However, it inhibits the synthesis of TXA2 through cPLA2 regulation. Taken together, our data reveal the critical role of C3G in the main pathways leading to platelet activation and aggregation through the regulation of Rap1b.C3G is a GEF (guanine nucleotide exchange factor) for Rap GTPases, among which the isoform Rap1b is an essential protein in platelet biology. Using transgenic mouse models with platelet-specific overexpression of C3G or mutant C3GΔCat, we have unveiled a new function of C3G in regulating the hemostatic function of platelets through its participation in the thrombin-PKC-Rap1b pathway. C3G also plays important roles in angiogenesis, tumor growth, and metastasis through its regulation of the platelet secretome. In addition, C3G contributes to megakaryopoiesis and thrombopoiesis. Here, we used a platelet-specific C3G-KO mouse model to further support the role of C3G in hemostasis. C3G-KO platelets showed a significant delay in platelet activation and aggregation as a consequence of the defective activation of Rap1, which resulted in decreased thrombus formation in vivo. Additionally, we explored the contribution of C3G-Rap1b to platelet signaling pathways triggered by thrombin, PMA or ADP, in the referenced transgenic mouse model, through the use of a battery of specific inhibitors. We found that platelet C3G is phosphorylated at Tyr504 by a mechanism involving PKC-Src. This phosphorylation was shown to be positively regulated by ERKs through their inhibition of the tyrosine phosphatase Shp2. Moreover, C3G participates in the ADP-P2Y12-PI3K-Rap1b pathway and is a mediator of thrombin-TXA Transgenic expression of C3G in platelets stimulates (i) megakaryocytic differentiation and proplatelet formation,2 (ii) platelet activation and aggregation,3 and (iii) α-granule secretion and platelet angiogenesis and metastasis.4 In addition, we have shown that C3G participates in the activation of Rap1 triggered by thrombin and PMA (phorbol 12-myristate 13-acetate) through the PKC pathway.3 Other investigations have demonstrated the formation of a ternary VASP/CrkL/C3G complex that activates platelet Rap1b.5C3G, also known as RapGEF1, is the primary activator of Rap1 GTPases, among which the Rap1b isoform plays a critical role in most platelet functions.2 (thromboxane A2) or epinephrine, stimulate GPCR-type surface receptors, while others, such as collagen and vWF (von Willebrand factor), stimulate immunoglobulin-like receptors. These various receptors trigger signaling cascades that converge in the activation of Rap1b, the most abundant GTPase in platelets.7 Thus, through its interaction with PAR-1 and PAR-4, thrombin activates Rap1b via two sequential activation waves involving PLC-CalDAG-GEFI and PKC-C3G.8 On the other hand, ADP, through its binding to purinergic P2Y12 receptors coupled with Gαi, stimulates Rap1b activation via a calcium-independent pathway that engages PI3K,11 although the GEF for Rap1b that mediates PI3K activities in platelets remains to be identified.7Most platelet agonists, such as thrombin, ADP (adenosine diphosphate), TXA2 also participates in the activation of Rap1 through its release and subsequent binding to TXA2 receptors. It has become increasingly clear that MAPKs participate in the synthesis of TXA2 by activating cPLA2.12 However, the precise contribution of MAPKs to other platelet functions remains controversial. Some studies suggest that both ERKs and p38 MAPKs are essential for platelet spreading, aggregation, thrombus formation and α-granule secretion,13 while others have suggested that these kinases do not contribute to platelet activation or aggregation.14 Neither of the two Rap1 isoforms mediates ERK or p38 MAPK activation in platelets,15 although a negative role for Rap1 in ERK and p38 MAPK activation has been demonstrated in various cell types, including hematopoietic cells.16 Moreover, in platelets, Raf-1 and B-Raf do not participate in the activation of ERK2 by thrombin, a role that has been attributed to PKC.17TXA18 which participate in the responses of most platelet agonists. In platelets, Src and PKC are reciprocally activated by transphosphorylation. Specifically, PKC phosphorylates Src at Ser12, a residue involved in cytoskeletal association and substrate affinity.19Full C3G activation requires its phosphorylation at residue Tyr504 by SFKs (Src-family kinases),17 However, ERKs are downstream targets of SFKs in the signaling pathway initiated by the binding of vWF to the GPIb-IX-V receptor, leading to TXA2 generation.19 Moreover, in MKs under thrombopoietin (TPO) stimulation, the SFK Lyn reduced ERK activity through the activation of PTPs (protein tyrosine phosphatases) such as Shp1.20 In fact, the Shp1 and Shp2 phosphatases are major regulators of megakaryopoiesis, thrombopoiesis, and platelet function.21 Recent studies showed an increase in the phosphorylation levels of ERKs in Shp2−/− platelets,22 suggesting the negative role of Shp2 in ERK activation. However, in other hematopoietic cells, Shp2 acts as a positive regulator of the Ras-ERK pathway downstream of cytokines and RTK receptors.23 In addition, ERKs were found to phosphorylate and inhibit Shp2 in pheochromocytoma PC12 cells in vitro.24Src does not contribute to the activation of ERKs induced by thrombin.2, as well as its role in the modulation of TXA2 synthesis through a negative feedback mechanism involving cPLA2.In this work, we confirmed the role of C3G in Rap1-mediated platelet activation and aggregation using a conditional knockout model. In addition, through the use of specific inhibitors, we explored the participation of transgenic (tg) C3G in platelet signaling pathways triggered by thrombin, PMA and ADP by three different approaches: (i) study of the differential sensitivities of tgC3G and tgC3GΔCat platelets to the inhibition of platelet activation and aggregation, (ii) study of the phosphorylation of C3G at Tyr504 by immunofluorescence confocal microscopy, and (iii) analysis of the activation of Rap1b in platelets of the different genotypes used. Our results support the participation of C3G in signaling pathways regulated by PKC-Src, PI3K, MAPKs and TXASuccessful abrogation of C3G in MKs and platelets was verified by analyses of genomic DNA in MKs and mRNA and protein expression in MKs and platelets Fig. . Some reRapgef1flox/flox;PF4-Cre+/− (hereinafter C3G-KO) mice and their controls  mice) revealed a significant bleeding diathesis in C3G-KO mice that was not observed in C3G-wt siblings  or MRS2179 (a P2Y1 inhibitor), followed by thrombin or ADP stimulation. Previously, we verified the inhibitory effects of these inhibitors and others used in this work on thrombin-induced platelet activation and aggregation  on thrombin-induced integrin αIIbβ3 activation  or wortmannin prior to thrombin stimulation. As shown in Fig. Overall, these results suggest that C3G participates in the ADP-P2Y12-PI3K-Rap1 pathway.32 α-granule secretion33, and TXA2 synthesis.12 In platelets, ERK activation is independent of Raf-1 and B-Raf but dependent on PKC and Src.34 Based on the functional relationships between C3G and these MAPKs in other systems,39 we evaluated whether C3G and these MAPKs contribute to platelet aggregation and activation through a common pathway.Several studies have suggested the participation of ERKs and p38 MAPKs in most platelet functions, including platelet aggregation and thrombus formation,Following the same reasoning described above, we monitored the sensitivities of thrombin-stimulated tgC3G, tgC3GΔCat and control platelets to selective inhibitors of these MAPKs: U0126 (an inhibitor of MEK1/2) and SB203580 (an inhibitor of p38α/β MAPK). TgC3G platelets were more sensitive to the inhibition of ERKs and p38α/β MAPKs than wtC3G platelets, since both inhibitors (mainly U0126) produced a significantly greater reduction in the levels of P-selectin on the surface Fig.  and in t1 In addition, an analysis of ERK phosphorylation in K562 clones with the overexpression or knockout of C3G revealed that C3G participates in the sustained activation of ERKs, leading to K562 differentiation  is one of the main tyrosine phosphatases that regulate platelet functions.To confirm that the Shp2 phosphatase is regulated by ERKs and responsible for the dephosphorylation of C3G, we studied whether Shp2 and pTyr504-C3G colocalize in tgC3G platelets. Manders’ colocalization coefficient analysis revealed that pTyr504-C3G and Shp2 indeed colocalized upon thrombin stimulation Fig. . This co40 All these results support the notion that Shp2 is the phosphatase regulated by ERKs that dephosphorylates and inhibits C3G.Finally, to verify that Shp2 negatively regulates C3G activation, we analyzed the levels of active Rap1 in the lysates of transgenic platelets treated with thrombin in the presence of U0126 and/or SHP099. Figure 2, a platelet agonist that amplifies platelet responses through its release and binding of specific receptors in the plasma membrane. The above results indicate that C3G participates in the ERK and p38 MAPK pathways, leading to platelet activation and aggregation. Since these pathways are also responsible for the synthesis and secretion of TXA2 through the activation of cPLA2,34 we investigated whether C3G plays a role in the regulation of TXA2 synthesis and whether it participates in platelet responses to TXA2. HPLC/mass spectrometry analysis of thrombin-stimulated platelets revealed that the levels of released TXB2 (the stable form of TXA2) were significantly lower in tgC3G platelets than in wtC3G platelets . Accordingly, C3G-KO platelets exhibited higher levels of p-cPLA2 than their wild-type controls in response to 1 U/ml thrombin ..42 This It is important to mention that due to the low C3G protein levels present in wild-type platelets, together with the lack of suitable phospho-C3G antibodies for western blotting, it is extremely difficult to analyze C3G phosphorylation in platelets with this technique. Therefore, we performed these analyses using confocal fluorescence techniques, which are much more sensitive than western blotting and provided highly reproducible results in this model.3 ADP activates Rap1b through two alternative pathways: the P2Y1-Gαq-PLCβ-CalDAG-GEFI and P2Y12-Gαi-PI3K pathways.10 Here, we show that C3G preferentially participates in the pathway activated by the ADP receptor P2Y12, which is supported by the significantly increased sensitivity of tgC3G platelets, compared to wtC3G platelets, to the inhibition of integrin αIIbβ3 activation by clopidogrel and wortmannin. This is reinforced by the fact that tgC3GΔCat platelets showed the opposite tendency. Accordingly, the activation of Rap1b induced by thrombin was also more sensitive to the inhibition of P2Y12 and PI3K in tgC3G platelets than in wtC3G platelets. Collectively, these results indicate that C3G participates in the ADP-P2Y12-PI3K pathway leading to Rap1b activation. In addition, our results show the poor contribution of C3G to P2Y1 responses, which is in agreement with the important role of CalDAG-GEFI in the activation of Rap1b by this pathway.10We previously found that transgenic C3G platelets exhibited greater activation and aggregation in response to ADP than their wild-type controls.13 Hence, both are phosphorylated in response to thrombin, and their inhibition decreases the activation and aggregation of wild-type platelets. The activation of ERKs by thrombin was determined at a high thrombin concentration (1 U/ml), a condition in which thrombin preferentially signals through PKC independently of ADP.43 This would explain the lack of the inhibitory effect of clopidogrel or 2-MeSAMP on thrombin-induced ERK phosphorylation. Transgenic C3G platelets were