To assess the efficacy of conservative management and embolisation in patients with spontaneous retroperitoneal haemorrhage.Single-centre retrospective case–control study of patients with spontaneous retroperitoneal haemorrhage treated conservatively or with embolisation. Patients aged ≥ 18 years were identified from CT imaging reports stating a diagnosis of retroperitoneal haemorrhage or similar and images reviewed for confirmation. Exclusion criteria included recent trauma, surgery, retroperitoneal vascular line insertion, or other non-spontaneous aetiology.Datapoints analysed included treatment approach (conservative or embolisation), technical success, clinical success, and mortality outcome.p < 0.01), and all-cause  and uncontrolled primary bleeding  mortality were higher with embolisation. However, embolised patients more commonly had active bleeding on CT , shock , and higher blood transfusion volumes . After one-to-one propensity score matching, differences in clinical success (p = 0.04) and all-cause mortality (p = 0.01) remained; however, difference in uncontrolled primary bleeding mortality did not (p = 0.07).A total of 54 patients met inclusion criteria, who were predominantly anticoagulated (74%), male (72%), older adults (mean age 69 years), with active haemorrhage on CT (52%). Overall mortality was 15%. Clinical success was more likely with conservative management (36/38) than embolisation (9/16; Conservative management of SRH is likely to be effective in most patients, even in those who are anticoagulated and haemodynamically unstable, with variable success seen after embolisation in a more unstable patient group, supporting the notion that resuscitation and optimisation of coagulation are the most vital components of treatment. The online version contains supplementary material available at 10.1007/s00270-023-03359-4. Spontaneous retroperitoneal haemorrhage (SRH) is defined as retroperitoneal bleeding that occurs in the absence of an incident cause such as trauma, surgery, or vascular line insertion –4. ThougConservative  measures including fluid resuscitation, blood transfusion, and cessation or reversal of anticoagulation are the mainstay of management and are highly successful in haemodynamically stable patients with SRH, as demonstrated by previous retrospective comparative studies between conservative and embolisation management approaches , 5–7; hoThe aim of this study was to compare the success rates of conversative management and embolisation in the treatment of SRH, including in those with haemodynamic instability.Approval for this single-centre retrospective case–control study was granted by our institutional review board (number 379/22). No funding was provided for this study.Age ≥ 18 yearsCT report text containing the term(s): ‘retroperitoneal haemorrhage’, ‘retroperitoneal haematoma’, ‘retroperitoneal bleed’, ‘retroperitoneal bleeding’, ‘psoas haemorrhage’, ‘psoas haematoma’, ‘psoas bleeding’, ‘iliopsoas haemorrhage’, ‘iliopsoas haematoma’, and/or ‘iliopsoas bleeding’CT images were reviewed to confirm the diagnosis of retroperitoneal haemorrhageCT images were reviewed to document the presence of active bleeding (blush of contrast) as a datapoint, including both cases with and without active bleeding at the time of CTThe study covered a 10-year period from 1 January 2012 to 1 January 2022. The Radiology Information System (RIS) was searched by the four members of the research team  to identify cases applying the following inclusion criteria:Documented recent history (< 4 weeks) of trauma, surgery, retroperitoneal vascular line insertion, and/or coronary angiographyEvidence or signs of recent trauma, surgery, retroperitoneal vascular line insertion, and/or coronary angiography on CT and/or other imagingPresence of any other clearly non-spontaneous aetiologyThe electronic medical records were reviewed in conjunction with the imaging data, and the following exclusion criteria applied:From the electronic medical records, the following datapoints were extracted and recorded based on values at time of presentation with SRH: age, sex, blood pressure, heart rate, haemoglobin (Hb) level, platelet level, INR, medications , COVID-19 status (2020 onwards), blood transfusion volume (within first 24 h), primary treatment method (conservative or embolisation), technical and clinical success rates, and outcome . Primary treatment method referred to the treatment approach implemented within the first 24 h; specifically, conservative management implies that fluid resuscitation, blood transfusion, and cessation or reversal of anticoagulation were implemented, without embolisation or surgery within the first 24 h  under direct supervision , with experience ranging from 1 to 18 years. Procedural technique typically involved arterial access via the right common femoral artery, insertion of a 5- or 6-Fr vascular sheath, aortic digital subtraction angiography via a pigtail catheter, then selective angiography via a 4- or 5-Fr diagnostic catheter and a 2.7-Fr microcatheter to achieve more distal access. The embolic agents deployed were gelatin sponge, coils, and NBCA glue, selected at the discretion of the operator.n = 39) male and of mean age 69 years (standard deviation (SD) 12 years). Seventy per cent (n = 38) of patients were taking anticoagulant medication, most commonly warfarin . Fifty-six per cent (n = 30) were taking antihypertensives, with 35% (n = 19) taking two or more agents. Two patients had COVID-19 at the time of SRH. Twenty per cent (n = 11) had acute shock , 37% (n = 20) had haemoglobin level < 8 g/dL, and 30% (n = 16) had INR ≥ 2, and 27% (n = 15) had significant renal impairment (eGFR < 30 mL/min/1.73 m2). CT showed active haemorrhage (as defined by blush of contrast) in 52% (n = 28) of cases. Twenty-six patients (48%) received more than 3 units of PRBCs during the first 24 h of treatment, with 4 (7.4%) receiving 10 or more units.A total of 190 patients were identified by the initial RIS search; after exclusion, a final cohort of 54 patients met inclusion criteria as shown in Fig. Of the 38 patients in whom primary management was conservative, clinical success was seen in 36 (94.7%) Table . One patPatients treated with embolisation were significantly more likely to have had active bleeding on CT and acute shock (shock index > 1) and received a significantly higher volume of blood transfusion in the first 24 h of care Table .Table 2Gp = 0.04) and received a significantly higher number of red blood cell transfusion units (p < 0.01) , with the most likely cause in 6 the uncontrolled primary bleeding , delayed rebleeding in 1, and sepsis in 1. Of the deceased patients, all but 1 had likely contributing medical comorbidities including coronary artery disease, congestive cardiac failure, bleeding diatheses, and sepsis. Comparing fatal and non-fatal cases, fatal cases were more likely to have presented with a shock index > 1 , INR ≥ 2.0 30%) significant renal impairment , and two or more antihypertensive medications at the time of SRH 35%), reflecting the typically elderly and medically comorbid cohort –5. Of re%, reflec0% signifThere are limitations of this study to acknowledge. Firstly, the sample size is relatively small for the period of time assessed, but similar to other published series given the low incidence of SRH , 11, 12.This study showed that conservative management of SRH may be effective in most patients, even in those who are haemodynamically unstable but therapeutic anticoagulated. It supports the notion that resuscitation and optimisation of coagulation are the most vital components of treatment in SRH. Embolisation had varying success in our cohort, with significantly higher mortality; however, this was likely because patients who underwent embolisation were more commonly those with acute shock, high transfusion volumes, and active haemorrhage on CT. As shown in other studies, mortality in SRH is high, and goals of treatment should include addressing the coagulopathy and not just arrest of haemorrhage.Supplementary file1 (DOC 99 kb)Below is the link to the electronic supplementary material.


