χ(2) modulation outside the crystal. With the used parameters of λ2 = 800 nm, m = 1, and Λ = 2 μm, we obtain a theoretical external emission angle of α = 23.6°.The periodic nonlinear structures lead to second harmonic generation via the nonlinear Raman-Nath diffraction, the emission angle of which is determined by the transverse phase matching condition, i.e., αČ = cos−1(n(λ2)/n(λ1))17, coincides with one of the Raman-Nath nonlinear diffraction orders. Here n(λ1) and n(λ2) are refractive indices of the fundamental and SH waves, respectively. In this nonlinear Bragg diffraction regime, Čerenkov process ensures fulfillment of the longitudinal, while nonlinear Raman-Nath diffraction transverse phase matching, giving rise to monotonic growth of the intensity of SH with propagation distance.The efficiency of transversely matched SHG is rather weak. Only the full-phase matching ensures monotonic flow of power from fundamental to second harmonic beams. Such condition can be relatively easily achieved in our multilayer domain structures by choosing the wavelength of fundamental beam to make Čerenkov second harmonic emission angle (Supplementary informationPeer Review File