consistently more sensitive to ERK and p38α/β inhibition, suggesting the participation of C3G in signaling pathways mediated by these MAPKs. In fact, thrombin-induced C3G phosphorylation at Ty504 was drastically inhibited by U0126 and SB203580, providing an explanation for the increased sensitivity of tgC3G platelet activation and aggregation to both inhibitors. These results suggest that C3G is positively regulated by these MAPKs. A functional relationship, both positive and negative, between C3G and these MAPKs has been well documented.39 In platelets, the contribution of C3G to the transient activation of ERKs and p38 MAPKs appears to be marginal. This is in agreement with our results in K562 cells, as well as those in other systems, showing that C3G-Rap1 participates in the sustained (and not transient) activation of ERKs.44 Instead, ERKs and p38 MAPKs are involved in pathways leading to C3G phosphorylation. Specifically, ERKs promote C3G phosphorylation through inhibition of the phosphatase Sph2, which is responsible for the dephosphorylation of C3G at Tyr504  and p38 MAPKs in platelet functions.2 synthesis.34 It has been suggested that TXA2, acting through its receptor, TXA2R, contributes to Rap1b activation in response to ADP and collagen but not thrombin.15 In contrast, our results are consistent with the existence of a TXA2-C3G-Rap1 pathway activated by thrombin, as suggested by (i) the greater sensitivity of tgC3G platelets to aspirin during thrombin-induced activation and aggregation; (ii) the inhibitory effect of aspirin on the phosphorylation of C3G induced by thrombin, which was more evident in tgC3G platelets; and (iii) the inhibitory effect of aspirin on C3G-mediated Rap1 activation induced by thrombin. Moreover, C3G might reduce the levels of TXA2 through modulating the activity of cPLA2, as also demonstrated in our C3G-KO model. All these results lead us to propose a model in which MAPKs, in response to thrombin, regulate the activation of Rap1 through a TXA2-TXA2R-C3G axis . This suggests that Rap1 activity is tightly modulated by compensatory mechanisms, highlighting its relevant role in platelet physiology. In contrast, tgC3G platelets were very sensitive to these inhibitors, indicating that the overexpression of C3G made platelets more dependent on this RapGEF. However, the data derived from our knockout model confirmed the important role of endogenous C3G in platelet activation and aggregation based on its GEF activity for Rap1, especially that in response to PMA and thrombin at a high concentration.2 signaling pathways. The activation of C3G by its phosphorylation at Tyr504 is regulated by PKC-Src and two mechanisms involving MAPKs: one that acts through inhibition of the Sph2 PTP and another that acts through the production of TXA2. Therefore, C3G is a Rap1 GEF with specific functions that are complementary to those of CalDAG-GEFI, allowing the tight modulation of Rap1 activity in platelets.In summary, endogenous C3G plays a physiological role in platelets by promoting Rap1 activation. In addition, the transgenic expression of C3G enhances thrombin- and ADP-mediated platelet activation and aggregation through its participation in the PKC-Src, P2Y12-PI3K, and p38/ERKs-TXAHence, C3G may play a relevant role in physiological and/or pathological processes involving platelets, such as cancer or cardiovascular diseases, and may represent a new biomarker and/or therapeutic target in platelets.Rapgef1 in which exons 17–21 were flanked by LoxP sites was generated as described.45 To delete C3G from MKs and platelets, Rapgef1flox/flox mice were crossed with PF4-Cre+/− transgenic mice,46 generating Rapgef1flox/flox; PF4-Cre+/− (C3G-KO) and Rapgef1flox/flox; PF4-Cre−/− (C3G-wt) offspring. The offspring were genotyped by PCR with the following primers: conditional and wild-type Rapgef1 alleles: C3G-KO-LoxF 5′-AGCCTGTTGGCAAGTTTGG-3′ and C3G-KO-LoxR 5′-CTGATGGAGAACCTAGCTGTGG-3′; PF4-Cre and wild-type alleles: PF4-prom-F 5′-CCC ATA CAG CAT ACC TTT TG-3′, PF4-prom-Cre-R 5′-TGC ACA GTC AGC AGG TT-3′ and PF4-prom-WT2-R 5′-TTA CAG CAT CGC CTT CCC CT-3′. Deletion of the flanked exons in MK DNA was monitored by PCR with the primers C3G-KO-LoxF and C3G-int21R (5′-GGACTGGAGCATCTTTCAG-3′)  Fig. .4 The human transgenes C3G (full-length) and C3GΔCat  were expressed under the control of the platelet-specific PF4 gene promoter. Transgenic C3G (tgC3G) lines 2C1 and 6A6 and transgenic C3GΔCat (tgC3GΔCat) line 8A3 were used.The transgenic mice models used in this work have been previously described.WtC3G and wtC3GΔCat mice were the control mice for tgC3G and tgC3GΔCat mice, respectively, while C3G-wt mice were the control mice for the C3G-KO model.All mice used in these studies were 10–14 weeks old, unless otherwise specified.g for 4 and 5 min. Platelets were pelleted by centrifugation at 1300 × g for 5 min and resuspended in Tyrode-Hepes buffer , 5 mM glucose) at 2 × 108 platelets/ml.Blood (0.5–1 ml) was collected by cardiac puncture from isoflurane (2%)-anesthetized mice into citrate tubes  and used to prepare platelet-rich plasma (PRP) by double centrifugation at 100 × g. Erythrocytes were lysed with red cell blood lysis buffer  for 15 min at 4 °C. MKs were isolated by BSA density gradient created by layering 1, 3, and 5% BSA in a Falcon tube. BM cells were gently introduced into the gradient, and after 1 h, MKs were collected from the bottom.BM cells were obtained from the femora and tibiae of mice by flushing with PBS and centrifuged for 5 min at 1300 × The spleen was digested with 1 mg/ml collagenase and dispase for 45 min at 37 °C while stirring. Cells were filtered using a 70 μm nylon cell strainer  and washed with cold PBS. Erythrocytes were lysed by incubation with RCB for 15 min at 4 °C. Cells were incubated with 1:50 anti-CD41-APC (eBioscience (ThermoFisher Scientific), 17-0411) and anti-CD61-PE  antibodies for 15 min at 4 °C. Double-labeled cells (MKs) were sorted using a BD FACSAria II cytometer.47Genomic DNA was purified from lysed MKs by precipitation with 5 M NaCl and ethanol, as described.3 C3G expression was monitored by qPCR using SYBR Green master mix  and the following primers: N-terminus: 190F 5′-GTGAGCAAAGAGGCAAGAGA-3′ and 288R 5′-CACAGCACTGGTGGACATAA-3′ and C-terminus: 2540F 5′- ATTTCCACAGCCACGAGATAG-3′ and 2654R 5′-CTCTTCTCCTCATTCTGCTCTT-3. β-Actin, which was used as a housekeeping gene, was amplified with the oligos F 5′-TAGACTTCGAGCAGGAGATGG-3′ and R 5′- CAAGAAGGAAGGCTGGAAAG-3′. Primers were designed with the PrimerQuest Tool , and Tm values were calculated with Oligo Calc: Oligonucleotide Properties Calculator . Data were analyzed using the 2-ΔΔ CT method.48cDNA was obtained from MKs and platelets as described.A 5 mm section of the tail tip from each anesthetized mouse was transected, and the tail was immersed in 37 °C PBS, following which the time until blood flow ceased was noted. The experiment was terminated after 8 min. Measurements were made in 3-week-old mice at weaning (before genotyping).C3G-KO and C3G-wt mice were anesthetized with a mixture of ketamine and valium , and the jugular vein was exposed. A mixture of 600 μg of collagen  and 60 μg of norepinephrine (Sigma)/kg of mouse body weight  or 150 μg of collagen and 15 μg of norepinephrine/kg of mouse body weight  was injected into the jugular vein. At the lethal dose, acute pulmonary thromboembolism occurred, and the mice died by asphyxiation, usually within 10 min. Therefore, the time to death was monitored. Mice that were still alive after 20 min were considered survivors. The sublethal dose induced thrombogenesis, which resulted in thrombocytopenia. This was measured as the decrease in platelet count. Prior to the injection of agonists, a small sample of blood (100–200 μl) was extracted from the contralateral jugular vein into an EDTA tube, and the number of platelets was determined by flow cytometry. Blood withdrawal was repeated 4 min after the injection of collagen/norepinephrine. The difference in platelet count is expressed as the percentage of platelet reduction. The formation of thrombi in the lungs was verified by immunohistochemical analysis of lung sections stained with hematoxylin/eosin. The samples were analyzed with the double-blind method so that we did not know the genotype of each mouse until the end of the histopathological analysis.Fifteen microliters of EDTA-anticoagulated blood was diluted in 500 μl of Tyrode-Hepes buffer. Thirty microliters of this dilution was stained with 1 μl of anti-mouse CD41-FITC  for 15 min and then diluted again to 1 ml. Platelets from 50 μl of this last dilution were measured on a BD Accuri™ C6 flow cytometer.Platelets were stimulated with 0.2, 0.5, or 1 U/ml thrombin; 0.2, 2, 5, or 10 μM PMA; or 10 μM ADP after treatment with the following inhibitors for 5 min: bisindolylmaleimide (5 μM), clopidogrel (100 μM), 2-MeSAMP (50 μM), MRS2179 , U0126 (20 μM), SB203580 (20 μM), wortmannin (100 nM), aspirin (2 mM), PP2 (10 μM) or SHP099 (20 μM).l-lysine-coated coverslips and allowed to settle for 50 min. Attached platelets were permeabilized with 0.2% Triton X-100 and blocked overnight in PBS with 1% BSA. The platelets were incubated with the following primary antibodies at RT for 2 h: Oregon Green® 514 phalloidin ; C3G-1008 antiserum49; Src  from Abcam (UK); p-C3G , SH-PTP2 , and cPLA2  from Santa Cruz Biotechnology, Inc. ; and phospho-cPLA2  from Cell Signaling Technology Inc. . This was followed by incubation (1 h at RT) with the following secondary antibodies as indicated: Cy3-conjugated goat anti-rabbit (Abcam); Cy5-conjugated goat anti-mouse ; and Alexa Fluor 568 goat anti-rabbit or Alexa Fluor 647 goat anti-mouse (Thermo Fisher Scientific). Images were obtained at the same exposure time with Zeiss LSM 515 and Leica TCS SP8 confocal microscopes, and pictures were processed using Zen 2.1 imaging software and LSM Image Browser. Colocalization was determined by Manders’ colocalization coefficient (M) analysis using ImageJ software with the JACoP plugin as described.50Platelets from four mice of each genotype were pooled and activated as indicated. After pretreatment with inhibitors for 5 min, the platelets were stimulated with 0.5 U/ml thrombin or 2 μM PMA for 1 min at 37 °C while stirring (900 rpm). The platelets were fixed for 15 min in 4% formaldehyde, placed onto poly-3Platelet activation was determined by flow cytometry via measuring the expression of P-selectin on the surface  as an indicator of platelet degranulation or the high-affinity conformation of the integrin αIIbβ3  as described previously.51 Briefly, 50 μl of citrate-anticoagulated blood was washed in Tyrode-Hepes buffer and divided into two populations. Each population was labeled with either anti-CD9-FITC or anti-CD9-PE for 15 min. After centrifugation to remove the excess antibodies, the blood was suspended in Tyrode-Hepes, and both populations were mixed. The mixture was incubated with the corresponding inhibitors for 2 min at RT, and aggregation was induced by the addition of 1 U/ml thrombin, 10 μM PMA or 10 μM ADP. The reaction was maintained at 37 °C with stirring at 900 rpm and stopped by the addition of a 9× volume of 0.5% formaldehyde in PBS. Aggregate formation was measured as the percentage of double labeling events.Platelet aggregation was determined as previously described.For both types of analysis, each data point corresponds to one animal.2, 2% NP-40, 2% glycerol, 2 mM Na3VO4, 50 mM NaF, 2 mM PMSF, 2 μM aprotinin, 2 μM leupeptin). Protein lysates were resolved by SDS-PAGE and transferred to PVDF membranes that were blotted using the following antibodies: anti-p-ERK (E-4) (sc-7383), anti-ERK 1 (sc-94), and anti-p38α (sc-535) from Santa Cruz