Randomness, however, imposes severe challenges fornanophotonics modeling, often constrained by the irregular geometryof the scatterers involved or the stochastic nature of the problemitself. In this Article, we resolve this conundrum by presenting auniversal theory of averaged light scattering of randomly orientedobjects. Specifically, we derive expansion-basis-independent formulasof the orientation-and-polarization-averaged absorption cross section,scattering cross section, and asymmetry parameter, for single or acollection of objects of arbitrary shape. These three parameters canbe directly integrated into traditional unpolarized radiative energytransfer modeling, enabling a practical tool to predict multiple scatteringand light transport in disordered nanostructured materials. Notably,the formulas of average light scattering can be derived under theprinciples of fluctuational electrodynamics, allowing the analogousmathematical treatment to the methods used in thermal radiation, nonequilibriumelectromagnetic forces, and other associated phenomena. The proposedmodeling framework is validated against optical measurements of polymercomposite films with metal-oxide microcrystals. Our work may contributeto a better understanding of light–matter interactions in disorderedsystems, such as plasmonics for sensing and photothermal therapy,photocatalysts for water splitting and CO Conventionalmodeling based on computational electromagnetics, such as the FiniteDifference or Finite Elements methods, are often unsuitable to quantifythe macroscopic optical properties of random media, namely, theirspecular and total transmittance/reflectance or the intensity distribution,all critical to assess the performance of these systems. Stochasticmethods appear as the most appropriate alternative to calculate theseproperties, yet, with few exceptions, their applicability is limitedto composite media containing subwavelength structures (effectivemedia approximations)6 or spherical particles(radiative transfer simulations).7 As aresult of the limitations in modeling, the majority of designs indisordered nanophotonic materials are driven by a phenomenologicalapproach, whereby multiple samples are fabricated and tested in aniterative process that is time-consuming and expensive.Predictingthe complex opticalphenomena manifesting in disordered nanomaterials represents a majorchallenge in the field of computational modeling. Plasmonic nanoparticledispersions for sensing and photothermal therapy,9 which describes thepropagation of the light specific intensity through a composite mediumcontaining a random distribution of independently scattering particles.It is notable that, in principle, the theory is applicable to arbitraryparticle geometries and groups of particles.9 In practice, however, radiative transfer modeling is most commonlyapplied to study light transport in composites with spherical particles.10 This is due to the scattering properties of the spherical particlesbeing independent of the direction and polarization of the incidentlight.11 In this particular scenario, thesolution of the radiative transfer equation (RTE) for unpolarizedlight requires three parameters: the particle’s absorptioncross section, Cabs, the scattering crosssection, Csca, and the asymmetry parameter,μsca.12 The latter is an indicator ofthe scattering anisotropy and a key element to calculate the angulardistribution of scattered fields.12Lighttransport in random media is commonly addressed through theradiative transfer theory,9 Under the independentscattering approximation, however, the correlation of the scatteredfield from different particles vanishes,9 and the scattering properties of an ensemble of randomly orientedparticles can be approximated by the orientation averaged from a singleparticle  are prevalent  or discrete dipoles in the DDA.21 For average scattering calculations, nonetheless,the expanded fields have to be transformed into spherical waves, andthe efficiency of the method is appreciably reduced.21The computation of orientationand polarization average scattering for arbitrary nanoparticlesis, however, nontrivial. Standard brute-force methods based on averagingover many plane-wave simulations at different angles of incidenceand polarizations can be computationally expensive.Cabs, Csca, and μsca for arbitrary-shaped scatterers. The formulas are independentof the wave basis and, therefore, can be implemented by integral-equationmethods for electromagnetic scattering, such as T-Matrix Method,9 BEM,20 or DDA.21 Based on these results, we evaluate the accuracylimits of other expressions for average light scattering commonlyused in the literature.23 (ii) In the next section,we demonstrate that the formulas of average light scattering can bederived through the principles of fluctuational electrodynamics and,hence, can be computed through the mathematical methods used in studiesof near-field thermal radiation,27 Casimir forces,27 and vacuum friction.29 In this context, wedevelop a computational application to numerically compute averagedlight scattering,30 which is based on thefluctuating-surface-current BEM.32 (iii) In thefollowing section, we validate the theory and simulation code foraverage scattering simulations against other analytical solutions.33 (iv) In the forth section, we analyze the advantagesof the theory of average light scattering against brute-force averagingbased on plane-wave simulations at different angles of incidence.(v) Next, we discuss how the three average light scattering parameterscan be applied for modeling of radiative transfer in disordered nanostructures.(vi) The accuracy of the modeling framework is demonstrated in thefinal section, showing excellent agreement with optical measurementsof polyethylene (PE) film composites with monoclinic vanadium dioxide[VO2(M)] microcrystals.In this Article, we present a universal theory ofaverage lightscattering from randomly oriented scatterers (single or collectionsof objects) of arbitrary shape and demonstrate a practical methodologyfor radiative transfer simulations in disordered nanostructures. Theresults section of the paperis organized into six sections: (i) Inthe first section, we derive the formulas for polarization-and-orientation-averaged 14 We particularlyfocus on the average absorption cross section, ⟨Cabs⟩, scattering cross section, ⟨Csca⟩, and asymmetry parameter, ⟨μsca⟩, where P index runs overthe two orthogonal polarizations, and k̂i is the direction of the incident field. The asymmetry parameter,μsca, defines the degree of anisotropy of scatteringrelative to k̂i:11k̂s isthe direction of the scattered field and psca is the scattering phase function.14 Bydefinition of psca, sca > 0 (μsca < 0) represents cases of forward (backward) anisotropicscattering and μsca = 0 represents isotropic scattering.As discussedpreviously, light scattering from a collection ofindependent scatterers of arbitrary morphology and randomly orientedin space 1is equi27 In this approach, the scattered fields are givenby Ei is theincident field, Supporting Information, eqs S4 and S5, respectively).The mathematical form of flreg is the sphericalwaves regular at the origin, Tll is theMie scattering coefficient, and † is the conjugate transposeoperator.27 In integral-equation methodsfor electromagnetic scattering, such as the T-Matrix Method,9 BEM,20 or DDA,21 the form of Our derivations are based on the Lippmann–Schwinger approach,a general formalism for electromagnetic scattering phenomena.Cabs and Csca for an incidentplane waveof amplitude E0 are given by :34k0 is thewavevector in free space, ⊗ is the tensor product, and Supporting Information, eq S2), with In this context, the formulas of sca is, to the best of ourknowledge,presented here for the first time:j in k̂ji and in the partial derivative ∂j, represents the global coordinates of thesystem . The formula is derived from the Lorentz forceof the scattered fields over the induced currents in an object .The formula of μCabs⟩ and⟨Csca⟩ are uniquely determinedby ⟨Ei ⊗ E†i⟩, also known as the free spaceself-correlator.27 For Ei in the form of monocromatic plane waves, this term is givenby the following :Becausethe operators sca⟩requires the following:Similarly, ⟨μSupporting Information, we derive the respective formulasfor BEM and T-Matrix using these expressions .Using Supporting Information, section 1.4). The light scattering parametersfor an individual particle particle n in the cluster,that is, ⟨Cabsn⟩, ⟨Cscan⟩, and ⟨μscan⟩, arealso obtained directly from these relations .The relations, Cabs⟩ and ⟨Csca⟩ found in the literature:23Cjabs, and Cjsca,  are, respectively,the absorption and scattering cross sectionsfor a plane wave polarized in the j-direction. Asdemonstrated in the Supporting Information (section 1.6), the expression ⟨Cabs⟩ ≈ 1/3 corresponds to a particularcase of Csca⟩ holds only if the polarizability of the objectis a diagonal tensor.Wefinalize this section by discussing a common approximation for⟨Cabs⟩, ⟨Csca⟩,and ⟨μsca⟩ share many similaritieswith the relations foundin studies of fluctuational electrodynamics, namely, thermal radiationand nonequilibrium electromagnetic forces.31 For example, in the framework of fluctuational electrodynamics,the thermal radiation absorbed by an isolated object, Pabsth, is27T is the temperatureof the environment, ω is the angular frequency, kB is the Boltzmann constant, and ℏ is the reducedPlanck constant. On the other hand, from light scattering theory,11Pabsth = ∫0∞ dω4π⟨Cabs⟩Bω(T), where Csca⟩ by replacing The trace formulas for ⟨29 To a first order approximation, the frictioncoefficient γf, can be expressed in terms of ⟨Cabs⟩, ⟨Csca⟩, and ⟨μsca⟩ as follows:Cpr⟩ = ⟨Cext⟩ –⟨μscaCsca⟩and ⟨Cext⟩ = ⟨Cabs⟩ + ⟨Csca⟩ are the average radiation pressure and extinctioncross sections, respectively.11Another relationcomes from theelectromagnetic friction induced by a moving photon gas on a stationaryobject.28 and numerical algorithms35 developed in the contextof nonequilibrium energy and momentum transfer can be used to compute⟨Cabs⟩, ⟨Csca⟩, and ⟨μsca⟩. For example, the thermal DDA35 and fluctuating current BEM31 for thermalradiation simulations, have explicit relations for