Quantum modeling of bioconjugated nanomaterials

In recent years, the bio-conjugated nanostructured materials have emerged as a new class of materials for the bio-sensing and medical diagnostics applications. In spite of their multi-directional applications, interfacing nanomaterials with bio-molecules has been a challenge due to somewhat limited knowledge about the underlying physics and chemistry behind these interactions and also for the complexity of biomolecules. The main objective of this dissertation is to provide such a detailed knowledge on bioconjugated nanomaterials toward their applications in designing the next generation of sensing devices. Specifically, we investigate the changes in the electronic properties of a boron nitride nanotube (BNNT) due to the adsorption of different bio-molecules, ranging from neutral (DNA/RNA nucleobases) to polar (amino acid molecules). BNNT is a typical member of III-V compounds semiconductors with morphology similar to that of carbon nanotubes (CNTs) but with its own distinct properties. More specifically, the natural affinity of BNNTs toward living cells with no apparent toxicity instigates the applications of BNNTs in drug delivery and cell therapy. Our results predict that the adsorption of DNA/RNA nucleobases on BNNTs amounts to different degrees of modulation in the band gap of BNNTs, which can be exploited for distinguishing these nucleobases from each other. Interestingly, for the polar amino acid molecules, the nature of interaction appeared to vary ranging from Coulombic, van der Waals and covalent depending on the polarity of the individual molecules, each with a different binding strength and amount of charge transfer involved in the interaction. The strong binding of amino acid molecules on the BNNTs explains the observed protein wrapping onto BNNTs without any linkers, unlike carbon nanotubes (CNTs). Additionally, the widely varying binding energies corresponding to different amino acid molecules toward BNNTs indicate to the suitability of BNNTs for the biosensing applications, as compared to the metallic CNTs. The calculated I-V characteristics in these bioconjugated nanotubes predict notable changes in the conductivity of BNNTs due to the physisorption of DNA/RNA nucleobases. This is not the case with metallic CNTs whose transport properties remained unaltered in their conjugated systems with the nucleobases. Collectively, the bioconjugated BNNTs are found to be an excellent system for the next generation sensing devices.

Development of a high performance parallel computing platform and its use in the study of nanostructures : clusters, sheets and tubes .

Small clusters of gallium oxide, technologically important high temperature ceramic, together with interaction of nucleic acid bases with graphene and small-diameter carbon nanotube are focus of first principles calculations in this work. A high performance parallel computing platform is also developed to perform these calculations at Michigan Tech. First principles calculations are based on density functional theory employing either local density or gradient-corrected approximation together with plane wave and gaussian basis sets. The bulk Ga2O3 is known to be a very good candidate for fabricating electronic devices that operate at high temperatures. To explore the properties of Ga2O3 at nonoscale, we have performed a systematic theoretical study on the small polyatomic gallium oxide clusters. The calculated results find that all lowest energy isomers of GamOn clusters are dominated by the Ga-O bonds over the metal-metal or the oxygen-oxygen bonds. Analysis of atomic charges suggest the clusters to be highly ionic similar to the case of bulk Ga2O3. In the study of sequential oxidation of these slusters starting from Ga2O, it is found that the most stable isomers display up to four different backbones of constituent atoms. Furthermore, the predicted configuration of the ground state of Ga2O is recently confirmed by the experimental result of Neumark's group. Guided by the results of calculations the study of gallium oxide clusters, performance related challenge of computational simulations, of producing high performance computers/platforms, has been addressed. Several engineering aspects were thoroughly studied during the design, development and implementation of the high performance parallel computing platform, rama, at Michigan Tech. In an attempt to stay true to the principles of Beowulf revolutioni, the rama cluster was extensively customized to make it easy to understand, and use - for administrators as well as end-users. Following the results of benchmark calculations and to keep up with the complexity of systems under study, rama has been expanded to a total of sixty four processors. Interest in the non-covalent intereaction of DNA with carbon nanotubes has steadily increased during past several years. This hybrid system, at the junction of the biological regime and the nanomaterials world, possesses features which make it very attractive for a wide range of applicatioins. Using the in-house computational power available, we have studied details of the interaction between nucleic acid bases with graphene sheet as well as high-curvature small-diameter carbon nanotube. The calculated trend in the binding energies strongly suggests that the polarizability of the base molecules determines the interaction strength of the nucleic acid bases with graphene. When comparing the results obtained here for physisorption on the small diameter nanotube considered with those from the study on graphene, it is observed that the interaction strength of nucleic acid bases is smaller for the tube. Thus, these results show that the effect of introducing curvature is to reduce the binding energy. The binding energies for the two extreme cases of negligible curvature (i.e. flat graphene sheet) and of very high curvature (i.e. small diameter nanotube) may be considered as upper and lower bounds. This finding represents an important step towards a better understanding of experimentally observed sequence-dependent interaction of DNA with Carbon nanotubes.