Biotechnology, Inc.; anti-phospho-p38 MAP kinase Thr180/Tyr182 (#9211) from Cell Signaling Technology Inc.; and anti-Rap1 (#610196) from BD Biosciences.Platelets suspended in Tyrode-Hepes buffer were lysed in the same volume of 2× modified RIPA buffer (100 mM Tris (pH 7.5), 400 mM NaCl, 5 mM MgCl2 was measured by liquid chromatography coupled to tandem mass spectrometry (LC/MS/MS) as previously described.52 TXA2 was detected via detection of its breakdown product, TXB2.Platelets were stimulated with 1 U/ml thrombin for 3.5 min while shaking (900 rpm). Then, the platelets were pelleted, and the supernatants were collected. The same volume of methanol was added to the supernatants, and the vials were purged with nitrogen prior to snap-freezing. Secreted TXA3 using GST-RalGDS RBD immobilized on glutathione-sepharose, which binds specifically and selectively to the GTP-bound form of Rap1b. Platelets were pretreated with different inhibitors for 5 min prior to stimulation with thrombin or PMA for 1 or 5 min.The activation of Rap1 was evaluated by pulldown assay as described previouslyPlatelet activation and aggregation in platelets treated with thrombin, PMA or ADP in the presence or absence of different inhibitors were monitored by flow cytometry as described above. The effects of the inhibitors on platelet activation and aggregation were calculated as the percentage of inhibition with the following formula:U-test was carried when the data were not normally distributed. Differences were considered significant when p < 0.05. The effect of lethal collagen/epinephrine injection on mouse survival was evaluated using Kaplan–Meier Plotter and the log-rank test (SigmaPlot 12 software).Data are represented as the mean ± SD (standard deviation) or SEM (standard error of the mean) as indicated. The Kolmogorov-Smirnov test was performed to determine if data fit a normal distribution. To compare two experimental groups for which the data were normally distributed, the unpaired Student’s t-test was carried out. The nonparametric Mann–Whitney Supplemental material


In vivo fertility results with a dry ice cold chain showed no statistical difference to the conventional LN method. In vitro bovine semen analyses also showed that storage under these conditions minimally affects characteristics associated with fertility. A dry ice cold chain system could leverage the global availability of LCO2 to expand the reach of AI and other cold storage applications of biological materials in low-resource settings.Artificial insemination (AI) is widely used in livestock industries to breed for desirable characteristics and increase yields. The standard practice of storing and transporting bovine semen uses liquid nitrogen (LN), a scarce commodity in many regions of the world. This study explored the feasibility of using dry ice, a more readily available alternative. We developed equipment that dispenses dry ice from widely available liquid carbon dioxide (LCO Over the last few centuries, selective breeding has developed dairy cattle breeds that have optimal productive life and produce large quantities of milk. By contrast, indigenous cows in the developing world survive harsh environments but are far less productive . RecogniPerhaps the greatest breakthrough allowing the expansion of the use of AI came in the 1950s when glycerol was discovered to act as a cryoprotectant for dairy bovine semen . This adInitially bovine semen was stored in dry ice or dry ice and ethanol . SubsequA study that more closely tracked storage duration indicated that dry ice appears equivalent to LN for up to 6 mo, after which bovine semen stored in dry ice loses fertilizing potential . These r2), on the other hand, is often widely distributed in low-resource settings due, primarily, to its use in the carbonated beverage industry  and stored in 180-L microbulk tanks from Chart Industries, . Tanks storage pressure was set to 2,400 kPA. Unless otherwise indicated, all other reagents used in this study were purchased from Sigma .For in vitro experiments, bovine semen was purchased from Accelerated Genetics  and All West Select Sires, Inc. . The purchased bovine semen used in all in vitro experiments were single ejaculates from three Holstein Bulls, diluted in egg yolk-citrate extender and packaged in 0.5-mL French straws. Easy Buffer B and Leja 4-chamber slides were purchased from IMV Technologies . LCOThe dry ice storage device consists of a vacuum flask with central tube where bovine semen straws are stored in a custom-designed cane that can be lifted to extract a straw. A King2L vacuum flask  was used as the storage device . The cen2 into dry ice directly  freezer set to −80 °C and a Kenmore 253.28042807  freezer set to −20 °C were used for in vitro experiments.2 microbulk tank using a high-precision platform scale Model PFK988-C600  and the resulting mass of dry ice produced in the storage device on a desktop scale Model SB8001 . The storage device heat leak was calculated by measuring the mass loss over time using the Model SB8001 scale and multiplying by the carbon dioxide enthalpy of sublimation (571 J/g).The percentage of liquid converted to solid was determined by measuring the change in the mass of the liquid in the LCOThree 36 AWG T-type thermocouples  were positioned inside a blank 0.5-mL semen straw  filled with epoxy  to secure their position. The instrumented semen straw  was placBovine semen straws stored in various devices for the times indicated in For each data point, a minimum of 500 sperm per straw were assessed using previously described methods . Brieflyn = 947) were inseminated between October 2, 2018 and March 1, 2019. This study was approved by the Makerere University School of Veterinary Medicine and Animal Resources Research Ethics Committee—SVAR IACUC/IRB (study SVARREC/07/2018).Six artificial insemination service providers (AISPs) were enrolled to inseminate cattle in greater Kampala and Mukono districts of Uganda. Dairy cattle were the target animals kept at smallholder farms and managed under best dairy practices, including nutrition, feeding, and maintaining dairy cattle vaccination schedules for East Coast Fever and Foot and Mouth Disease. Farmers provided consent to participate in the study. Cows , frozen using common practices, and shipped to the collection point and subsequently stored in LN or LN vapor. All semen had a sperm cell density of 10 million units per straw and initial motility greater than 55%. Bovine semen was randomly placed within AISPs’ charged LN Dewars or CO2 at any given time. LN Dewars were topped up with LN at least once per week and dry ice storage devices were topped up with dry ice at least every third day. Semen inventory was replenished as needed when cryogen was topped up. Semen was maintained within the device for no longer than 14 d. AISPs were trained on the use of the dry ice Dewars handling and insemination practices. Nonreturn rate was determined 21 d (range 18–24 d) following insemination by cow owner or managers assessment. Nonreturn rate, defined as cows not returning to estrus 21 d postinsemination, was evaluated as a binary outcome. A 35-d pregnancy diagnosis follow-up was carried out on a subset of the inseminated cattle that did not return on heat (n = 188) by a veterinarian. The pregnancy diagnosis follow-up was randomly assigned to cows that were first sorted by a technician and cryogen. The diagnosis was made using a SonoFarm mini sonogram with a rectal palpation probe .Each cryogen was alternated every 14 d with half the AISPs using LN and the other LCOAISPs input data associated with insemination and nonreturn status into a custom data collection form generated in Open Data Kit via smartphone and a custom i-cloud data system. Collected data included insemination date and time, client farmer, geographical position system (GPS) location, cow parity or heifer status, body condition score (BCS), cow identification, identification (ID) of the bull served, photograph, and 21-d status. In some cases, not all data fields were recorded.A body condition score for each cow was determined at each insemination using the BCS Cowdition App . Only cattle with a score between 3.0 and 4.0 were included in the study analysis.t-tests corrected using the Bonferroni–Dunn method to generate multiplicity-adjusted P values. The impact of consecutive transfers of bovine semen straws between LN and −80 °C on sperm viability, motility, and acrosome integrity were analyzed using one-way analysis of variance, correcting for multiple comparisons using the Sidak test. A two-sample t-test for equality of proportions without continuity correction in the R statistical environment  or the R v 3.1.1 statistical environment . Experimironment  was perf2 tanks commonly distributed in low- and middle-income countries. For this study, we developed simple equipment using readily available parts that interfaces with LCO2 tanks to produce dry ice on demand and a compatible dry ice storage device capable of holding bovine semen straws for AI outreach  for at least 3.5 d in the laboratory environment . Between 3.5 and 6 d, the bottom of the straws maintained a dry ice temperature, but the middle and tops of the straws warmed  translating to 257 g/day (SD = 117 g/day) dry ice sublimation.To assess the thermal performance of the dry ice storage device, the temperature was measured with instrumented bovine semen straws placed adjacent to bovine semen straws within the cane  or attacs warmed . The dry3. If increased hold time is desired, the dry ice density can be increased to 800 kg/m3 using a combination of manual compression and refilling with the dry ice maker. The dry ice maker delivered a 30–35% liquid-to-solid conversion efficiency from a 180-L microbulk tank.The dry ice maker can produce densities of approximately 500 kg/mP > 0.99) or the device for up to 6 d (P > 0.15). On day 7, the dry ice dissipated in the device, the canister warmed to ambient temperature, and only 21% of the sperm remained viable. Sperm from bovine semen straws transferred from LN to −20 °C significantly lost viability within the first day (P < 0.0001) and maintained approximately 20% viability thereafter.To assess the effects of storing bovine semen in the dry ice storage device, sperm viability was determined for bovine semen straws transferred from LN to a fully charged dry ice storage device, a −80 °C freezer, or a −20 °C freezer . There wP < 0.0004) or the storage device . Surprisingly, the percentage of motile sperm stored in the devices was stable thereafter up to 6 d, despite the warming of the top and middle of the straws between 3.5 and 6 d (P > 0.073). Motility of sperm stored at −80 °C and in the devices did not differ for 6 d. On day 7, sperm motility decreased concurrent with all regions of the straw warming above −77 °C.We performed similar experiments to monitor the effects on sperm motility . The perP > 0.99) or transferred to and held in the device for up to 6 d (P > 0.96). At day 8, bovine semen stored in the device lost acrosome integrity (P < 0.0001), coinciding with straws warming to ambient temperature . Subsequent transfers had no further impact on sperm motility  is not significant.To assess whether the use of the dry ice cold chain for AI outreach affects conception rates, the study carried out an artificial insemination trial in urban and peri-urban Kampala, Mpigi Wakiso, and Mukono districts, Uganda. Over the course of 5 mo, six AISPs performed a total of 948 insemination services, of which 741 collected nonreturn rate data, 392 with LN and 349 with dry ice. The 21-d nonreturn rate for the dry ice cold chain system was 76.5%  as compared to 79.1%  with the conventional LN cold chain. A