Φabs that can be adapted to compute ⟨Cabs⟩ and ⟨Csca⟩. Onthe other hand, the fluctuating current BEM also includes routinesto compute 32 which canbe adapted for ⟨μsca⟩.Asillustrated by 32 The code is implemented as an application of the SCUFF-EM software36 and can be acceded here.30 Similar to other simulation tools based on BEM,38 our code supports objects of arbitrary morphology and groups ofobjects , offering a convenient platform to explore the full potential ofthe average scattering theory presented here.In thiscontext, we developed a computational code for averagelight scattering simulations, based on the fluctuating surface-currentBEM formulation for nonequilibrium energy and momentum transfer.33 The dimer consists of two silver spheres ofdiameter, D = 200 nm, separated by a gap of (i) Δx = 2 nm and (ii) Δx = 200 nm. Thelight scattering parameters of a single sphere obtained from Mie ScatteringTheory11 are also plotted as a reference.To validate the average scattering theory and BEMsimulation code, we consider the problem of light scattering by arandomly oriented sphere dimer 2, which 33 , showing excellent agreement up to Lmax/λ ≳ 2.5, where Lmax is the longest ellipsoid axis. At shorter wavelengths,there is a discrepancy of ∼5% associated with the size of themesh used in BEM simulations. Even with this discrepancy, the resultsare consistent with the predictions from the analytical solution,allowing to validate the theory presented here.As a second test,we consider the problems of average scatteringfrom randomly oriented oblate and prolate spheroids, which has a knownsolution under the T-matrix approach.Csca⟩ by averaging over many plane-wave simulations at differentangles of incidence (brute-force averaging). In terms of the Lippmann–Schwingerapproach to scattering and using m indicates a plane-wavesimulation at a particular angle of incidence and polarization and M is the total number simulations.Consider,for example, the computation of ⟨Csca⟩ using brute-forceaveraging. From this formula, we can deduct the steps required byintegral-equation methods of electromagnetic scattering, that is:1.Emi using the particular basis.Compute the expansionof 2.M times.Repeat “step 1” 3.Determinethe mathematical form of 4.Emi, Replace Similar to otherformulas derived in this work, Emi. Consequently, the computationof ⟨Csca⟩ is reduced toonly two steps:1.Determine the mathematical form of 2.Replace Becausethis approach requires less steps than brute-forceaveraging, it could potentially enable more efficient computationof ⟨Csca⟩. The same argumentsapplies for ⟨Cabs⟩ and ⟨μsca⟩. Note, however, that the computational cost ofeach technique is relative to the particular algorithm implemented.Thus, specially for problems where M is small, brute-forceaveraging could be performed with higher computational speed and lessmemory requirements.Onthe other hand, as illustrated by 9Iλ is the specific radiative intensity (defined as the energy fluxper unit solid angle), fv is the volume fraction, Vp is the effective volume of the scatterers, k̂·∇rIλ is the rate of change of Iλ at the position r and direction k̂; and ⟨psca(cosθ)⟩ is the orientation and polarization averaged scatteringphase function, where cos θ = k̂·k̂′.For unpolarized light and under theindependent scattering approximation, the steady-state RTE for randomlyoriented scatterers in a nonabsorbing host issca.12 For example, the Henyey–Greenstein model,127 adding-doubling,41 and discrete ordinate.12Commonly, solutions of Cabs⟩, ⟨Csca⟩, and ⟨μsca⟩ constitute a complete set to model radiative transfer incomposites with scatterers of arbitrary morphology. As demonstratedin the next section, this modeling framework enables the quantitativeprediction of the macroscopic radiative properties of a composite,such as the total transmittance (Ttot),specular transmittance (Tspec), and totalreflectance (Rtot).As evidenced by 2(M) microcrystalsembedded in a polyethylene (PE) matrix (2(M) microcrystalsgiven its well-defined and highly anisotropic morphology  spectrum.11Wedemonstrate the accuracy of the previously discussed modelingframework by comparing the radiative transfer simulations againstoptical measurements of a composite based on VO) matrix 3a. We corphology 3b, provi2(M) microcrystals ensemble using a characteristic sample. Thesize distribution of the bars length (L) and width(W) is shown in Cabs⟩, ⟨Csca⟩, and ⟨μsca⟩ of single VO2(M) bars for λ = 3–8μm, considering the range of W and L dictated by the size distribution. The spectrum λ> 8 μm is excluded in the simulations due to the large uncertaintyin the refractive index of VO2(M), which is strongly conditionedby crystal orientation, growth method, strain, and partial oxidation.42 As shown in Cabs⟩, ⟨Csca⟩, and ⟨μsca⟩ are strongly sensitive to W. Onthe other hand, the three parameters are less sensitive to changesin L, with negligible variations for L > 15 μm . In addition to the VO2(M) bars, we noted smalltraces of VO2(M) flakes in the sample, such as the oneshown in 2(M) flakes are represented by the computationalmodel in First, we derived the average light scattering parameters of theVOCabs⟩,⟨Csca⟩, and ⟨μsca⟩ of the VO2(M) microcrystals ensemble. Using the parameters ⟨Cabs⟩, ⟨Csca⟩,and ⟨μsca⟩ of the VO2(M)microcrystals ensemble, together with Monte Carlo simulations of radiativetransfer /PE composite film(2(M) and thickness of the film. The optical measurements show excellentagreement with the range predicted by simulations, which is furtherconfirmed by comparing the spectral mean of Ttot, Tspec, and Rtot (table in 2(M) microcrystals .The parameters⟨ensemble4a, were ite film4b. The rtable in 4b. The aCabs⟩, ⟨Csca⟩, and ⟨μsca⟩ can be implemented by any integral-equation method for electromagneticscattering. Moreover, because these relations are exclusively definedin terms of the operators 34 the limits of forward or backward scatteringof randomly oriented particles can be explored through the asymmetryparameter formula /PE composite films. The radiativetransfer formula for randomly oriented particles  at the right-hand side of The parameters ⟨articles 8 can be 2(M)/PE compositefilms can be also applied to other composite media, with either dielectrics7 or metal scatterers,10 providing that the distance between particles is large enough toignore the effects of short-range correlations. For more complex problems,such as clustered particles or more dense particle distributions,44 the methodology can be extended using the formulationfor multiple objects . In this case, ⟨Cabs⟩, ⟨Csca⟩,and ⟨μsca⟩ must be obtained from simulationsover a properly chosen collection of particles that better representthe effects from short-range correlations. The method, thus, couldprovide key insights to many problems in disordered nanophotonics,such as the effects of agglomeration into the optical absorption ofgold nanostars or the impact of multiple scattering in the light trappingof heterostructured photocatalysts, as we will discuss in future works.The methodology used in the studyof VO2(M) microcrystals with low-density PE and ultrahigh-molecular-weight PE at a weight ratio of VO2(M)/LDPE/UHMWPE = 1:40:40. Themixture was then melt-pressed into a film at 200 °C. The VO2(M) crystals were produced by hydrothermal synthesis usingour previously developed procedure.45 Thephase of the crystals was confirmed by X-ray diffraction and Ramanspectroscopy . The volume fraction of the VO2(M) microcrystals was estimated from the weight ratio and the densitiesof VO2(M) (4.230 g/cm3),46 LDPE (0.925 g/cm3), and UHMWPE (0.940 g/cm3). A micrometer was used to characterize the thickness ofthe film. The reported thickness corresponds to five measurementson different sections of the sample.The composite was fabricated by dry mixing of VO2(M)/polyethylene compositefilm were measured with a Fourier transform infrared spectrometer and a mid-IR integrating sphere (Pike Technologies).The total and specular transmittanceand total reflectance of the VO30 SCUFF-EM36 is an open-source software for electromagneticsimulations based on the BEM. The meshing of the objects is basedon triangular panels and was carried by GMSH.47Simulations of orientation-and polarization-average light scattering were performed using theSCUFF-EM application AVESCATTER.photon) and fateof a photon are estimated by selecting the shortest path between theparticle’s scattering (Λsca) and absorption(Λabs), the absorption of the host (Λhost), or diffraction (ΛFresnel), whereFresnel is given by the shortest distance betweenthe photon and an interface. In materials with more than one kindof particle, Λabs = min(Λabsi) and Λsca = min(Λscan), where Λabsn and Λscan are, respectively, the absorption and scatteringpath from the particle n.Radiativetransfer simulations were performed by our own code for Monte Carlosimulations of unpolarized light. The algorithm consists of simulatingthe trajectories of many individual photons as they interact withparticles and interfaces until they are either absorbed by particlesor exit the simulation domain. The initial condition of each photonis given by the position and direction of the light source. At eachsimulation step, the optical path (Λphoton = ΛFresnel), a photon iseither reflected or transmitted by a random selection, with the probabilitiesof each event proportional to the respective energy flux defined byFresnel laws. If the photon is absorbed by a particle (Λphoton = Λabs) or the host material (Λphoton = Λhost), the event is terminated andthe simulation continues with a new photon at the initial conditions.For a scattered photon (Λphoton = Λsca), the new direction is determined by7g = ⟨μsca⟩.In the case of diffraction at a 1 mm distance belowthe slab. In all the simulations, we considered 1000000 photons perwavelength. For the validation of our code, refer to