Synthesis of novel solid materials from carbon dioxide and carbon monoxide

The increase of atmospheric CO2 has been identified as the primary cause for the observed global warming over the past century. The geological and oceanic sequestration of CO2 has issues, such as cost and leakage as well as effects on sea biota. The ideal solution should be the conversion of CO2 into useful materials. However, most processes require high energy input. Therefore, it is necessary to explore novel processes with low energy demands to convert CO2 to useful solid materials. Amorphous carbon nitride and graphone received much attention due to their unusual structures and properties as well as their potential applications. However, to date there has been no attempt to synthesize those solid materials from CO2. Lithium nitride (Li3N) and lithium imide (Li2NH) are important hydrogen storage materials. However, their optical properties and reactivity has not yet studied. This dissertation research is aimed at the synthesis of carbon nitrides and graphone from CO2 and CO via their reaction with Li3N and Li2NH. The research was focused on (1) the evaluation of Li3N and Li2NH properties, (2) thermodynamic analysis of conversion of carbon dioxide and carbon monoxide into carbon nitride and other solid materials, (3) synthesis of carbon nitride from carbon dioxide, and (4) synthesis of graphone from carbon monoxide. First, the properties of Li3N, Li2NH, and LiNH2 were investigated. The X-ray diffraction measurements revealed that heat-treatment at 500°C introduce a phase transformation of β-Li3N to α-Li3N. Furthermore, the UV-visible absorption evaluation showed that the energy gaps of α-Li3N and β-Li3N are 1.81 and 2.14 eV, respectively. The UV-visible absorption measurements also revealed that energy gaps are 3.92 eV for Li2NH and 3.93 eV for LiNH2. This thermodynamic analysis was performed to predict the reactions. It was demonstrated that the reaction between carbon dioxide and lithium nitride is thermodynamically favorable and exothermic, which can generate carbon nitride and lithium cyanamide. Furthermore, the thermodynamic calculation indicated that the reaction between carbon monoxide and lithium imide can produce graphone and lithium cyanamide along with releasing heat. Based on the above thermodynamic analysis, the experiment of CO2 and Li3N reaction and CO and Li2NH were carried out. It was found that the reaction between CO2 and Li3N is very fast and exothermic. The XRD and element analysis revealed that the products are crystal lithium cyanamide and amorphous carbon nitrides with Li2O and Li2CO3. Furthermore, TEM images showed that carbon nitrides possess layer-structure, namely, it is graphene-structured carbon nitride. It was found that the reaction between Li2NH and CO was also exothermic, which produced graphone instead of carbon nitride. The composition and structures of graphone were evaluated by XRD, element analysis, TEM observation, and Raman spectra.