two-sample test for equality of proportions without continuity correction indicated that the nonreturn rate difference . Pregnancy was detected in 56.8%  and 55.1%  of cows inseminated with bovine semen that used the dry ice and LN cold chains, respectively  is not significant. We did not observe obvious patterns associated with the outcomes of the different cold chains being affected by insemination location, dam breed, sire breed, or individual inseminators  or improving the thermal performance of the storage device.The flask used in the current study has a 6-d hold time, which may be insufficient for some AISPs. Significant opportunity exists to design dry ice equipment capable of storing more products, products with different dimensions, and improving hold times. For instance, a two- to three-factor improvement on hold time is possible by increasing the dry ice density to commercial grade (~1,500 kg/mObservations of in vitro characteristics of bovine semen quality are consistent with the dry ice cold chain maintaining bovine semen fertility. In this study, we observed that when bovine semen is stored within the storage device, sperm viability and acrosome integrity are maintained for 6 d, which is consistent with previous work  that demAt first glance, the gross motility decreases do not appear to be consistent with nonreturn results. That is, if motility decreases by 20%, should nonreturn and pregnancy rates also decrease? The observation that conception was unaffected suggests that the transfer of bovine semen from LN to dry ice temperatures primarily affects the motility of a subpopulation of sperm that does not contribute to fertility.Experiments where we repeatedly transferred bovine semen between −196 and −80 °C reinforce this inference. If cryogenic damage indiscriminately affects sperm upon transitioning between −196 and −80 °C, then a stepwise decrease in motility would be expected to accompany repeated transfers. We measured motility decreases only after the initial transfer to −80 °C. The observation that motility was consistent thereafter suggests that susceptible and more robust sperm populations exist within the same bovine semen straw.While repeatedly transferring bovine semen from LN to dry ice temperatures did not deleteriously affect in vitro characteristics of bovine seminal biology, these measurements are imprecise predictors of fertility (Rodriguez-Martinez, 2003Data in this study provides foundational support for the transfer of bovine semen from LN to a dry ice cold chain for limited durations. If LN is available, then bovine semen freezing, storage, and transport should continue to be performed using conventional protocols. If LN is unavailable, our data show that bovine semen can be transferred to a dry ice cold chain for short duration storage and/or transportation with minimal, if any, effects on fertility.2 tanks could enable the collection, storage, and transportation of various labile biological materials from remote settings to more centralized testing facilities. Additional studies are needed to evaluate how to operationalize this system and evaluate the economics of this approach.Based on these findings, we expect that this alternative cold chain could enable greater geographical outreach of AI. The system also has the potential to support the delivery of other biological materials that are transported in LN in low-resource settings, such as East Coast Fever stabilate . SimilarSupplementary data are available at Translational Animal Science online.S1 Fig. Schematic of the central tube with list of materials.S2 Fig. Schematic of the straw holder with list of materials.S3 Fig. Schematic of the dry ice producing adaptor with list of materials.S4 Fig. Schematic of the top cover for the dry ice producing adaptor.txaa012_suppl_Supplementary_Figure_S1Click here for additional data file.txaa012_suppl_Supplementary_Figure_S2Click here for additional data file.txaa012_suppl_Supplementary_Figure_S3Click here for additional data file.txaa012_suppl_Supplementary_Figure_S4Click here for additional data file.


Outcomes were accuracy of screw placement evaluated on postoperative CT using the modified Gertzbein and Robbins scale, operative time, blood loss, postoperative drainage, lower back and leg pain evaluated using a visual analogue scale (VAS), lumbar function evaluated using the Oswestry disability index (ODI), and complication rates.Based on the inclusion and exclusion criteria, 80 patients with lumbar degenerative disease who attended the spinal surgery department of the Beijing Jishuitan Hospital between January 2017 and April 2018 were enrolled in the present study. Patients were randomized 1:1 to undergo percutaneous robot‐assisted minimally invasive pedicle screw insertion  than in the control group (93.1% [162/174]). Clinical outcomes showed significant differences between the experimental and control groups in operative time, intraoperative blood loss, and postoperative VAS for lower back pain in the immediate postoperative period.Robot‐assisted pedicle screw insertion in OLIF is an effective strategy for the management of elderly patients with lumbar degenerative diseases. Population aging has become a challenge to healthcare systems globally. In particular, the incidence of spinal degenerative disease is rising. Surgical treatment of spinal degenerative disease usually involves lumbar intervertebral fusion and pedicle screw internal fixation. However, this approach may be challenging in elderly patients, especially in those with severe orthopaedic degeneration and osteoporotic vertebrae, as pedicle screw insertion may breach the cortical wall, which can cause nerve damage, decrease the holding strength of the screw, and increase the risk of bone cement leakagevia an oblique anterior approach, which reduces bone destruction and blood loss compared to traditional posterior lumbar interbody fusion. However, posterior fixation using freehand fluoroscopy‐assisted pedicle screw insertion with an open technique is associated with trauma and complications during and after surgery.Evidence suggests that the safety of fixation in spinal degenerative disease is enhanced by controlling the trajectory of the pedicle screw to obtain accurate screw placement without compromising the integrity of the cortical boneNew technologies offer clinicians additional options. “TiRobot” Fig. , an orthIn this study, we compared the clinical outcomes of percutaneous robot‐assisted minimally invasive pedicle screw insertion versus freehand fluoroscopy‐assisted pedicle screw insertion in elderly patients undergoing an OLIF procedure. Our research questions included the following. First, is percutaneous robot‐assisted minimally invasive pedicle screw insertion in patients undergoing an OLIF procedure feasible and safe? Second, does percutaneous robot‐assisted minimally invasive pedicle screw insertion result in a stable internal fixation, reduced surgical trauma, and early postoperative recovery in elderly patients with lumbar degenerative diseases? Third, what perioperative complications are associated with percutaneous robot‐assisted minimally invasive pedicle screw insertion?Inclusion criteria followed the P, participant; I, intervention; C, comparison; O, outcome; S, study design principle: (i) Participant (P): patients aged ≥55 years with lumbar degenerative disease who were undergoing an OLIF procedure; (ii) Intervention (I): percutaneous robot‐assisted minimally invasive pedicle screw insertion; (iii) Comparison (C): freehand fluoroscopy‐assisted pedicle screw insertion by a traditional open technique; (iv) Outcome (O): accuracy of screw placement, operative time, blood loss, postoperative drainage, lower back and leg pain evaluated using a visual analogue scale (VAS), lumbar function evaluated using the Oswestry disability index (ODI), and complication rates; and (v) study design (S): randomized controlled trial. Exclusion criteria were: (i) age <55 years; (ii) presence of systemic infection or local infection in the target surgical site; (iii) presence of malignant tumor; or (iv) patients who refused surgery. Patients were randomized 1:1 to undergo percutaneous robot‐assisted minimally invasive pedicle screw insertion  or freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique (control group). All patients underwent surgery performed by the same team of experienced surgeons.Preoperative imaging using X‐ray, CT, and MRI was performed in all patients to confirm diagnosis and surgical indication. All patients underwent a two‐step surgical procedure that included OLIF and posterior fixation with pedicle screws.First, patients were placed in the right lateral position, and the target segment was located with fluoroscopy. An incision was made, a K‐wire was inserted into the intervertebral space, and a dilator was introduced over the K‐wire Fig. . The nucNext, patients were placed in the prone position. In the experimental group, a guide wire was introduced through a percutaneous incision on the back, and pedicle screws were inserted using a minimally invasive robot‐assisted technique Fig.  Correct Accuracy of pedicle screw placement was assessed on postoperative thin‐cut CT scans by a blinded, independent radiologist based on the modified Gertzbein and Robbins scale in which screws were graded as: A, without breach of the cortical layer of the vertebral body or pedicle; B, cortical breach of <2 mm; C, cortical breach of ≥2–<4 mm; D, cortical breach of ≥4–<6 mm; and E, cortical breach of ≥6 mmThe duration of the entire surgery, the anterior procedure, and the posterior procedure were recorded. The duration of the entire surgery was defined as the time taken to perform all procedures after anesthesia, including positioning the patient, exposing the operative area, inserting the cage and screws, wound suture, and changing the patient's position between the anterior and posterior procedures. The duration of the anterior procedure was defined as the time taken to place the patient in the right lateral position, disinfect operation area, perform the anterior oblique approach and intervertebral fusion, and suture and dress the wound. The duration of the posterior procedure was defined as the time taken to place the patient in the prone position, disinfect operation area, perform posterior pedicle screw fixation, and suture and dress the wound.Intraoperative blood loss was measured as the volume of blood lost during surgery, calculated as the sum of the fluid in the suction bottle and the amount of blood in the gauze.Postoperative drainage was measured as the volume of blood lost after surgery, calculated as the sum of the fluid in the drainage bottle.A visual analogue scale (VAS) was used to evaluate lower back and leg pain. Using a VAS ruler, the score was determined by measuring the distance (cm) on the 10‐cm line between the “no pain” anchor and the patient's mark, providing a range of scores from 0 to 10. A higher score indicated greater pain intensity. Patients described their lower back and leg pain intensity as 0 (no pain) to 10 (worst pain ever).Lumbar function was evaluated before surgery, immediately after surgery, and at a 6‐month follow‐up using the ODI. The ODI is a principal condition‐specific outcome measure used in the management of spinal disorders and to assess patient progress in routine clinical practice. The ODI includes 10 sections: pain intensity, personal care, lifting, walking, sitting, standing, sleeping, sex life, social life, and traveling. Each section comprises six statements that are scored from 0 to 5. Intervening statements are scored according to rank. If more than one box is marked in each section, the highest score is