The genomic fabric paradigm (GFP) characterizes the transcriptome topology by the transcripts’ abundances, the variability of the expression profile, and the inter-coordination of gene expressions in each pathophysiological condition. The expression variability analysis provides an indirect estimate of the cell capability to limit the stochastic fluctuations of the expression levels of key genes, while the expression coordination analysis determines the gene networks in functional pathways. This report illustrates the theoretical bases and the mathematical framework of the GFP with applications to our microarray data from mouse models of post ischemic, and constant and intermittent hypoxia-induced heart failures. GFP analyses revealed the myocardium priorities in keeping the expression of key genes within narrow intervals, determined the statistically significant gene interlinkages, and identified the gene master regulators in the mouse heart left ventricle under normal and ischemic conditions. We quantified the expression regulation, alteration of the expression control, and remodeling of the gene networks caused by the oxygen deprivation and determined the efficacy of the bone marrow mono-nuclear stem cell injections to restore the normal transcriptome. Through the comprehensive assessment of the transcriptome, GFP would pave the way towards the development of personalized gene therapy of cardiac diseases. Personalized (or precision medicine) has become a focal area of interest and development in medicine of the 21st century. This is because the individual variances of biological response to environmental factors and drug therapies may substantially alter the outcomes of disease progression and therapeutic success. Understanding the genetic and epigenetic mechanisms regulating these variabilities due to the factors, such as race, sex, age, medical history, diet, stress, exposure to toxins, and individual habits, etc., could be critical for designing a clinical strategy tailored for each patient. For example, 70 microRNAs identified in whole blood samples via next generation sequencing were linked to the risk of recurrent myocardial infarction and future stent thrombosis, ascompared to coronary artery disease (CAD) patients without the subsequent events [Gene expression profiling is a very important tool to individualize the molecular mechanisms responsible for the pathophysiological characteristics and tailor the appropriate therapy for each individual e.g., ,4,5), bu,5, bu4,5REV is an indirect measure of the strength of the homeostatic mechanisms that ensure the right expression of key genes by limiting their random fluctuations caused by the stochasticity of the chemical reactions and environment unsteadiness within narrow intervals. On the other hand, COR, accounting for the “Principle of Transcriptomic Stoichiometry” (PTS) , determiWe have shown previously that the transcriptome topology is strongly dependent on race/strain , sex 1010, age , and regThe (cardio)genomic fabric approach is illustrated here by using publicly available microarray data from a mouse model of post-ischemic heart failure (PIHF) ,20 and f6 bone marrow mononuclear stem cells. The transcriptomes were profiled 59 days after induction of myocardial infarction and 49 days after cell therapy. Total 12 mice (n = 4 per group) were used in this experiment and divided into: normal untreated (“NN”), infarcted untreated (“IN”), and infarcted treated (“IT”). As mentioned in Refs. [As described in Ref. , the myoin Refs. , the expiO2 = 21%). For three groups of 4 mice each, denoted by “I1”, “I2”, “I4”, FiO2 was alternated between 21% and 11% every 4 min, 24 h/day 1, 2 or 4 weeks. Finally, for other three groups of 4 mice each, denoted by “C1”, “C2”, “C4”, FiO2 was kept constant at 11% for the entire period [In the hypoxia study, neonatal CD1 mice were placed in Biospherix hypoxia chambers in the second day of their life and kept there for 1, 2, or 4 weeks. Three groups of 4 mice each, denoted by “N1”, “N2”, “N4”, were kept under normal atmospheric conditions  genomic fabric of a functional pathway in a particular region of myocardium as the transcriptome associated to the most interconnected and stably expressed gene network responsible for that pathway in that heart region. We define the Prlr) in N1 means that the average expression of this gene is 4.31 × larger than that of the median gene in N1 .In each condition, the independent characteristics AVE, REV, and COR of every gene were averaged over the valid spots probing that gene  of individual genes and the pathway relative expression control (PREC) of the (cardio) genomic fabrics: Higher positive REC values indicate genes whose random fluctuations of the expression level are strongly limited by the cellular homeostatic mechanisms within narrow intervals as their right expressions are critical for the cardiac physiology. By contrast, large negative RECs are associated with less controlled genes useful for cell adaptation to environmental changes. Thus, REC indicates the priorities of the cell in regulating the transcription machinery. Similarly, high positive PRECs are associated with critically important pathways for the preservation of the phenotypic expression fluctuations and negative PRECs with adapting pathways. One may observe that REC = 0 set the baseline for genes and PREC = 0 the baseline for the pathways. As presented in the Results section below, REC and PREC are sensitive to the external factors such as ischemia and oxygen deprivation.2) expressions of two genes across biological replicas  significantly synergistically, antagonistically, and independently expressed gene pairs, albeit it cannot determine which of the paired genes is the master. Thus, COR determines the statistically significant gene networks in each condition, refining the gene “wiring” in functional pathways constructed by dedicated software such as: QIAGEN Ingenuity Pathway Analysis [COR is the Pearson product-moment correlation coefficient between the  scoring that combines the expression control and expression coordination with each and other genes . The topBy stably transfecting two human thyroid cancer cell lines with four genes, we proved that expression manipulation of a gene has transcriptomic consequences proportional to the GCH of that gene . Becausex” (negative for down-regulation). Some analyses require also a less than 0.05 p-value of the heteroscedastic t-test of the two means equality. However, such absolute fold-change cut-off might be too stringent for very stably expressed genes across biological replicas and low local technical noise, while for other genes it might be too relaxed. Therefore, while maintaining the p-value < 0.05 condition, we determine the absolute fold-change cut-off for the expression ratio “x” separately for each quantified gene to account for both biological variability and the technical noise of the probing spot(s) ([When comparing two conditions (for instance “IN” with “NN” in the infarct experiment), traditional transcriptomic analysis uses uniform, arbitrarily introduced cut-off for the absolute fold-change (1.5× or 2.0×) of the expression ratio “spot(s)  Regulation (WIR) [x”, WIR takes also positive values for up-regulated genes and negative values for the down-regulated ones ([A more informative measure is the on (WIR)  that taked ones  Transcriptomic Distance” (ITD). ITD is the magnitude of the 3D vector whose orthogonal components reflect the relative changes in the average expression level, expression variability , and expression correlations    Distance (PTD), much more accurate in ranking the pathways according to their alteration than the percentage of regulated genes.Both WIR and ITD can be further averaged for a given functional pathway “Γ” as the weighted pathway regulation (WPR) and Γ”. Traditionally, such comparison is done by comparing the numbers of regulated genes with and without the treatment (when each gene is considered as a uniform contributor). One can determine the transcriptomic effect of a treatment by comparing the alterations before and after that treatment. The comparison may encompass all genes or may be restricted to a particular functional pathway “Gene Expression Recovery    representing the percent reduction of the transcriptomic distance in response to the treatment.Now, we add the The PIHF experiment quantified the expression levels of 10,408 unigenes in all 12 samples from the groups “NN”, “IN”, “IT”, n = 4/group), from which the GFP was extracted in each condition 10,408 AVEs + 10,408 REVs + 54,158,028 CORs = 54,178,844 values. Thus, the GFP increased the size of the workable data in each condition by 5206 times. With respect to “NN”, 579 genes  were significantly (according to our composite criterion) up-regulated and 1222 (11.74%) were down-regulated in “IN”. The treatment with bone marrow mononuclear stem cells partially recovered the normal expression levels of the genes, leaving 256 (2.46%) up-regulated and 667 (6.41%) down-regulated in the “IT” group as compared with the “NN” controls. Interestingly, the treatment went even further by flipping the significant down-regulation of 19 genes and the significant up-regulation of 15 genes to their opposites. In the hypoxia experiment, 9716 unigenes were adequately quantified in all 36 samples from the groups “N1”, “I1”, “C1”, “N2”, “I2”, “C2”, “N4”, “I4”, “C4” (n = 4/group), from which GFP extracted in each condition 47,214,902 values. This is an increase by 4860 times of the information used in the traditional analysis limited to the AVEs. According to our criterion, with respect to the control group “N1”, 9.43% of the genes were up- and 11.72% were down-regulated in the group “I1”, and 6.13% were up- and 4.30% down-regulated in “C1”. With respect to “N2”, 10.48% of the genes were up- and 18.94% were down-regulated in “I2”, and 22.02% up- and 18.92% down-regulated in “C2”. Finally, with respect to “N4”, 4.08% were up- and 2.14% down-regulated in “I4”, while in “C4”, 6.01% were up- and 6.71% down-regulated.Hspb6 , is an important modulator of energy pathways and xenobiotic metabolism [The genes with the largest expression level were: traction . Nr1i3, tabolism .Ank2-ankyrin 2) for 34 inflammatory response genes in the heart left ventricle of mice subjected for the first week of their life to normal atmospheric conditions (“N1”), intermittent hypoxia (“I1”), or constant hypoxia (“C1”). Ank2 of the same genes for the 2 and 4 weeks of hypoxia exposures. The value 1 for the expression correlation of Ank2 with itself is the validation