PROPERTIES AND STRUCTURES OF Li-N BASED HYDROGEN STORAGE MATERIALS

Traditional transportation fuel, petroleum, is limited and nonrenewable, and it also causes pollutions. Hydrogen is considered one of the best alternative fuels for transportation. The key issue for using hydrogen as fuel for transportation is hydrogen storage. Lithium nitride (Li3N) is an important material which can be used for hydrogen storage. The decompositions of lithium amide (LiNH2) and lithium imide (Li2NH) are important steps for hydrogen storage in Li3N. The effect of anions (e.g. Cl-) on the decomposition of LiNH2 has never been studied. Li3N can react with LiBr to form lithium nitride bromide Li13N4Br which has been proposed as solid electrolyte for batteries. The decompositions of LiNH2 and Li2NH with and without promoter were investigated by using temperature programmed decomposition (TPD) and X-ray diffraction (XRD) techniques. It was found that the decomposition of LiNH2 produced Li2NH and NH3 via two steps: LiNH2 into a stable intermediate species (Li1.5NH1.5) and then into Li2NH. The decomposition of Li2NH produced Li, N2 and H2 via two steps: Li2NH into an intermediate species --- Li4NH and then into Li. The kinetic analysis of Li2NH decomposition showed that the activation energies are 533.6 kJ/mol for the first step and 754.2 kJ/mol for the second step. Furthermore, XRD demonstrated that the Li4NH, which was generated in the decomposition of Li2NH, formed a solid solution with Li2NH. In the solid solution, Li4NH possesses a similar cubic structure as Li2NH. The lattice parameter of the cubic Li4NH is 0.5033nm. The decompositions of LiNH2 and Li2NH can be promoted by chloride ion (Cl-). The introduction of Cl- into LiNH2 resulted in the generation of a new NH3 peak at low temperature of 250 °C besides the original NH3 peak at 330 °C in TPD profiles. Furthermore, Cl- can decrease the decomposition temperature of Li2NH by about 110 °C. The degradation of Li3N was systematically investigated with techniques of XRD, Fourier transform infrared (FT-IR) spectroscopy, and UV-visible spectroscopy. It was found that O2 could not affect Li3N at room temperature. However, H2O in air can cause the degradation of Li3N due to the reaction between H2O and Li3N to LiOH. The produced LiOH can further react with CO2 in air to Li2CO3 at room temperature. Furthermore, it was revealed that Alfa-Li3N is more stable in air than Beta-Li3N. The chemical stability of Li13N4Br in air has been investigated by XRD, TPD-MS, and UV-vis absorption as a function of time. The aging process finally leads to the degradation of the Li13N4Br into Li2CO3, lithium bromite (LiBrO2) and the release of gaseous NH3. The reaction order n = 2.43 is the best fitting for the Li13N4Br degradation in air reaction. Li13N4Br energy gap was calculated to be 2.61 eV.

MAGNETO-PHOTONIC CRYSTALS FOR OPTICAL SENSING APPLICATIONS

Among the optical structures investigated for optical sensing purpose, a significant amount of research has been conducted on photonic crystal based sensors. A particular advantage of photonic crystal based sensors is that they show superior sensitivity for ultra-small volume sensing. In this study we investigate polarization changes in response to the changes in the cover index of magneto-optic active photonic band gap structures. One-dimensional photonic-band gap structures fabricated on iron garnet materials yield large polarization rotations at the band gap edges. The enhanced polarization effects serve as an excellent tool for chemical sensing showing high degree of sensitivity for photonic crystal cover refractive index changes. The one dimensional waveguide photonic crystals are fabricated on single-layer bismuth-substituted rare earth iron garnet films ((Bi, Y, Lu)3(Fe, Ga)5O12 ) grown by liquid phase epitaxy on gadolinium gallium garnet substrates. Band gaps have been observed where Bragg scattering conditions links forward-going fundamental waveguide modes to backscattered high-order waveguide modes. Large near-band-edge polarization rotations which increase progressively with backscattered-mode order have been experimentally demonstrated for multiple samples with different composition, film thickness and fabrication parameters. Experimental findings are supported by theoretical analysis of Bloch modes polarization states showing that large near stop-band edge rotations are induced by the magneto-photonic crystal. Theoretical and experimental analysis conducted on polarization rotation sensitivity to waveguide photonic crystal cover refractive index changes shows a monotonic enhancement of the rotation with cover index. The sensor is further developed for selective chemical sensing by employing Polypyrrole as the photonic crystal cover layer. Polypyrrole is one of the extensively studied conducting polymers for selective analyte detection. Successful detection of aqueous ammonia and methanol has been achieved with Polypyrrole deposited magneto-photonic crystals.