used. If all10 sections are completed, the score is calculated as follows: total scored out of total possible score ×100. If one section is missed (or not applicable) the score is calculated: ) × 100%. Here, 0%–20% is considered mild dysfunction, 21%–40% is considered moderate dysfunction, 41%–60% is considered severe dysfunction, and 61%–80% is considered disability. For cases with a score of 81%–100%, patients are either long‐term bedridden or exaggerating the impact of pain on their life.Complication rates in the experimental or control groups were calculated as cases with complications/total cases.t‐test. Categorical variables, including number of patients, sex, and number of screws, are reported as a frequency or percentage, and between‐group comparisons were made with the χ2‐test. Significance was set at P < 0.05.Statistical analyses were conducted using SPSS 19.0 . Continuous variables including age, mean operative time, intraoperative blood loss, postoperative drainage, and VAS and ODI scores, are reported as mean and standard deviation. Between‐group comparisons were made with the independent sample This study was approved by the ethics committee of the Beijing Jishuitan Hospital, and all patients provided written informed consent.This study included 80 patients (31 men and 49 women) with a mean age of 63.80 years . Among them, there were 34 cases of lumbar spondylolisthesis, 27 cases of lumbar spinal stenosis, 12 cases of lumbar intervertebral disc herniation, and 7 cases of lumbar instability. In the experimental group, 40 patients (16 men and 24 women), with a mean age of 63.45 years , underwent percutaneous robot‐assisted minimally invasive pedicle screw insertion. In the control group, 40 patients (15 men and 25 women), with a mean age of 64.22 years , underwent freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique. There were no significant differences in baseline demographic characteristics between groups (Table P < 0.05).A total of 344 pedicle screws were inserted in 80 patients;170 pedicle screws were inserted in the experimental group and 174 pedicle screws were inserted in the control group. With percutaneous robot‐assisted minimally invasive pedicle screw insertion, trajectories were Grade A in 167 screws, Grade B in 3 screws, and Grade C, D, or E in 0 screws. With freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique, trajectories were Grade A in 162 screws, Grade B in 11 screws, Grade C in 1 screw, and Grade D or E in 0 screws. Accurate pedicle screw placement (Grade A) was significantly higher with percutaneous robot‐assisted minimally invasive pedicle screw insertion (98.2% [167/170]) compared to freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique (93.1% [162/174]) . Mean operative time for the anterior procedure was not significantly different for robot‐assisted pedicle screw insertion (103.88 ± 37.03 min) compared to freehand fluoroscopy‐assisted pedicle screw insertion (100.75 ± 28.57 min) (P > 0.05). Mean operative time for the posterior procedure was significantly shorter for robot‐assisted pedicle screw insertion (77.13 ± 30.97 min) compared to freehand fluoroscopy‐assisted pedicle screw insertion (110.75 ± 27.00 min) (P < 0.05).Mean operative time was significantly shorter for percutaneous robot‐assisted minimally invasive pedicle screw insertion (196.25 ± 62.85 min) compared to freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique (230.63 ± 55.06 min)  compared to those undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique (7.28 ± 1.45). The immediate postoperative VAS score for lower back pain was significantly improved in patients undergoing robot‐assisted pedicle screw insertion (2.15 ± 1.15) compared to those undergoing freehand fluoroscopy‐assisted pedicle screw insertion (3.35 ± 0.92). The 6‐month follow‐up VAS score for lower back pain was not significantly different for patients undergoing robot‐assisted pedicle screw insertion (1.20 ± 0.82) compared to those undergoing freehand fluoroscopy‐assisted pedicle screw insertion (1.23 ± 0.66).The preoperative, immediate postoperative, and 6‐month follow up VAS scores for leg pain were not significantly different for patients undergoing percutaneous robot‐assisted minimally invasive pedicle screw insertion  compared to those undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique .The preoperative, immediate postoperative, and 6‐month follow‐up ODI scores were not significantly different for patients undergoing percutaneous robot‐assisted minimally invasive pedicle screw insertion  compared to those undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique .P < 0.05). Postoperative drainage was 0 mL in patients undergoing robot‐assisted pedicle screw insertion and 249.00 ± 102.73 mL in those undergoing freehand fluoroscopy‐assisted pedicle screw insertion  compared to those undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique (237.50 ± 167.47 mL) (One patient undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique experienced an infection at the surgical site. One patient undergoing percutaneous robot‐assisted minimally invasive pedicle screw insertion experienced weakness in the left hip flexor. Two patients undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique experienced complications. One patient experienced weakness in the left hip flexor and the other had delayed wound healing. All complications were resolved at 1 month postoperatively.The present study compared the effects of percutaneous robot‐assisted minimally invasive pedicle screw insertion with freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique on clinical and functional outcomes in elderly patients undergoing an OLIF procedure. The findings showed that 98.2% of pedicle screws had a perfect intrapedicular localization following percutaneous robot‐assisted minimally invasive pedicle screw insertion, compared to 91.6% for freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique, confirming that the accuracy of robot‐assisted pedicle screw placement technology exceeds that of the human freehand technique.Precisely determining the location and orientation of pedicle screw placement is challengingMean operative time was significantly shorter for percutaneous robot‐assisted minimally invasive pedicle screw insertion compared to freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique. There was no significant difference in mean duration of the anterior procedure with robot‐assisted pedicle screw insertion compared to freehand fluoroscopy‐assisted pedicle screw insertion. This was not surprising as both techniques require insertion of an intervertebral fusion cage. However, mean operative time for the posterior procedure was 33.62 min shorter for robot‐assisted pedicle screw insertion compared to freehand fluoroscopy‐assisted pedicle screw insertion. Robot‐assisted pedicle screw insertion requires small surgical incisions, causes minimal trauma to soft tissue, and achieves a high accuracy of screw placement. In contrast, freehand fluoroscopy‐assisted pedicle screw insertion requires a large incision, extensive exposure of soft tissue, and suture and dressing of the wound, and can involve repeated fluoroscopy and adjustment of the screw position. These data suggest that robot‐assisted minimally invasive, percutaneous pedicle screw insertion in OLIF is more time‐effective than a freehand technique.Visual analogue scale scores for lower back and leg pain were substantially improved in the postoperative period compared to before surgery in patients undergoing percutaneous robot‐assisted minimally invasive pedicle screw insertion and in those undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique, suggesting that patients in this study were suffering from nerve compression preoperatively. There were no significant differences in VAS scores for lower back pain before surgery or at the 6‐month follow‐up, or in VAS scores for leg pain before surgery, in the immediate postoperative period, and at the 6‐month follow up in patients undergoing robot‐assisted pedicle screw insertion compared to freehand fluoroscopy‐assisted pedicle screw insertion. In the immediate postoperative period, robot‐assisted pedicle screw insertion was associated with significantly less lower back pain and patients were more mobile, likely because their procedure required a smaller incision. At the 6‐month follow up, all incisions had healed, and VAS scores in patients undergoing robot‐assisted pedicle screw insertion and freehand fluoroscopy‐assisted pedicle screw insertion were similar. These findings confirm that OLIF is effective for the treatment of lumbar degenerative diseases with nerve compressionLumbar function, as evidenced by ODI scores, was substantially improved in the postoperative period compared to before surgery in patients undergoing percutaneous robot‐assisted minimally invasive pedicle screw insertion and in those undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique. There were no significant differences in lumbar function before surgery, in the immediate postoperative period, and at the 6‐month follow up in patients undergoing robot‐assisted pedicle screw insertion compared to those undergoing freehand fluoroscopy‐assisted pedicle screw insertion. This was unexpected as pain after surgery was more severe in patients that underwent freehand fluoroscopy‐assisted pedicle screw insertion, but the finding may have been the result of postoperative analgesia.Intraoperative blood loss and postoperative drainage were significantly less in patients undergoing percutaneous robot‐assisted minimally invasive pedicle screw insertion compared to those undergoing freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique. Robot‐assisted pedicle screw insertion is associated with less soft‐tissue damage. The surgeon can more precisely predict the trajectory of the screw such that the placement of each screw requires a 1‐cm skin incision, followed by blunt separation of fascia and muscle, with minimal damage to soft tissues and blood vessels. As the wound and soft tissue damage are minimal during robot‐assisted pedicle screw insertion, there is no postoperative bleeding; therefore, postoperative drainage tubes are not needed. Freehand fluoroscopy‐assisted pedicle screw insertion requires a 10‐cm skin incision, separation of a broad range of soft tissues, including muscle, and exposure of the bilateral lamina to the lateral side of the facet joint. More surgical procedures are needed, which leads to longer operative times and increased intraoperative blood loss. Postoperative drainage is substantial, which could result in blood loss and have adverse effects on hemodynamic stability.This study was associated with several limitations. First, there is a paucity of data linking accuracy of screw placement to clinical outcomes. Further large size studies with a longer follow up are required to confirm the clinical relevance of our findings. Second, subgroup analyses exploring the effect of patients’ baseline demographic and clinical variables on our outcomes were not performed due to small sample sizes. These data are important to inform patient selection and will be a topic of future research.Percutaneous robot‐assisted minimally invasive pedicle screw insertion was more accurate than freehand fluoroscopy‐assisted pedicle screw insertion using a traditional open technique in elderly patients with lumbar degenerative diseases undergoing OLIF. Robot‐assisted pedicle screw insertion in OLIF is time effective, ensures internal fixation stability, reduces surgical trauma, accelerates early postoperative recovery, and decreases the risk of surgical complications.