of the correctness of the COR analysis. Although Ank2, encoding Ankyrin-B, one major player in cardiac physiology [ysiology ). CoordiGCH analysis was used to establish the hierarchies of the genes in the conditions “NN”, “IN”, and “IT”. Tmem186, with GCH = 53.21 in “NN”, 1.03 in “IN”, and 2.57 in “IT”), CD164 antigen , and ATPase type 13A2 .For the conditions analyzed here, the gene master regulators (GMRs–top GCH scorers) are: transmembrane protein 186  was shown to protect cardiomyocytes from hypoxia/reoxygenation injury by reducing the production of reactive oxygen species and cell apoptosis [Pcsk7 (proprotein convertase subtilisin/kexin type 7) was also associated with cardiovascular disease phenotypes [Tuba1c  was previously identified to predict the outcome of a linear combination of circadian rhythm pathway genes [Fam171a2  in the heart was recently correlated with the PR interval of an electrocardiogram, suggesting a role for the cardiac conduction system [omplex I , while tutophagy . Existinpoptosis . The 4thenotypes . On the ay genes . The abun system . Thus, tIn the traditional analysis of the percentages of significantly up-/down-regulated genes, each affected gene is considered as a uniform +1 or −1 contributor to the overall transcriptomic regulation. Moreover, this measure is limited to the significantly regulated genes according to the criterion established by the investigator, frequently an arbitrary absolute fold-change cut-off. In our study, the absolute fold-change cut-off is determined separately for each expressed gene pending on its expression variability across biological replicas and the technical noise of the probing spot(s) in the microarray .A better way to quantify the contributions of the individual genes to the overall transcriptomic alteration is to use the WIR score. Although still limited to the change in the expression level, WIR not only considers all genes but weights their contribution according to the total absolute change of their expression level and the statistical confidence in their regulation. This measure was previously used to quantify the transcriptomic alterations in the left ventricle of a mouse model of Chagasic cardiomyopathy , in the Tpm1  in “IN” (2.18×) is larger than that of the not significantly regulated Tpm4 , both WIR and ITD scores are larger for Tpm4  than for Tpm1  in “IN”. Such findings impose a reconsideration of what really matters in the transcriptome changes. Interestingly, while Tpm1 is one of the main hypertrophic cardiomyopathy genes [Nevertheless, the most comprehensive measure is the ITD that takes into account the alterations of all independent characteristics of the individual genes. The new measures reveal that genes neglected because their expression ratios did not pass the threshold to be considered as significantly regulated may still have contributions to the transcriptome alteration through affected expression control mechanisms and remodeling of the gene networks. For instance, although the expression ratio of the significantly up-regulated hy genes , Tpm4 ishy genes .Gnas gene, encoding the stimulatory alpha subunit of the protein complex guanine nucleotide-binding protein (G protein), had the largest contribution to the transcriptomic alteration in “IN” . Although, no longer significantly regulated in “IT” (x = −1.12), Gnas still contributes to the transcriptomic differences with respect to the control “NN” . It was recently reported that a somatic mutation of Gnas is associated with focal, idiopathic right ventricular outflow tract (RVOT) tachycardia [Both “WIR” and “ITD” analyses revealed that for this pathway, the regulation of the hycardia .Adra1b , Atf2 (activating transcription factor 2), Atp1b2 , Bcl2 (B-cell leukemia/lymphoma 2), Cacnb2 , Calm2 , Fxyd2 (FXYD domain-containing ion transport regulator 2), Gnas  complex locus), Kcne1 , Ppp1cc , Ppp2r2d , Rapgef4 (rap guanine nucleotide exchange factor (GEF) 4), Scn7a , and Tpm1 .Thirteen genes of this pathway were significantly regulated by the infarct: Adra1b, involved in the positive regulation of the blood pressure [Adra1a: x = −1.19, CUT = 1.65; Adra1d: x = −1.44, CUT = 1.73), their regulations were not statistically significant. However, because of larger differences in REVs and CORs, both genes had higher contributions to the overall alteration of the transcriptome than Adra1b, with ITD = 1.62 (Adra1a) and ITD = 1.67 (Adra1d). It was reported that the stimulation of these alpha-adrenergic receptors can protect cardiomyocytes against ischemia by regulating the influx of glucose [One may note that pressure , was sigpressure  were als glucose .Adra1b, Atp1b2, Bcl2, Cacnb2, Calm2, Fxyd2, Gnas, Ppp1cc, Ppp2r2d, Rapgef4, Scn7a, and Tpm1. Kcne1 remained down-regulated, while the normally expressed Cacna2d1  and Ppp2r5e , epsilon isoform) in “IN” condition were down-regulated by the treatment. Therefore, for this pathway, {DX} = 7, {UX} = 5, {XD} = 2, {XU} = 0, {DD} =1, {UU} = 0, {UD} = 0, {DU} = 0, so that GER = 66.67%. WPR(NN→IN) = 36.10 and WPR(NN→IT) = 13.63, making WPR = 62.24%. The transcriptomic distance analysis returned: PTD(NN→IN) = 37.11, PTD(NN→IT) = 11.29, resulting CPR = 69.59%.Adra1b with the other genes from the adrenergic signaling in cardiomyocytes. Adra1b, one of the six subtypes of the adrenergic receptors that control the heart contractility (inotropism) and rate (chronotropism), mediates its action by association with G proteins that activate a phosphatidylinositol–calcium second messenger system. In mouse, the alpha1-adrenergic receptors play adaptive roles in the heart and protect against the development of heart failure [p < 0.05) significant synergistically or antagonistically expressed with Adra1b in at least one of the three conditions. However, the percentages of the synergistically, antagonistically, and independently expressed partners were computed for the entire pathway. Adra1b in each condition. failure . Figure Adra1b in this pathway from 13.9% to 24.1% and that of the antagonistic partnership from 1.3% to 8.9%. This very substantial strengthening of the Adra1b inter-coordination with many other genes of the pathway makes Adra1b a very important target to recover the altered heart functions. The treatment (panel (c)), reduced back the expression coordination to 11.4% synergism and 1.3% antagonism, and further decoupled numerous other genes from their correlation with Adra1b (panel (d): Akt1 , Atf2, Atf4 (activating transcription factor 4), Atp1a3 , Cacnb2, Camk2a, Ppp2r2d, and Ppp2r5d , delta isoform). However, the treatment antagonistically coupled the independently expressed Atf6b (activating transcription factor 6 beta) and Adra1b under ischemic conditions.Interestingly, as shown in panel (b), the infarct increased the synergistic partnership of The present study provides the theoretical bases of the (cardio)genomic fabric approach in identifying key gene regulatory factors. The theory is applied to expression data from the hearts of mouse models of common myocardial pathologies such as hypoxia and myocardial infarction with or without treatment with bone marrow mononuclear stem cells. Nevertheless, in a really personalized application, the biological replicas of diseased and normal cells should come from the same individual. Such a procedure has been already used to compare samples collected from each cancer nodule and surrounding normal tissue from surgically removed tumors of the thyroid ,31, kidnThrough considering three independent groups of characteristics for each individual gene in each condition P3 generation and arrhythmias in mouse hearts expressing constitutively active alpha1B-adrenergic receptors [One of our primary focuses was on the key genes regulating myocardial adrenergic signaling, such as Adra1b, , by meaneceptors . Howevereceptors .Adra1b networking following myocardial infarction (group IN) and normalization by the post-myocardial infarction stem cell treatment (group IT) (Crem (CAMP-responsive element modulator) coordination with Adra1b was switched from synergistic in “NN” to antagonistic in “IN”, and practically independent in “IT”, indicating a major change in the interaction of the two genes. While the critical role of Crem in β-adrenoreceptor-mediated cardiac dysfunction is documented [Crem and Adra1b and how such an interaction might impact the heart physiology. Since Crem is a transcription factor that mediates high-glucose response in cardiomyocytes [Our present study further revealed the remodeling of the roup IT) . The coocumented , there imyocytes , its relSo far, the GFP power to characterize the organization of the transcriptome was successfully tested in several other studies on neurological diseases (e.g., ,57,58,59