IN-SITU TEM PLASMA CHIP NANOFABRICATION AND CHARACTERIZATION

A silicon-based microcell was fabricated with the potential for use in in-situ transmission electron microscopy (TEM) of materials under plasma processing. The microcell consisted of 50 nm-thick film of silicon nitride observation window with 60μm distance between two electrodes. E-beam scattering Mont Carlo simulation showed that the silicon nitride thin film would have very low scattering effect on TEM primary electron beam accelerated at 200 keV. Only 4.7% of primary electrons were scattered by silicon nitride thin film and the Ar gas (60 μm thick at 1 atm pressure) filling the space between silicon nitride films. Theoretical calculation also showed low absorption of high-energy e-beam electrons. Because the plasma cell needs to survive the high vacuum TEM chamber while holding 1 atm internal pressure, a finite element analysis was performed to find the maximum stress the low-stress silicon nitride thin film experienced under pressure. Considering the maximum burst stress of low-stress silicon nitride thin film, the simulation results showed that the 50 nm silicon nitride thin film can be used in TEM under 1 atm pressure as the observation window. Ex-situ plasma generation experiment demonstrated that air plasma can be ignited at DC voltage of 570. A Scanning electron microscopy (SEM) analysis showed that etching and deposition occurred during the plasma process and larger dendrites formed on the positive electrode.

Styrene Based Ion Exchange Resins with Oxine Functionalized Groups

Oxine ligands placed on styrene base ion exchange resins selectively remove iron and gallium from acidic solutions. After loading, the oxine resin is stripped of the loaded metals and used again for further metal removal. The resins can be used for process streams, acid rock drainages, or any other iron or gallium containing solution.

Development of a multifunctional platform for extra- and intracellular ionic activities recording

We present the development of a multifunctional platform equipped with an array of silicon nitride micropipettes with dimensions allowing the implementation of extra- and intracellular operations. Micropipettes with outer diameter that ranges from 6 mum down to 300 nm and with walls thicknesses of 500 down to 150 nm are presented. The generic technology developed to fabricate these micropipettes has a number of advantages, including the ability to be implemented as ion-selective electrodes for (A) intracellular and (B) extracellular recordings and as (C) local drug microdispensers.

Development of an array of ion-selective microelectrodes aimed for the monitoring of extracellular ionic activities

In this study, we present the development and the characterization of a generic platform for cell culture able to monitor extracellular ionic activities (K+, NH4+) for real-time monitoring of cell-based responses, such as necrosis, apoptosis, or differentiation. The platform for cell culture is equipped with an array of 16 silicon nitride micropipet-based ion-selective microelectrodes with a diameter of either 2 or 6 microm. This array is located at the bottom of a 200-microm-wide and 350-microm-deep microwell where the cells are cultured. The characterization of the ion-selective microelectrode arrays in different standard and physiological solutions is presented. Near-Nernstian slopes were obtained for potassium- (58.6 +/- 0.8 mV/pK, n = 15) and ammonium-selective microelectrodes (59.4 +/- 3.9 mV/pNH4, n = 13). The calibration curves were highly reproducible and showed an average drift of 4.4 +/- 2.3 mV/h (n = 10). Long-term behavior and response after immersion in physiological solutions are also presented. The lifetime of the sensors was found to be extremely long with a high recovery rate.

A rare case of a large spinal meningioma with mediastinal extension and malignant behavior classified histologically as benign

AIM To report a rare case of a spinal WHO grade I meningioma extending through intervertebral foramina C7 to D4 with an extensive mediastinal mass and infiltration of the vertebrae, and to discuss the malignant behavior of a tumor classified as benign. METHODS (Clinical Presentation, Histology, and Imaging): A 54-year-old man suffered from increasing lower back pain with gait difficulties, weakness and numbness of the lower extremities, as well as urge incontinence. CT scan of the thorax and MRI scan of the spine revealed a large prevertebral tumor, which extended to the spinal canal and caused compression of the spinal cord at the levels of C7 to D4 leading to myelopathy with hyperintense signal alteration on T2-weighted MRI images. The signal constellation (T1 with and without contrast, T2, TIR) was highly suspicious for infiltration of vertebrae C7 to D5. Somatostatin receptor SPECT/CT with (111)In-DTPA-D: -Phe-1-octreotide detected a somatostatin receptor-positive mediastinal tumor with infiltration of multiple vertebrae, dura, and intervertebral foramina C7-D4, partially with Krenning score >2. Percutaneous biopsies of the mediastinal mass led to histopathological findings of WHO grade I meningioma of meningothelial subtype. RESULTS (Therapy): C7 to D4 laminoplasty was performed, and the intraspinal, extradural part of the tumor was microsurgically removed. Postoperative stereotactic radiation therapy was done using the volumetric modulated arc therapy (VMAT) technique (RapidArc). No PRRNT with (90)Y-DOTA-TOC was done. CONCLUSIONS Due to the rare incidence and complex presentation of this disease not amenable to complete surgical resection, an individualized treatment approach should be worked out interdisciplinarily. The treatment approach should be based not only on histology but also on clinical and imaging findings. Close clinical and radiological follow-up may be mandatory even for benign tumors.