The ice- and organic-rich permafrost of the northeast Siberian Arctic lowlands (NESAL) has been projected to remain stable beyond 2100, even under pessimistic climate warming scenarios. However, the numerical models used for these projections lack processes which induce widespread landscape change termed thermokarst, precluding realistic simulation of permafrost thaw in such ice-rich terrain. Here, we consider thermokarst-inducing processes in a numerical model and show that substantial permafrost degradation, involving widespread landscape collapse, is projected for the NESAL under strong warming (RCP8.5), while thawing is moderated by stabilizing feedbacks under moderate warming (RCP4.5). We estimate that by 2100 thaw-affected carbon could be up to three-fold (twelve-fold) under RCP4.5 (RCP8.5), of what is projected if thermokarst-inducing processes are ignored. Our study provides progress towards robust assessments of the global permafrost carbon–climate feedback by Earth system models, and underlines the importance of mitigating climate change to limit its impacts on permafrost ecosystems. Siberian Arctic permafrost contains vast stores of carbon, the fate of which is dependent on the climate. Here the authors use models of future scenarios to show that under the direst climate changes up to 2/3 of the stored organic carbon could thaw. In unglaciated regions, climate-driven accumulation and melting of ground ice have been key processes in the evolution of these landscapes, resulting in history-dependent landscapes and landforms with distinct ground ice distributions9. There is emerging evidence that the present-day ground ice distribution governs permafrost thaw pathways, and thus how landscapes evolve in the future13—particularly given the expected warming of the Arctic climate15. Thawing of ice-rich permafrost and melting of massive ground ice induce landscape change termed thermokarst, which results in characteristic landforms across ice-rich permafrost terrain16  lack the structure and physical processes relevant to represent thermokarst, and might thus substantially underestimate future permafrost degradation and the permafrost carbon–climate feedback.Today’s permafrost landscapes have been shaped by climatic, geomorphic and ecological processes during the Last Glacial Period and the Holocene18, as the landscapes’ history led to abundance of ice- and organic-rich permafrost deposits24 , permafrost temperatures in the NESAL are yet amongst the coldest in the Arctic with observed and simulated present-day mean annual ground temperatures lying mostly within the range −8 to −12 °C30. In projections of ESMs, the NESAL are one of the most stable permafrost regions, with near-surface permafrost largely remaining thermally stable beyond 2100, even under the strong RCP8.5 warming scenario34. However, these models do not take into account thermokarst-inducing processes and associated feedbacks, which can be expected to occur in the NESAL due to the abundance of massive ground ice in form of ice wedges23, making the model projections highly questionable.Permafrost in the northeast Siberian Arctic lowlands  that are underlain by massive ice wedges in the subsurface, as wedge ice constitutes the dominant type of excess ground ice in the NESAL38  to widespread landscape collapse (RCP8.5). We find that lateral sediment transport moderates thaw after initial ice-wedge degradation, leading to stabilised landscapes by 2100 under RCP4.5. For RCP8.5, we find that substantial amounts of the NESAL’s organic carbon stocks might be affected by thaw within the present century, despite the projected stability of the region in previous ESM projections. This study emphasises the necessity of representing thermokarst-inducing processes in ESMs and provides significant progress towards achieving this goal. More broadly, our results underline the importance of mitigating climate change if we are to limit its impacts on permafrost ecosystems.Recent developments constitute significant progress towards the process-based simulation of subgrid-scale heterogeneity and ground subsidence37 to represent the spatial heterogeneity in surface and subsurface characteristics of ice-wedge terrain, which is typically characterised by polygonal patterned ground  remained stable throughout the simulation period, with the exception of water-logged YD where shallow surface water bodies formed. We thus restrict the following analysis of the landscape evolution to the warming scenarios RCP4.5 and RCP8.5. The simulations for LB and HD were initialised with undegraded LCPs, featuring water-covered centres and elevated rims overlaying intact ice wedges Fig. . Within 7  and their lateral interactions , the simulations under contrasting hydrological conditions are reflective of a broad range of permafrost thaw dynamics at the microscale.The correspondence between simulated and observed degradation pathways, together with the comprehensive site-level comparison between simulated and observed permafrost characteristics conducted in a preceding workNext, we assess the degradation of permafrost that is associated with the dynamic evolution of the different types of ice-wedge terrain. Figure First, substantial permafrost degradation was projected under the RCP4.5 and RCP8.5 warming scenarios, which is reflected in both increasing thaw depth relative to the soil surface, and ground subsidence resulting from excess ice melt. Simulated maximum thaw depths increased significantly within the twenty-first century Fig. , with re12, can be expected to occur as a widespread phenomenon across the cold permafrost of the NESAL within the twenty-first century, if warming exceeds RCP2.6 projections. Similar degradation of very cold, ice-rich permafrost has recently been reported for the High Canadian Arctic41. Both simulations and observations highlight the particular vulnerability of ice-rich permafrost landscapes to climate warming, which is despite very low permafrost temperatures at present30. It should be stressed that permafrost models without representation of excess ground ice can only simulate the gradual increase in thaw depth, but not the additional degradation through ground subsidence and associated feedbacks.The degradation of ice wedges, which has so far only been observed locally within the study areaSecond, after initial degradation, stabilisation of permafrost was projected towards the end of the twenty-first century under the moderate RCP4.5 warming scenario, but permafrost continued to degrade beyond 2100 under the strong RCP8.5 warming scenario. This qualitative difference between these two warming scenarios was found for all landscape types and hydrological conditions, except for water-logged Yedoma deposits. Under RCP4.5, the maximum thaw depths did not increase significantly during the final one to two decades of the simulations Fig. , g, h, w39  and the accumulation of sediment from melted excess ice layers promote the stabilisation of the landscapeThird, the abundance of excess ground ice exerts a strong control on the rate and magnitude of permafrost thaw. For instance, under well-drained conditions and RCP8.5 Fig. , the dif9 and numerical models that represent thermokarst-inducing processes in ice-rich terrain. Models lacking these processes likely underestimate permafrost thaw systematically. This is supported by the results of the reference runs with a simplistic representation of permafrost thaw dynamics , ground ice content has less influence on the magnitude and pace of permafrost degradation than in landscapes with high ice abundance , where positive feedback mechanisms produce more rapid thawing, resulting in severe permafrost degradation and landscape collapse. Hence, robust projections of permafrost thaw require knowledge of present-day ground ice distributionFourth, the hydrological regime of thawed ground tipped as a consequence of ice-wedge degradation to a dominance of either saturated or unsaturated conditions, depending on the specified hydrological conditions. At the beginning of the simulations, the fractions of saturated and unsaturated conditions in the thawed ground were of comparable magnitude, irrespective of whether the system is water-logged or well-drained. This was particularly the case for landscapes with undegraded ice-wedge polygons, i.e., pronounced LCP microtopography (LB and HD). Note that the presence of saturated ground conditions in the well-drained settings is possible, for instance, due to wet conditions after snowmelt and precipitation events, or due to higher water levels in the depressed polygon centres, which are hydrologically isolated from the well-drained troughs. The subsidence of ground above melting ice wedges changes lateral water fluxes, mainly due to subsiding polygon rims no longer acting as barriers between polygon centres and inter-polygonal troughs. Under water-logged conditions, thaw subsidence led to inundation of the entire model domain, reflected in vanishing fractions of unsaturated conditions as soon as excess ice melt occurred Fig. . Under w12, making the hydrological regime more sensitive to the surrounding conditions37. The water-logged cases correspond to situations where ice-wedge degradation leads to the development of deep water-filled troughs, and potentially the formation of thermokarst ponds and lakes. As soon as inter-polygonal troughs connect to an external drainage point, this can cause drainage of the entire landscape12, leaving unsaturated high-centred polygons, drained troughs or conical thermokarst mounds  with the estimated total areas of each landscape type  within the NESAL  were contained in the active layers of the simulated landscapes, and thus potentially accessible for microbial decomposition. Deepening of the active layers in combination with melting of excess ground ice caused thawing of additional carbon that was initially stored in perennially frozen soil layers. During the first half of the twenty-first century, the amounts of thawed organic carbon were projected to increase steadily, and the differences between the runs with excess ice and the reference simulations were small. By 2050, an additional 1.7 GtC (RCP2.6), 1.8 GtC (RCP4.5) and 2.5 GtC (RCP8.5), respectively, became subject to thawed conditions according to the reference runs. These numbers are within the respective ranges projected by the simulations with excess ice, reflecting that the increase was mainly attributable to active-layer deepening. However, during the second half of the twenty-first century excess ice melt set in under the RCP4.5 and RCP8.5 scenarios, leading to ground subsidence and an acceleration of permafrost thaw due to positive feedbacks Fig. . Thereby47), but do not take into account thermokarst-inducing processes and deep carbon stocks which would become accessible through these processes. This is particularly problematic for cold permafrost regions like the NESAL where—even under RCP8.5—projected gradual thaw is limited (only ~5.3% of the NESAL’s carbon pools become subject to thaw in our reference runs), but thermokarst-inducing process could cause thawing of 2–12 times  of the amount projected for gradual thaw only. ESMs might thus substantially underestimate the amounts of carbon becoming accessible for microbial decomposition under a warming climate, particularly in cold and seemingly stable permafrost regions like the NESAL.These results suggest that in regions like the NESAL