To understand the molecular structure–property relationships governing LLT, herein, we examine ion dynamics of two other quaternary phosphonium ILs containing long alkyl chains in cation and anion. We found that IL with the anion containing branched –O–(CH2)5–CH3 side chains does not reveal any signs of LLT, while IL with shorter alkyl chains in the anion brings a hidden LLT, i.e., it overlaps with the liquid-glass transition. Ambient pressure dielectric and viscosity measurements revealed a peculiar behavior of ion dynamics near Tg for IL with hidden LLT. Moreover, high-pressure studies have shown that IL with hidden LLT has relatively strong pressure sensitivity compared to the one without first-order phase transition. At the same time, the former exposes the inflection point indicating the concave-convex character of logτσ(P) dependences.Although the first-order liquid–liquid phase transition (LLT) has been reported to exist in various systems , it is still one of the most challenging problems in the field of physical science. Recently, we found that this phenomenon occurs in the family of trihexyl(tetradecyl)phosphonium [P This is because a change of cation or anion can significantly tune the physicochemical properties of IL. Good chemical and thermal stability, high ionic conductivity (> 10−4 S cm−1), negligible vapor pressure, and non-flammability make ILs promising electrolyte2 and green solvents for applications in electrochemistry3, biology, and pharmacology5.In the past decades, the interest in ionic liquids (ILs), fluids composed solely of ions, has risen tremendously, especially in the fields of chemistry, materials science, and energy research6. Furthermore, they exhibit relatively low viscosity and thus enhanced ionic conductivity at RT conditions8. The origin of these essential features has been examined over the years by several groups. Among the molecular factors which may contribute to the lower viscosity of phosphonium ILs the size of the phosphorous atom, the charge distribution, and the flexibility of bond and dihedral angles were examined. Furthermore, a large volume of phosphonium cations that result from the shielding of phosphonium core by charge-neutral alkyl groups and bring lower electrostatic friction between counterions was also considered10.Compared to cyclic ILs containing imidazolium, pyrrolidinium, or piperidinium cations, quaternary phosphonium (P) ILs have many valuable physicochemical properties, e.g., enhanced hydrophobicity and significantly wider electrochemical windowσdc) is closely coupled to their structural (α) relaxation11, which is related to the viscosity (η) by the Maxwell equation, η = G∞/τα12. Thus, the classical vehicle mechanism characterizes the ion transport in phosphonium ILs. Furthermore, these materials have been reported in the literature as good glass-formers, i.e., they can form an amorphous solid if sufficiently fast cooling is applied13. Over a relatively narrow temperature range, from RT to the temperature of liquid-glass transition (Tg), the viscosity of P-ILs increases dramatically, even by ten orders of magnitude. At the same time, σdc decreases in the same manner, commonly described by a single Vogel-Fulcher-Tamman (VFT) equation 0 is a pre-exponential factor, and D quantifies the departure of experimental data from the Arrhenius law. An alternative measure of the non-Arrhenius conductivity and fluidity behavior is the fragility index mP defining the steepness of the temperature dependence of various transport properties at Tg. The phosphonium ionic liquids studied so far fall into the intermediate range of fragilities (mP = 46–60) compared to other ionic liquids and glassformers in general14.Extensive investigations of charge transport in phosphonium ionic liquids have shown that the dc conductivity . This peculiar behavior, reported for five different +-based ILs, has been recognized as the dielectric signature of the first-order liquid–liquid phase transition (LLT). Strictly speaking, two isotropic liquid states of different dc-conductivity behavior were found to exist within a single IL. As a molecular origin of this unique phenomenon, enhanced ordering of cation alkyl chains in non-polar domains was postulated from XRD and IR experiments16.Furthermore, it has been shown that LLT occurs at elevated pressure. Namely, isothermal compression triggers the LLT, with the τσ at LLT being independent of temperature and pressure conditions. The time scale of ion dynamics at LLT was found anion-specific, i.e., dependent on anion size, geometry, conformational flexibility, and the strength of interionic interactions15. Furthermore, it was postulated that large anions most likely complicate the ordering of the alkyl chains in the non-polar domains and consequently prevent the LLT15.Such a well-defined physical picture of ion dynamics of P-RTILs has been upended by recent studies of trihexyl(tetradecyl)phosphonium + cation and phosphorus-based anions with long alkyl chains as well. The results of dielectric experiments performed over a wide temperature range revealed that both examined ILs display the conventional dc-conductivity behavior without a clear sign of LLT. However, a more detailed analysis of experimental data indicated that one of the chosen ILs exhibits a hidden LLT. High-pressure dielectric experiments performed for both ILs, have shown distinct differences in their pressure sensitivity of ion dynamics. Furthermore, another unique phenomenon called “inflection point” has been observed for one of examined herein ILs.To further advance the issue of liquid–liquid phase transition in ionic systems, herein we focus on ion dynamics of two ILs containing + cation and anions: bis(2-ethylhexyl) phosphate ([BEHP]-) and bis phosphinate ([BTMPP]−). The chemical structures are displayed in Fig. - structure, two six-carbon chains are attached to phosphorus through the oxygen atom. On the other hand, five carbon chains characterize the [BTMPP]- anion. The van der Waals volume of anions, determined by the Bondi method18, is equal to 3 and 3. Consequently, the former provides more sterical hindrance that might affect the alignment of the nonpolar alkyl chains of  cation, suggested as the origin of the liquid–liquid transition. Moreover, oxygen atoms in [BEHP]− make the side chains polar, which can also influence the LLT.The ILs examined in this work are two quaternary phosphonium ionic liquids with hydrophobic P666,4+ cation666,14][BTMPP] and [BEHP]. Importantly, before the experiments, both examined samples were extensively dried at 343 K under vacuum for 12 h. The DSC thermograms obtained at a cooling rate of 10 Kmin−1 of examined ILs are given in Fig. Differential scanning calorimetry (DSC) measurements have been performed for initial characterization of P666,4[BTMPP] 666,14][BTMPP] and [BEHP] ILs through the liquid-glass transition, temperature-dependent dielectric experiments have been performed. Herein, we employed two formalisms, complex electric modulus M*(f) and complex conductivity σ*(f), to present the obtained data. Both of them are commonly adopted to express the charge transport properties of conducting materials21. The representative dielectric spectra of [BEHP] and [BTMPP] measured over eight decades of frequency (10−2–106 Hz) in a wide temperature range are illustrated in Fig. M”(f) recorded in a supercooled liquid state takes the form of a well-resolved peak, so-called a conductivity relaxation (denoted as σ-process), which shifts toward lower frequencies upon cooling. This behavior reflects the suppressed mobility of ions and is in keeping with the cooling effects revealed in all kinds of ionic glass formers22. Further decreasing temperature below the calorimetric Tg brings the modulus peak out of the experimental window, and a well-distinguished secondary mode (β) becomes visible. Similar to the conductivity relaxation, the β-process move toward lower frequencies on cooling; however it is far less temperature-dependent. At the same time, the real part of complex conductivity σ’(f) is characterized by three clearly visible regions: (i) a frequency-independent dc-conductivity (σdc) that is proportional to the number of ions and their mobility, (ii) a power-law behavior obeyed on the high-frequency side, (iii) a decrease of σ’ from σdc denoting the electrode polarization effect. Note that both formalisms, M”(f) and σ’(f), adopted herein for data analysis, provide information on the ion mobility in a supercooled liquid state; however, compared to modulus representation, dc-plateau is well visible above room temperature. Therefore, the temperature dependence of σdc over 11 orders of magnitude can be examined. At the same time, only the modulus representation offers a characterization of dynamics in a glassy state.To characterize the ion dynamics of [BEHP] and [BTMPP] in more detail. For this purpose, a numerical fitting analysis of M”(f) data, in terms of the Havriliak−Negami function  data of both examined ILs obeys the Arrhenius law 666,14][BEHP] and [BTMPP], respectively. Considering the relatively low activation energy of these modes, one can assume their intramolecular origin—specifically, rotations of anion or cation alkyl chains. The higher Ea determined for relaxation of 5-carbon anion’s chains can be rationalized by more extended branching compared to the side groups of [BEHP]- anion. The coupling model (CM) predictions have been performed to confirm the intramolecular origin of secondary modes. As can be seen in Fig. τJG  for [BTMPP] and [BEHP] does not match with the relaxation times of the β-process, indicating their intramolecular nature.The obtained temperature variations in 666,14][BEHP] and [BTMPP] in a supercooled liquid state thoroughly, first, we focus on the shape of the conductivity relaxation process. At first sight in Fig. - and [BTMPP]- anions follow the behavior of typical ionic glass-formers24 rather than -based ILs with the liquid–liquid phase transition  function, βKWW takes the value between 0 and 1, and it is lower for the broader and more asymmetric peaks25. As presented in Fig. βKWW = 0.6 and 0.56 describes the M”(f) spectra of [BEHP] and [BTMPP], respectively. When compared to other -based ILs, the examined herein fluids reveal quite broad M”(f) peaks, i.e., they are characterized by a relatively broad distribution of the relaxation times , whereas an increase of anion size to [BEHP]- or [BTMPP]- brings higher heterogeneity .To describe the ion dynamics of [BEHP] and [BTMPP]. The temperature dependence of viscosity has been determined and analyzed in terms of the fractional Walden rule, Ληk- = const 26. to verify this assumption. For this purpose, dc-conductivity needs to be converted to molar conductivity according to the relation, Λ = σdcMmolρ−1. The temperature evolution of density ρ and viscosity η obtained experimentally for [BEHP] and [BTMPP] are presented in Fig. −3 KCl aqueous solution that is a fully dissociated electrolyte with equally mobile ionic species28. As presented, the fractional exponent k is slightly lower than the unity (k = 0.97) for both studied ILs. This means that charge transport is indeed strongly coupled to structural dynamics at any T in the supercooled liquid state. From Fig. 666,14][BEHP] and [BTMPP] fall below the ideal line indicating that, in analogy to other phosphonium ILs29, ionization is not complete in these materials.The next important aspect of ion dynamics in a supercooled state is the temperature behavior of dc-conductivity entclass1pt{minimaσdc(T−1) and η(T−1) dependences of [BEHP], while for [BTMPP], the VFT fit deviates slightly from experimental points. For typical glass-forming