Differential uptake of (68)Ga-DOTATOC and (68)Ga-DOTATATE in PET/CT of gastroenteropancreatic neuroendocrine tumors

PURPOSE Abundant expression of somatostatin receptors (sst) is a characteristic of neuroendocrine tumors (NET). Thus, radiolabeled somatostatin analogs have emerged as important tools for both in vivo diagnosis and therapy of NET. The two compounds most often used in functional imaging with positron emission tomography (PET) are (68)Ga-DOTATATE and (68)Ga-DOTATOC. Both analogs share a quite similar sst binding profile. However, the in vitro affinity of (68)Ga-DOTATATE in binding the sst subtype 2 (sst2) is approximately tenfold higher than that of (68)Ga-DOTATOC. This difference may affect their efficiency in detection of NET lesions, as sst2 is the predominant receptor subtype on gastroenteropancreatic NET. We thus compared the diagnostic value of PET/CT with both radiolabeled somatostatin analogs ((68)Ga-DOTATATE and (68)Ga-DOTATOC) in the same patients with gastroenteropancreatic NET. PATIENTS AND METHODS Twenty-seven patients with metastatic gastroenteropancreatic NET underwent (68)Ga-DOTATOC and (68)Ga-DOTATATE PET/CT as part of the workup before prospective peptide receptor radionuclide therapy (PRRT). The performance of both imaging methods was analyzed and compared for detection of individual lesions per patient and for eight defined body regions. A region was regarded as positive if at least one lesion was detected in that region. In addition, radiopeptide uptake in terms of the maximal standardized uptake value (SUV(max)) was compared for concordant lesions and renal parenchyma. RESULTS Fifty-one regions were found positive with both (68)Ga-DOTATATE and (68)Ga-DOTATOC. Overall, however, significantly fewer lesions were detected with (68)Ga-DOTATATE in comparison with (68)Ga-DOTATOC (174 versus 179, p < 0.05). Mean (68)Ga-DOTATATE SUV(max) across all lesions was significantly lower compared with (68)Ga-DOTATOC (16.9 ± 6.8 versus 22.1 ± 12.0, p < 0.01). Mean SUV(max) for renal parenchyma was not significantly different between (68)Ga-DOTATATE and (68)Ga-DOTATOC (12.6 ± 2.6 versus 12.6 ± 2.7). CONCLUSIONS (68)Ga-DOTATOC and (68)Ga-DOTATATE possess similar diagnostic accuracy for detection of gastroenteropancreatic NET lesions (with a potential advantage of (68)Ga-DOTATOC) despite their evident difference in affinity for sst2. Quite unexpectedly, maximal uptake of (68)Ga-DOTATOC tended to be higher than its (68)Ga-DOTATATE counterpart. However, tumor uptake shows high inter- and intraindividual variance with unpredictable preference of one radiopeptide. Thus, our data encourage the application of different sst ligands to enable personalized imaging and therapy of gastroenteropancreatic NET with optimal targeting of tumor receptors.

Electrodes for Long-Term Esophageal Electrocardiography

The emerging application of long-term and high-quality ECG recording requires alternative electrodes to improve the signal quality and recording capability of surface skin electrodes. The esophageal ECG has the potential to overcome these limitations but necessitates novel recorder and lead designs. The electrode material is of particular interest, since the material has to ensure conflicting requirements like excellent biopotential recording properties and inertness. To this end, novel electrode materials like PEDOT and silver-PDMS as well as established electrode materials such as stainless steel, platinum, gold, iridium oxide, titanium nitride, and glassy carbon were investigated by long-term electrochemical impedance spectroscopy and model-based signal analysis using the derived in vitro interfacial properties in conjunction with a dedicated ECG amplifier. The results of this novel approach show that titanium nitride and iridium oxide featuring microstructured surfaces did not degrade when exposed to artificial acidic saliva. These materials provide low electrode potential drifts and insignificant signal distortion superior to surface skin electrodes making them compatible with accepted standards for ambulatory ECG. They are superior to the noble and polarizable metals such as platinum, silver, and gold that induced more signal distortions and are superior to esophageal stainless steel electrodes that corrode in artificial saliva. The study provides rigorous criteria for the selection of electrode materials for prolonged ECG recording by combining long-term in vitro electrode material properties with ECG signal quality assessment.