which host cold, ice- and organic-rich permafrost deposits, substantially larger amounts of permafrost organic matter could thaw and expose carbon to mineralisation than what is projected by models like ESMs that employ a simplistic representation of permafrost thaw dynamics. Such global-scale models project significant amounts of thaw-affected permafrost carbon for the end of the twenty-first century , where the same feedbacks cause rapid and deep thaw .In conclusion, the process-based simulations presented in this study provide evidence for a substantial potential for unlocking of vast amounts of currently frozen organic carbon pools in cold ice-rich lowlands, through thermokarst-related permafrost thaw in response to a warming climate. Thermokarst-inducing processes merit representation in ESMs as they could significantly contribute to the global permafrost carbon–climate feedback13 that represents the surface topography of ice-wedge terrain using three tiles37: polygon centres, polygon rims and inter-polygonal troughs. Each tile has a one-dimensional vertical representation of the subsurface, for which the thermal and hydrological dynamics were simulated by solving the heat-conduction equation with phase change, combined with a hydrology scheme for unfrozen ground56. The snow scheme simulated the dynamic build-up and ablation of the snow pack as well as infiltration and refreezing of rain and meltwater. The model takes into account lateral fluxes of heat, water and snow between the tiles, assuming a circular symmetry for individual ice-wedge polygons  was varied between different model runs in order to prescribe different hydrological conditions.We used a version of the CryoGrid 3 land surface model10, which was implemented into CryoGrid35 to simulate the subsidence of the soil surface resulting from melting of excess ground ice. Soil layers with ice contents above the natural porosity were considered to contain excess ice. Excess water is moved upwards upon thawing of soil layers containing excess ice, while mineral and organic sediment is routed downwards. This scheme reflects the main process causing the degradation of ice-wedge polygons37. Second, we used the non-linear hillslope diffusion scheme by Roering et al.57, which has been adapted for periglacial environments in previous studies59. This scheme describes the lateral erosion of mineral and organic sediment, which is an important process promoting the stabilisation of ice-wedge polygons39.The geomorphological evolution of ice-wedge terrain was represented in our model by the combination of two process. First, we used the excess ground ice scheme introduced by Lee et al.-1] between two adjacent tiles i and j. We neglected diffusive contributions to qsed, and restricted the lateral sediment transport to advective fluxes, which occur after rapid ground subsidence that gives rise to steep terrain gradients. Advective fluxes were calculated as follows , contact lengths (Lij) and areas (Ai). Keff [m2 s−1] is a transport coefficient composed of a subaerial (Kland) and a subaquaeous (Kwater) part, depending on the surface conditions of both tiles . Undegraded YD, which are underlain by relict ice-wedge polygons, do not show a pronounced surface microtopography, so we assumed a flat surface .The three different landscape types  to 0.4 m (YD) thickness was placed above the ice wedges of all types. Organic, mineral and ice contents of LB, HD and YD were based on a total of 984 soil samples from different sites of all landscape types within the NESAL . For the RCP2.6 scenario, we took anomalies from CCSM4 projections and applied them repeatedly to the period from 2000 until 2014 of the RCP4.5 forcing data. Due to the central location of the Lena River delta within the NESAL, we assumed the current climate characteristics and future climate trends throughout the NESAL to be comparable with those expected for the Lena River delta. Differences in current climate characteristics within the NESAL were assumed to be negligible compared with the differences expected from the climate warming scenarios.We used meteorological forcing data for the central Lena River delta; these data have been used in previous studies using CryoGrid 3eres), which was connected to the trough tile  or eres = −0.2 m (YD) to reflect water-logged, and eres = −10.0 m to reflect well-drained hydrological conditions. The initial temperature profiles of all 12 simulations were based on the borehole data, and a subsequent 50-year spin-up period using historical forcing data (10/1949-12/1999). The analysed period of the simulations was from 01/2000 until 12/2099.For each landscape type , we conducted simulations under three climatic forcing scenarios  and two contrasting hydrological conditions . The two contrasting hydrological conditions were prescribed through fixed elevations of the external water reservoir  with a setting of CryoGrid 3, which is comparable with the design of ESM land surface schemes. These runs were conducted using a one-dimensional subsurface representation without excess ice  agreed well with observations. The correspondence between simulated and observed degradation pathways and landforms provides further evidence for the validity of our modelling approach , the sediment transport coefficients , the field capacity (θfc) and the natural porosity of ice-rich soil layers (ϕnat). Results of the sensitivity analysis are provided in Supplementary Fig. In order to ensure the robustness of our results and to identify critical processes, we conducted a sensitivity analysis in which single-model parameters deviated from their default values. The parameters were related to different processes, and included the fresh snow density  and the altitude of the external water reservoir (ares = aC + eres), we distinguished five different states of the surface microtopography  throughout each year that contain a non-zero fraction of air; the remaining fraction of thawed cells is saturated. Note that this definition takes into account changing thaw depths and changing water table levels throughout the year.2; Fig. 61, drained lake basins  were assumed to comprise 69% of the mapped Yedoma region62 (excluding existing lakes), while the remaining 31% of were considered as undisturbed Yedoma deposits  from the area estimates for all landscape types. In total, the NESAL cover about 493,000 km2 (34%) of the overall study region. Note that the NESAL region mapped according to the criteria above largely falls into regions with high or very high thermokarst landscape coverage of types Lake and Hillslope mapped in an expert assessment18.Our overall region of interest is the northeast Siberian Arctic, defined as all landmass north of 66°N within the political borders of Yakutia (~1,462,000 kmThe organic carbon contents assumed for the ground stratigraphies of the different landscape types in the simulations were based on a large number of soil samples from several study sites within the NESAL Table . The groSupplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Movie 1Supplementary Movie 2Supplementary Movie 3Supplementary Movie 4Supplementary Movie 5Supplementary Movie 6Supplementary Movie 7Supplementary Movie 8Supplementary Movie 9Supplementary Movie 10Supplementary Movie 11Supplementary Movie 12


We study the transport properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the bands leading to a linear form of selftrapping. In the strong nonlinearity regime, the dynamics of the excitations depends strongly on the local environment around the initial excitation site that leads to a highly fluctuating selfrapping profile. For a binary nonlinear disorder, it is shown that the spreading of the flat band fundamental mode, is completely inhibited for a finite fraction of all cases. This fraction corresponds to the fraction of times the same value of (random) nonlinearity is assigned to all sites of the fundamental mode. In the semiclassical approach to the problem, the vibrational coordinates are treated classically while the electron is treated quantum mechanically. Further, if the vibrational degrees of freedom are assumed to be enslaved to the electronic ones, one arrives to an effective electronic equation known as the Nonlinear Discrete Schrödinger (DNLS) equation5 (see below). Other instance where selftrapping can appear is in solid-state physics where excitonic trapping barrier and lattice defect production can occur in crystals11.The phenomenon of selftrapping of excitations in nonlinear lattices has been an active research field for many years, from the time it was realized that some solutions of the coupled electron-phonon problem in biomolecules, featured stable, propagating localized excitations, termed discrete solitons. At the time, it provided a possible way to understand the propagation of excitations along some molecules13 and Bose-Einstein condensates in coupled magneto-optical traps15. One of the striking features of the DNLS equation (see below) is that it leads to discrete solitons: the localization of the excitation in a small region of the lattice and capable of propagating for relatively long distances along a quasi onedimensional chain, with little dispersion. Along the years the DNLS has been examined for several lattices and various dimensionalities, and under a variety of conditions ranging from disorder in the on-site energies18, effect of nonlinear impurities24, nonlocal effects25, disorder of the nonlinear parameter26, and long-range effects27. Perhaps the most striking feature observed is the robustness of the discrete soliton, under many of these conditions. Its existence can be argued based on the local character of the DNLS  of the lattice . Later on, we will also excite the fundamental flat band mode of these lattices and examine its time evolution under nonlinear disorder.The Nonlinear Schrödinger (DNLS) equation is given by n − simplex. The last one is not a lattice, but an array of n equally-coupled sites in dimension D = n − 1 and is almost completely degenerate, as we will show below. For D = 0 we have a single site (n = 1), for D = 1 we have a dimer (n = 2), for D = 2 we have an equilateral triangle (n = 3), for D = 3 we have a regular tetrahedron (n = 4), and so on. For each lattice we have also indicated the form of its fundamental flat band mode. For instance, for the Lieb lattice, this mode is a kind of ring A, − A, A, − A which is characterized for having no transversal time evolution due to complete phase cancellation42.This is also true for the stub and diamond lattices. We will see that, when the initial site for the dynamical evolution of an observable overlaps partially with the flat band mode, it gives rise to partial trapping at small nonlinearity.Figure R = N, while for a completely localized state, R = 1, where N is the number of sites.In order to ascertain the trapping of the excitation, we define the time-average probability at the initial site as P0⟩ in the absence of random nonlinearity, χn = χ. Results are shown in Fig. 44. As shown on Fig. χ → 0, the selftrapping curves approach either a value O(1/N), or a finite value. Both type of curves differ on the initial excitation site inside the lattice. For instance, in the case of the Lieb lattice, when the initially excited site fall on a site with coordination number equal to two , the amplitude of finding the excitation at the initial site, can be expanded in terms of the eigenstates of the