liquids, such a result designates the existence of the intermediate temperature, Tb, identified with the onset of complex dynamics30. Strictly speaking, there are two regions of complex (T < Tb) and simple (T > Tb) dynamics, characterized by different VFT behavior. Interestingly, considering ILs, only the materials containing imidazolium cation and [TCM] anion revealed a clear Tb point31. To confirm or exclude the presence of Tb for [BEHP] and [BTMPP], the Stickel operator has been employed for dielectric and mechanical data. According to the literature, derivative analysis of temperature variations of the relaxation time (or any other dynamic quantity), 32. On the other hand, when two VFT equations are required to parameterize the experimental data, two linear regions intersect at Tb. The results of the Stickel analysis of τσ(T−1) for studied ILs are presented in Fig. 666,14][BTMPP] displays a different behavior than [BEHP]. Namely, for the latter one, the Stickel plot reveals a single slope while clear deviation from linear behavior is observed for [BTMPP]. However, in contrast to the Stickel graph of any other glass-forming liquid revealing Tb31, the slope of 666,14][BTMPP] follows the behavior of -based ILs revealing a liquid–liquid phase transition. The observed effect is not as significant as for [TCM] or [TAU], where the LLT was detectable as an abrupt decrease of the Stickel operator, but surprisingly it fully mimics the 666,14][BOB], which undergoes a hidden LLT  is much more extensive for [BTMPP]. Consequently, M”(f) maximum moves out of the experimental window already at 300 MPa, while for [BEHP] 480 MPa is not enough. This effect is better visualized when the conductivity relaxation times τσ are plotted vs. pressure. From Fig. τσ(P) dependences of [BTMPP] follow the non-Arrhenius behavior, while logτσ grows linearly with increasing pressure for [BEHP]. The same is observed for σdc dependences . Since within the available pressure range, only a few isotherms of [BEHP] reach the time scale of 100 s, the experimental data have been fitted by using the pressure version of the Arrhenius relation: 666,14][BTMPP] pressure counterpart of VFT law (Tg/dP coefficient (k1/k3)33. As expected, markedly different values of dTg/dP (in the limit of ambient pressure) are obtained for [BTMPP] and [BEHP]; that is 174 K/GPa and 90 K/GPa, respectively. Interestingly, dTg/dP of [BOB] is between these two limits. The obtained results suggest that in [BEHP], there are strong van der Waals interactions between alkyl chains of cations and anions. Such a constituted structure becomes hard to break and thus is weakly sensitive to compression. The same is impossible for [BTMPP] due to the branched 5-carbon chains of the anion. Consequently, squeezing seems to strongly reduce the free volume between the alkyl chains and brings significant pressure sensitivity of Tg.The dτσ dependences, one can notice that volume-activated law quite well parameterizes the data of [BEHP]. However, pVFT deviates from experimental points, especially at high temperatures and low pressures. Therefore, in the next step, we employed Avramov entropic model34 for data analysis. The mathematical expression of this model isτ∞ denotes the conductivity relaxation times at high temperatures, Tr is a reference temperature , logτg = 2 since we previously defined Tg as the temperature at which τ = 100 s, and Π, k, α0, and β are fitting parameters. A significant advantage of this model is that it accounts for isothermal and isobaric conductivity relaxation times simultaneously. Although it was introduced to predict the viscosity of glass-formers at various temperature and pressure conditions, the Avramov model has been satisfactorily applied to describe the ion dynamics of aprotic ionic liquids, where viscosity controls ion transport35. As displayed in Fig. τσ data for both studied ILs. However, when the fitting curves have been transferred to conventional representation  dependences. Precisely, the apparent activation volume τσ(P) dependences, constant ΔV is expected, while for non-Arrhenius logτσ(P), it continuously increases with pressure. ΔV(P) determined at various T conditions for [BEHP] and [BTMPP] are depicted in Fig. ΔV of [BEHP] is markedly lower and weakly dependent on pressure, especially at high temperatures. Furthermore, it decreases with increasing temperature, which is typical for glass-forming liquids. Compared to activation volume determined for imidazolium-based ionic liquids, it is markedly larger36, which reflects the big size of relaxing ions. On the other hand, unusual behavior of ΔV(P) is observed for [BTMPP]. In particular, the activation volume decreases upon compression at the lower pressure range and increases with pressure in the higher pressure region. Consequently, ΔV(P) reveals a clear minimum called an inflection point that indicates the concave-convex character of logτσ(P) dependences.Coming back to the discussion on see Fig. b, a poordata of P66,14[BTMPP] are presented in Fig. V(P) dependences of [BTMPP]. From Fig. Tinfl(P = 0.1 MPa) equal to 238 K, which is above the dynamic glass transition temperature.Here, data of P66,14[NTf2]41, glycerol42 and 2-butyl-1-octanol. Interestingly, all of them can form supermolecular structures due to the strong H-bonding network. In this context, one could expect that [BTMPP], as well as [BOB], reveal some ordering tendencies that affect their ion dynamics at ambient and elevated pressure and finally become the origin of the LLT.Interestingly, so far, only a few glass formers have been compressed strongly enough to observe the inflection point experimentally666,14][BEHP]) and trihexyltetradecylphosphonium bis phosphinate  over a wide temperature and pressure range. These materials can be classified as good glass-forming liquids, as confirmed by DSC scans. However, at the same time, there is no clear calorimetric evidence of the liquid–liquid phase transition being observed previously for other -based ILs. Furthermore, the dynamics of examined ILs shows the features typical for ionic conductors, that is non-exponential behavior of conductivity relaxation peak M”(f) and non-Arrhenius temperature dependence of τσ(T−1). Although the dielectric parameters  did not reveal any signs of LLT, a detailed analysis of τσ(T−1) and η(T−1) dependences revealed an unusual curvature of Stickel plot for [BTMPP]. Such a peculiar behavior of ion dynamics near Tg has not been observed before for any other phosphonium IL, instead of [BOB], for which the LLT was postulated to overlap the liquid-glass transition. Thus, one can conclude that LLT and Tg occur in close vicinity for IL with [BTMPP]- anion. At the same time, an increase in the Stickel slope at Tb can be identified as the fingerprint of changes in ion dynamics accompanying LLT. The high-pressure dielectric measurements revealed that the ion dynamics of [BTMPP] is much more similar to [BOB] than to [BEHP]. In particular, τσ(P) of the latter follows the volume-activated law, while non-Arrhenius behavior characterizes the isotherms of the first two ILs. Specifically, the concave-convex character of logτσ(P) dependences has been observed for [BTMPP] and [BOB]. Consequently, a unique phenomenon called an inflection point was found to characterize the high-pressure dynamics of ionic systems with hidden LLT.In summary, we examined the dielectric properties of trihexyltetradecylphosphonium bis(2-ethylhexyl) phosphate  and trihexyltetradecylphosphonium bis phosphinate  were purchased from io-li-tec Ionic Liquids Technologies as transparent liquids . The purity tests, including NMR, have been made, and they agree with those provided by Iolitec. The bright yellow color can indicate the halide impurities in [BTMPP]. Before the experiments, samples were dried overnight in a Vacutherm oven . The color of the samples did not change after drying. The water content of both ILs is less than 0.1%, determined by Metrohm 899 coulometer.Investigated ionic liquids trihexyltetradecylphosphonium bis(2-ethylhexyl) phosphate  were sealed in aluminum crucibles (40 μL) with pierced lid. Each IL was measured from 123.15 to 303.15 K with a 10 K min−2–107 Hz were performed at ambient pressure using a Novo-Control GMBH Alpha dielectric spectrometer. The same stainless steel electrodes (diameter = 15 mm) with a fixed distance (0.1 mm) provided by the quartz ring were used for both studied ILs. During the measurements, the temperature was controlled by a Quatro system using a nitrogen gas cryostat with an accuracy of 0.1 K. The Karl Fisher test made after the dielectric experiments did not show moisture uptake. The dielectric measurements at elevated pressure were carried out by means of a high-pressure system developed by Unipress over a frequency range from 10−2 to 106 Hz with a specially designed capacitor. The capacitor was filled with the studied sample and sealed by a Teflon capsule during the measurements. Then the whole part was placed in the high-pressure chamber and compressed using silicone oil. The pressure was controlled with a resolution of 1 MPa by means of the Unipress setup, and a Weiss fridge adjusted the temperature within 0.1 K.We have used a glove box to prepare samples for dielectric measurements. The dielectric measurements in a wide frequency range of 10−1 (10 points per decade) with strain equal to 0.01% in the vicinity of the liquid glass transition. The strain was increased by one order of magnitude with every 10 K. The relative uncertainty of the reported viscosity measurements ur(η) from calibration, temperature and pressure control did not exceed 7%.The viscosity was measured employing an ARES G2 Rheometer. In the supercooled liquid region, aluminum parallel plates of diameter 4 mm were used. The rheological experiments were performed in the frequency range from 0.1 to 100 rad sDensity was measured in the temperature range from 283.15 to 363.15 K using a vibrating-tube densimeter DMA 4500 M . The apparatus was calibrated directly before measurements with dry air and bi-distilled water. The water was freshly degassed (by boiling) before use. The viscosity-related errors were automatically corrected in full range.Supplementary Figures.