Periodontal and peri-implant wound healing following laser therapy

Laser irradiation has numerous favorable characteristics, such as ablation or vaporization, hemostasis, biostimulation (photobiomodulation) and microbial inhibition and destruction, which induce various beneficial therapeutic effects and biological responses. Therefore, the use of lasers is considered effective and suitable for treating a variety of inflammatory and infectious oral conditions. The CO2 , neodymium-doped yttrium-aluminium-garnet (Nd:YAG) and diode lasers have mainly been used for periodontal soft-tissue management. With development of the erbium-doped yttrium-aluminium-garnet (Er:YAG) and erbium, chromium-doped yttrium-scandium-gallium-garnet (Er,Cr:YSGG) lasers, which can be applied not only on soft tissues but also on dental hard tissues, the application of lasers dramatically expanded from periodontal soft-tissue management to hard-tissue treatment. Currently, various periodontal tissues (such as gingiva, tooth roots and bone tissue), as well as titanium implant surfaces, can be treated with lasers, and a variety of dental laser systems are being employed for the management of periodontal and peri-implant diseases. In periodontics, mechanical therapy has conventionally been the mainstream of treatment; however, complete bacterial eradication and/or optimal wound healing may not be necessarily achieved with conventional mechanical therapy alone. Consequently, in addition to chemotherapy consisting of antibiotics and anti-inflammatory agents, phototherapy using lasers and light-emitting diodes has been gradually integrated with mechanical therapy to enhance subsequent wound healing by achieving thorough debridement, decontamination and tissue stimulation. With increasing evidence of benefits, therapies with low- and high-level lasers play an important role in wound healing/tissue regeneration in the treatment of periodontal and peri-implant diseases. This article discusses the outcomes of laser therapy in soft-tissue management, periodontal nonsurgical and surgical treatment, osseous surgery and peri-implant treatment, focusing on postoperative wound healing of periodontal and peri-implant tissues, based on scientific evidence from currently available basic and clinical studies, as well as on case reports.

Targeted cancer diagnosis with radiolabeled endostatin

Nuclear imaging is used for non-invasive detection, staging and therapeutic monitoring of tumors through the use of radiolabeled probes. Generally, these probes are used for applications in which they provide passive, non-specific information about the target. Therefore, there is a significant need for actively-targeted radioactive probes to provide functional information about the site of interest. This study examined endostatin, an endogenous inhibitor of tumor angiogenesis, which has affinity for tumor vasculature. The major objective of this study was to develop radiolabeled analogues of endostatin through novel chemical and radiochemical syntheses, and to determine their usefulness for tumor imaging using in vitro and in vivo models of vascular, mammary and prostate tumor cells. I hypothesize that this binding will allow for a non-invasive approach to detection of tumor angiogenesis, and such detection can be used for therapeutic monitoring to determine the efficacy of anti-angiogenic therapy. ^ The data showed that endostatin could be successfully conjugated to the bifunctional chelator ethylenedicysteine (EC), and radiolabeled with technetium-99m and gallium-68, providing a unique opportunity to use a single precursor for both nuclear imaging modalities: 99mTc for single photon emission computed tomography and 68Ga for positron emission tomography, respectively. Both radiolabeled analogues showed increased binding as a function of time in human umbilical vein endothelial cells and mammary and prostate tumor cells. Binding could be blocked in a dose-dependent manner by unlabeled endostatin implying the presence of endostatin receptors on both vascular and tumor cells. Animal biodistribution studies demonstrated that both analogues were stable in vivo, showed typical reticuloendothelial and renal excretion and produced favorable absorbed organ doses for application in humans. The imaging data provide evidence that the compounds quantitate tumor volumes with clinically-useful tumor-to-nontumor ratios, and can be used for treatment follow-up to depict changes occurring at the vascular and cellular levels. ^ Two novel endostatin analogues were developed and demonstrated interaction with vascular and tumor cells. Both can be incorporated into existing nuclear imaging platforms allowing for potential wide-spread clinical benefit as well as serving as a diagnostic tool for elucidation of the mechanism of action of endostatin. ^