simplex. We obtain, N≥2 it increases monotonically with N, approaching 1 at N → ∞. Thus, the reason for this linear trapping resides on the large amount of degeneracy. Something similar occurs in a periodic lattice with a flat band, where all the states inside the flat band are degenerate.For the simplex, closed form results have been obtained previously for a general caseχn. We take now χn from a binary distribution χn = χ or 0, with 50–50% probability, and χ = V, 2V, 3V, 4V, 5V, 6V. Instead of computing the realization-average of (time-averaged) ⟨Po⟩ as would be the usual procedure, we decided to do a scatter plot of ⟨P0⟩ for each nonlinear disorder realization and combine all of them. Results are shown in Fig. Now we examine the effect of randomness in the nonlinear parameter χ and that the nearby sites also have nonlinearity χ. If χ is large, there will be a tendency to create a selftrapped mode with localization length ξ. Since most of the excitation is contained inside a region of length ξ, the value of nonlinearity outside ξ is of no importance. In other words, a cluster of nonlinear sites can support a nonlinear localized mode, where the nonlinearity of the rest of the sites away from the trapped mode becomes unimportant. The result for this case is that we will have a selftrapping transition around 4V ref. 43. The second important case is when the initial site has nonlinearity χ but it is surrounded by a cluster of purely linear sites (χ = 0). In this case we are really talking about a nonlinear impurity, whose selftrapping transition happens around 3V ref. 40, depending on the position of the initial site and the geometry of the lattice. A third important case is when the initial site and its close vicinity have sites with zero nonlinearity. Here, the excitation will tend to decay quickly and propagate away. Since the amplitude of this wave becomes smaller and smaller as it propagates, nonlinear effects (χ∣Cn∣2) will become less and less important, and the excitation will ultimately escape in a ballistic manner. Here, ⟨P0⟩ will be very small, O(1/N). Since the conditions at and near the initial site are random, the system will jump from one behavior to the other, from realization to realization. The main behaviors are clear, however, and would have been missed if we have employed a usual average of ⟨P0⟩. The behavior that is not so random occurs at small nonlinearity values. There, the important thing is whether the initial site has or not overlap with the fundamental flat band mode of the lattice. If there is no overlap ⟨P0⟩ will be O(1/N), while when there is overlap, ⟨P0⟩ will be finite, as explained in section III.The explanation for this behavior lies on the observation that, the nonlinearity at the initial site as well as the local environment around this initial site is random. First, let us assume that the nonlinearity at the initial site is 42. It was found that the presence of nonlinear disorder was only relevant at the beginning of the time evolution. At later times, the mean square displacement quickly converges to a ballistic profile σ(t)2 ~ t2. This was explained as the weakening of nonlinearity as the height of the wave front decreases as it spreads on the lattice. Based on normalization grounds, the amplitude of the propagating wave behaves as O(1/N) rendering the nonlinear term χ∣Cn∣2 unimportant at asymptotically long times.Having explained the main features of dynamical selftrapping in the presence of nonlinear disorder, we examine now how this disorder affects the transport of localized excitations and the dynamical evolution of the fundamental flat band modes of several lattices. The case of a one dimensional lattice with nonlinear disorder was treated in ref. It is interesting to see if similar behavior also holds for higher dimensional lattices which also possess flat bands. Figure σ2(t) to the value for the one dimensional ballistic case, 2(Vt)2. We see that after a short interval, all curves converge quickly to the ballistic case, ⟨σ2⟩ ~ t2, as in the purely one dimensional case. In case (a) however, the ‘speed’ σ/Vt is lower than in case (b). This is probably due to the fact than in the first case, the initial site has overlap with the fundamental ring mode, giving rise to partial linear trapping. This renormalizes the amount of the wave that can propagate to infinity, giving rise to a lower speed. Another contribution to the decrease of the speed comes from nonlinearity, as seen already in one dimensional chains26.We consider two cases: One, where the initial site is also part of the fundamental flat band mode , and the other where is not . We have also normalized R(t) of the fundamental flat band modes in the presence of random nonlinearity. The shape of these modes depend on the particular geometry of the lattice, but they are characterized by a distribution of amplitudes and phases designed to effect an exact phase cancellation that impedes the propagation of the wave beyond a small region, typically consisting on a few sites. Some examples are shown in Fig. Finally, we compute the time evolution of the participation ratio R(t) vs time for the diamond lattice, for different nonlinearity disorder  (results for the other two lattices are similar). We immediately notice that the scatter plots reveals two regimes: A spreading one where R(t) increases monotonically with time, and a completely localized regime, where the initial size of the fundamental modes does not change in time, no matter the strength of random nonlinearity. Close scrutiny at the numerics reveals that R(t) remains constant whenever the nonlinear parameter is the same for both initial sites. Since this happens in half of the cases, there is a 50% probability for R(t) to remain at its initial value. This happens for all values of  examined. In addition, we notice a rich behavior for R(t) at high χ, where the slope of R(t) is smaller than in the case of low χ and strong oscillations appear. We found that the explanation of this phenomenon lies in the value of χ and the existence of some internal selftrapping dynamics: For the diamond lattice, the system of interest consists on two sites that are excited with the same amplitude but opposite phases, and each one is assigned a value of random nonlinearity χ1, χ2 ∈ {0, χ}. When χ1 = χ2, that is,  or , R(t) will remain at its initial value R = 2. To get to a propagation regime, we need different nonlinear coefficients. Let us assume, without loss of generality, that χ2 = 0. Now, let us consider the case where χ1 = χ > χc, the critical nonlinearity needed to trap an excitation inside a given nonlinear site and its immediate surroundings. After the (double) excitation, the amplitude deposited at site with χ2 = 0 propagates away from the initial vicinity, while the site with χ1 = χ or some of its adjacent sites will trap a portion of the initial amplitude. The end result is a finite fraction of the initial excitation trapped inside the immediate vicinity of the initial site. The rest of the excitation propagates away from this region and, after a short while, this propagation is almost indistinguishable from propagation in a nonlinear-free medium. This is due to the fact that the excitation fraction on each site decreases in time , making the value of the nonlinear parameter irrelevant for propagation purposes at long times. Now, the trapping of a substantial fraction at the vicinity of the initial site, causes R(t) to grow more slowly as compared to the case without nonlinearity, since the number of effectively excited sites is located inside a relatively small region. The higher the value of the nonlinearity, the larger the trapping effect and thus, the slower and slower the increase of R(t). The trapped fraction can be roughly defined as ∣A(t)∣2 = ∑nn∣Cn(t)∣2, where the sum is over the nearest neighbors of the initial nonlinear site. Now, observation of the dynamical evolution of this trapped fraction ∣A(t)∣2 reveals that, due to its internal dynamics, the trapped fraction oscillates in time, with a substantial change in amplitude. This causes R(t) to oscillate as well, since when the amplitude increases, R(t) decreases due to a concentration of the trapped portion in a smaller region, while the opposite happens when the amplitude decreases. In Fig. A(t)∣2 and the oscillations in R(t), that illustrates this point. It is the combination of selftrapping at the initial site and the oscillatory dynamics of the trapped fraction, that lead to the rich dynamical behavior shown in Fig. R(t). The persistence of R(t) when both nonlinear parameters are the same, can be easily explained from the basic equations  remains constant, regardless of nonlinearity on sites outside the fundamental mode. These fractions are 1/4, 1/8 and 1/2, for the stub, lieb and diamond lattices, respectively and correspond to the fraction of times the same value of (random) nonlinearity is assigned to all sites of the fundamental mode.Figure χ], and proceeded to compute ⟨P0⟩ and R(t) for all lattices. The stub lattice case is shown in Fig. χ value, the trapped portion is now spread over a finite range, instead of taking (roughly) two values as before , we see in Fig. R(t) = 2 has disappeared. This is due to the fact that it is very unlikely that the two initial sites are assigned the same random value of χ. At short times, Fig. χ1 and χ2 were similar, leading to an initial propagation R(t) ~ 2, but for short times only.Now, one might wonder how much of the previous results will still hold in the presence of a different kind of nonlinearity distribution. To see that, we assigned the value of the nonlinear parameter at each site according to a uniform distribution [0, ore Fig. . This is42, make these flat band lattices and their accompanying flat band modes promising candidates for optical applications, as in long-distance diffraction-free transmission of information.In this work we have examined the selftrapping and transport properties of localized excitations on various nonlinearly-disordered lattices characterized for having a spectra with flat bands in the linear limit. We found that the presence of high degeneracy due to the presence of flat bands has a strong impact on trapping and transport in this system. The presence of disorder in the nonlinearity causes a fluctuating environment at the initial site, making the system jump between the selftrapped state and the free state. At small nonlinearity, flat bands effects cause linear selftrapping provided the initial site belongs to one of the fundamental flat band modes. The mean square displacement showed a ballistic character at long times, with the nonlinear disorder playing a minor role only. The evolution of the participation ratio of a fundamental flat band mode, in the presence of this nonlinear disorder, showed a strong dependence on the values of nonlinearity on the flat band sites: When their nonlinearity values are different, the participation ratio expand monotonically with time. However, when the flat band sites share the same value of the nonlinearity parameter, the participation ratio remains constant, no matter the values of nonlinearity outside the flat band sites. For the lattices considered in this work, the most stable one against random binary nonlinear disorder is the diamond lattice. The robustness of the flat band mode (in a finite fraction of cases) against finite nonlinear disorder, combined with stability against other perturbations