Radiative thermal engineering with subwavelength metallic bodies is a key element for heat and energy management applications, communication and sensing. Here, we numerically and experimentally demonstrate metallic thermal emitters with narrowband but extremely stable emission spectra, whose resonant frequency does not shift with changes on the nanofilm thickness, the angle of observation and/or polarization. Our devices are based on epsilon-near-zero (ENZ) substrates acting as material-based high-impedance substrates. They do not require from complex nanofabrication processes, thus being compatible with large-area and low-cost applications. Radiative thermal engineering with subwavelength metallic bodies is a key element for heat and energy management applications, communication and sensing. Increasing the speed and dynamic range of the modulation expedites the performance of communication devices,12,13 the impact of nonequilibrium dynamics,14,15 photo-thermal modulation16 and metal-to-insulator transitions17,18 empowering negative differential thermal emittance,19 temperature-independent emission,20 and thermal homeostasis.21,22 Furthermore, concentrating the absorption within a deeply subwavelength region catalyzes basic research on sub-nanometer and atomically-thin metallic materials,23,24 and their nonlocal25 and quantum26 response.The emission and absorption of infrared radiation by subwavelength metallic bodies is the basic operating principle behind a variety of technologies including thermal camouflage,7 nanoresonators,27–29 photonic crystals,30,31 resonant multi-layered structures,32–35 metasurfaces,36,37 transformation optics38 and angle selective filters,39 to name a few. These different strategies could be adapted to concentrate the absorption/emission within a subwavelength metallic body. However, all these approaches, albeit different, share common properties arising from the fact that they rely on the excitation of resonant modes.Conventional approaches to the design of narrowband and partially coherent thermal emitters include the use of structured surfaces supporting leaky modes,via frequency shifts and in homogeneous broadening. Finally, the need of fabricating nanostructures capable of supporting specific resonant modes limits their applicability for large-area, large-scale and low-cost thermal emitters.First, their emission spectrum is polarization- and angle-dependent, following the spatial dispersion of the resonances. This property is convenient for the design of selective emitters, but avoids the design of emitters with a stable emission spectrum. Similarly, the resonant frequency is defined by the geometry of the nanostructure. Therefore, fabrication tolerances modify the spectrum 40,41 low-profile antennas,42,43 reconfigurable antennas,44,45 anti-radar surfaces46,47 and suppressing surface waves.48 By contrast, material-based HISs take advantage of the material properties of a dispersive medium to implement a HISs without the need of fabricating a metamaterial construct.49,50 Here, we numerically and experimentally demonstrate that material-based HISs exhibit an unusually stable absorptivity/emissivity spectrum, characterized by a narrow band peak, whose frequency position is independent of the geometry of the metallic film, the angle of observation and polarization.Here, we propose the use of epsilon-near-zero (ENZ) substrates, acting as a material-based high-impedance surfaces (HISs), as a pathway to obtain spectrally stable emitters. HISs consist of metamaterial constructs that replicate the boundary conditions of an artificial magnetic conductor (AMC). Thus, HISs enforce a maximum of the electric field tangential to its surface, strengthening the interactions with thin metallic films. HISs have been successfully employed at microwave frequencies to develop electromagnetic absorbers,51 including supercoupling,52 photonic doping,53 geometry-invariant resonators54 and frequency pinning of nanoantenna resonances.55 All of these effects are based on wavelength expansion and spatial delocalization in ENZ media. By contrast, here we take advantage of the extreme boundary conditions of ENZ media to induce a stable emission peak in an otherwise nonresonant metallic film, thus opening a new route to geometry-invariant phenomena in ENZ media. We believe that our results introduce a novel class of thermal emitters, and represent an important step forward in the development of practical ENZ-based technologies.Our results resonate with previous works highlighting geometry-independent phenomena in ENZ media,2We start by numerically investigating the spectral performance of material-based HISs (high-impedance surfaces) against variations of the geometry, angle of observation and polarization. As a particular material platform, the absorptivity/emissivity of a titanium (Ti) thin film, deposited on top of a silicon carbide (SiC) substrate is studies. In this doing so, we will find that material-based HISs, implemented with ENZ substrates, exhibit an unusually stable absorptivity/emissivity spectrum. To highlight that this is not how conventional nanostructured thermal emitters behave, we provide the comparative case studies with a Salisbury screen and a grating supporting a leaky mode (sketches of the geometries can be seen in 2.156εSiC(ω) = ε∞(ω2− ωp2 + iωωc)/(ω2 − ω02 + iωωc), with normalized medium impedance . The plasma frequency ωp is located around a wavelength of λp = 10.3 μm, where SiC behaves as an ENZ medium, εSiC(ωp) → 0. Thus, a SiC substrate acts as a material-based HIS, ZSiC(ωp) ≫ 1, that enhances the tangential electric fields on its surface, and strengthens the interaction between electromagnetic fields and ultra-thin metallic films. On the other hand, the resonance frequency ω0 is located around a wavelength of λ0 = 12.55 μm, where the permittivity of SiC acquires very high permittivity values |εSiC(ω0)| ≫ 1. Consequently, near the resonance frequency a SiC substrate acts as a low-impedance surface, ZSiC(ω0) → 0, with a behavior similar to that of metallic mirrors.Silicon carbide (SiC) is characterized by a relative permittivity with a Lorentzian dispersion profile,Because the high-impedance character of SiC substrates directly arises from its material properties, it avoids the need of complex nanofabrication processes, as it is the case in conventional, metamaterial-based, HISs. Furthermore, here we demonstrate that material-based HISs exhibit a narrowband but extremely stable spectral response. First, the strong frequency dispersion of SiC near its plasma frequency leads to a narrowband absorptivity/emissivity response, enabling for the design of partially coherent thermal emitters without the need of nanostructuring a high quality-factor resonant structure. Similarly, because the substrate impedance sweeps a wide range of values around the plasma frequency, changes in the geometry, angle of observation and/or polarization do not induce significant frequency shifts. In this manner, material-based HISs are characterized by an unusually stable emission spectrum.57 we numerically calculate thermal emissivity from the metallic film through its absorptivity (see Methods). εr > 1. Also, we re-emphasize that this figure of merit corresponds to the absorption taking place only within the ultra-thin metallic film. Again, the frequency position of the maximum peak is extremely stable, remaining fixed at λ = 10.3 μm in the studied range from 1 nm to 20 nm thickness. Despite the fact that all studied film thicknesses are deeply subwavelength, films with similar characteristics induce important frequency shifts in conventional thermal emitters, as we will show in the following examples.We illustrate this point by performing full wave numerical simulations (see Methods) on a titanium (Ti) thin film deposited on top of a SiC substrate. Following the local form of Kirchhoff's law,The robustness of the emission frequency against variations of the metallic film thickness provides with important technological advantages. For example, accurately controlling the nanometric film thickness over a large area is an important technical challenge. Similarly, producing a high-quality thin-film with a small roughness requires from a carefully controlled fabrication process. Material-based HISs exhibit a stable spectral response against variations of the thin film geometry. Thus, they provide an interesting alternative for large-area, large-scale applications, as well as for low-cost nanofabrication techniques.θ = 0° and grazing incidence corresponds to θ = 90°. Our numerical simulations reveal that changing the observation angle does not induce a frequency shift in the film absorptivity/emissivity. In other words, the metal film will exhibit a peak of thermal emission at a fixed frequency, independently of the direction along which it is measured. Because no geometrical resonance is used to induce a narrow linewidth, one can simultaneously observe angularly-independent and narrowband thermal emission.Due to the rotational symmetry of the system, the response at normal incidence is the same for both TE and TM polarizations in 2.2It can be concluded from our numerical simulations that material-based HISs enable thermal emitters with a spectrally stable response. Importantly, we remark that this is not how conventional partially coherent emitters behave. To illustrate this point, we next compare its performance with the spectral response of Salisbury screens and nanostructured surfaces.2.2.158,59 that recently has gained popularity in the design of thermal emitters.60,61 A Salisbury screen basically consists of a three layer structure, formed by a resistive layer, placed on a λ/4 spacer on top of a metallic mirror.The Salisbury screen is a popular absorber in microwave engineering62 which exhibits a high dielectric constant (εGe ≃ 16) at infrared frequencies. Salisbury screens implemented with spacers with a lower dielectric constant feature wider bandwidths and a stronger angular variability  spacer, is satisfied. It corresponds to the λ/4 resonance of a conventional Salisbury screen, composed of a purely resistive layer. However, as the thickness of the film increases, the impact of its internal inductance can no longer be neglected, shifting the resonance to higher frequencies . However, for films in the deep nanometer scale size-dependent effects might affect the results.3via FTIR spectroscopy. First, we demonstrate the robustness against variations of the thickness of the metallic film by fabricating six samples with different Ti film thicknesses  deposited on top of 4H-SiC substrates with 220 μm thickness via e-Beam evaporation. Photographs of the fabricated samples are reported in We experimentally demonstrate the spectral stability of material-based HISs by fabricating several samples of titanium (Ti) metallic films deposited on top of a silicon carbide (SiC) substrate, and characterizing them via FTIR spectroscopy (see Methods). Unfortunately, the film absorptivity/emissivity cannot be directly measured from FTIR reflectivity measurements, which provide the collective response of film plus substrate system. Therefore, the film absorptivity/emissivity was retrieved by measuring the reflectivity difference, i.e., by subtracting from the reflection of a bare SiC substrate the reflection from a SiC substrate with the thin film placed on it: ATi ≃ RSiC − RTiSiC ) with fitted values ωp = 3.93 × 1015 rad s−1 and ωc = 1.06 × 1015 rad s−1. Numerical predictions based on this fitted lossier Drude model match well with the experimental results as shown in Normal incidence experiments were conducted with unpolarized light and a FTIR infrared microscope  = ε∞(ω2 − ωp2 + iωωc)/(ω2 − ω02 + iωωc), with normalized medium impedance . In the Theory and numerical results section, titanium and aluminum were modeled with tabulated data.68,69 In the Experimental results section, titanium was modelled with an effective Drude model: εfilm = 1 − ωp2/(ω(ω + iωc)) with fitted values ωp = 3.93 × 1015 rad s−1 and ωc = 1.06 × 1015 rad s−1. We note that the validity of the numerical predictions and calculations extend until the deep nanometer scale, where size dependent effects should be included.64–66Silicon carbide was modeled with a Lorentzian permittivity,4.2via Fourier Transform Infrared Spectroscopy (FTIR) with a microscope Hyperion 3000, and the oblique incidence measurements with the coupled accessory A513/Q in the Bruker Vertex 80v spectrometer.The samples were fabricated in the ISO7 cleanroom at UPNA facilities evaporating Ti on 4H-SiC wafer with an Angstrom Engineering e-Beam evaporator. The six samples are shown in the 5via ENZ substrates, exhibit an unusually stable and narrowband emission spectrum. By contrast with conventional partially coherent emitters, it was demonstrated that the peak emission frequency is very robust against variations on the system geometry , the angle of observation, and polarization. In addition, this unique property is achieved without the use of complex nanofabrication processes, opening the pathway to large-area, large-scale and low-cost applications. Our study has focused on samples composed of Ti metallic layers deposited on top of SiC substrates. However, we expect that similar conclusions hold for other material choices both for the metallic films , and ENZ substrate . We believe that our study reveals a new class of emitters, which might be of interest for a variety of technologies build around of heat and energy radiative management. Beyond thermal emitters, the absorption of infrared radiation by ultra-thin metallic films is the basis of optoelectronic devices, photothermal modulation and basic research on atomically-thin materials, for which a narrowband emitter with an exceptionally stable spectrum might also be of interest.Our results numerically and experimentally demonstrate that material-based HISs, implemented There are no conflicts to declare.NA-005-D2NA00633B-s001