Mathematical modelling of oxygen transport to tissue

 The equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood flowing along a co–axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non–linear reactions between oxygen and haemoglobin in blood and between oxygen and myoglobin in tissue; (ii) diffusion of oxygen in both the axial and radial directions; and (iii) convection of haemoglobin and plasma in the capillary. A non–dimensional analysis is carried out to assess some assumptions made in previous studies. It is predicted that: (i) there is a boundary layer for oxygen partial pressure but not for haemoglobin or myoglobin oxygen saturation close to the inflow boundary in the capillary; (ii) axial diffusion may not be neglected everywhere in the model; (iii) the reaction between oxygen and both haemoglobin and myoglobin may be assumed to be instantaneous in nearly all cases; and (iv) the effect of myoglobin is only significant for tissue with a low oxygen partial pressure. These predictions are validated by solving the full equations numerically and are then interpreted physically. Received: 13 October 2000 / Revised version: 12 June 2001 / Published online: 17 May 2002     

Cryosurgery with pulsed electric fields

This study explores the hypothesis that combining the minimally invasive surgical techniques of cryosurgery and pulsed electric fields will eliminate some of the major disadvantages of these techniques while retaining their advantages. Cryosurgery, tissue ablation by freezing, is a well-established minimally invasive surgical technique. One disadvantage of cryosurgery concerns the mechanism of cell death; cells at high subzero temperature on the outer rim of the frozen lesion can survive. Pulsed electric fields (PEF) are another minimally invasive surgical technique in which high strength and very rapid electric pulses are delivered across cells to permeabilize the cell membrane for applications such as gene delivery, electrochemotherapy and irreversible electroporation. The very short time scale of the electric pulses is disadvantageous because it does not facilitate real time control over the procedure. We hypothesize that applying the electric pulses during the cryosurgical procedure in such a way that the electric field vector is parallel to the heat flux vector will have the effect of confining the electric fields to the frozen/cold region of tissue, thereby ablating the cells that survive freezing while facilitating controlled use of the PEF in the cold confined region. A finite element analysis of the electric field and heat conduction equations during simultaneous tissue treatment with cryosurgery and PEF (cryosurgery/PEF) was used to study the effect of tissue freezing on electric fields. The study yielded motivating results. Because of decreased electrical conductivity in the frozen/cooled tissue, it experienced temperature induced magnified electric fields in comparison to PEF delivered to the unfrozen tissue control. This suggests that freezing/cooling confines and magnifies the electric fields to those regions; a targeting capability unattainable in traditional PEF. This analysis shows how temperature induced magnified and focused PEFs could be used to ablate cells in the high subzero freezing region of a cryosurgical lesion.     

Freezing of nonwoody plant tissues. III. Videotape micrography and the correlation between individual cellular freezing events and temperature changes in the surrounding tissue

A new technique was developed for the observation and recording on videotape of thermal and microscopic changes that occur simultaneously during the freezing of cucumber tissue. The freezing process occurs in two steps. Nucleation and growth of ice crystals in the continuous extracellular liquid phase is followed by nucleation and growth of ice crystals in individual supercooled cells. The freezing of cells in rapid succession causes the average temperature to remain constant for a short time. This mechanism explains the second freezing plateau found in most plant tissue freezing curves.     

Microwave-assisted specific chemical digestion for rapid protein identification

We have developed a rapid microwave-assisted protein digestion technique based on classic acid hydrolysis reaction with 2% formic acid solution. In this mild chemical environment, proteins are hydrolyzed to peptides, which can be directly analyzed by MALDI-MS or ESI-MS without prior sample purification. Dilute formic acid cleaves proteins specifically at the C-terminal of aspartyl (Asp) residues within 10 min of exposure to microwave irradiation. By adjusting the irradiation time, we found that the extent of protein fragmentation can be controlled, as shown by the single fragmentation of myoglobin at the C-terminal of any of the Asp residues. The efficacy and simplicity of this technique for protein identification are demonstrated by the peptide mass maps of in-gel digested myoglobin and BSA, as well as proteins isolated from Escherichia coli K12 cells.     

An analytical study of cryosurgery in the lung.

The process of freezing in healthy lung tissue and in tumors in the lung during cryosurgery was modeled using one-dimensional close form techniques and finite difference techniques to determine the temperature profiles and the propagation of the freezing interface in the tissue. A thermal phenomenon was observed during freezing of lung tumors embedded in healthy tissue, (a) the freezing interface suddenly accelerates at the transition between the tumor and the healthy lung, (b) the frozen tumor temperature drops to low values once the freezing interface moves into the healthy lung, and (c) the outer boundary temperature has a point of sharp inflection corresponding to the time at which the tumor is completely frozen.     

In situ localization of cartilage extracellular matrix components by immunoelectron microscopy after cryotechnical tissue processing

Localization and distribution of proteoglycans within rat growth plate cartilage were investigated by immunoelectron microscopy. By use of a mixture of three monoclonal antibodies directed against chondroitin sulfate chains and of post-embedding staining by protein A-gold, the immunosensitivity and resolution achieved by electron microscopy within tissue processed by high-pressure freezing, freeze-substitution, and low-temperature embedding were compared with those in tissue preserved by three alternative procedures (i.e., mild chemical fixation in combination with either low-temperature embedding or conventional embedding, and high-pressure freezing and freeze-substitution followed by conventional embedding). The loss of matrix components incurred during each stage of high-pressure freezing, freeze-substitution, and low temperature embedding was also determined by measuring the loss of [35S]-proteoglycans from tissue labeled in vivo, and the results compared with previously determined estimates for tissue processed using conventional techniques. Immunosensitivity, determined as the number of gold particles per unit area, was highest in tissue processed by high-pressure freezing, freeze substitution, and low-temperature embedding. Comparable results (with a reduction of only 3-7%) were achieved within tissue preserved by mild chemical fixation followed by low-temperature embedding. In both procedures where conventional embedding was adopted, sensitivity was considerably reduced (by 51% for high-pressure freezing and freeze substitution and by 74% for mild chemical fixation). Loss of matrix components was negligible during all stages of high-pressure freezing, freeze-substitution, and low-temperature embedding. Such information, and that derived from morphological inspection of the various matrix compartments in cartilage processed by high-pressure freezing, freeze-substitution, and low-temperature embedding (J Cell Biol 98:277, 1984), together demonstrate that application of this technique results in successful immobilization of proteoglycans in situ within cartilage matrix. Although loss of proteoglycans from mildly fixed cartilage embedded under low-temperature conditions is minor, morphological examination of this tissue reveals considerable shifting of proteoglycans within matrix compartments. Hence, even though immunosensitivity may be high, resolution is poor. The beauty of the high-pressure freezing, freeze-substitution, and low-temperature embedding technique is that it combines high immunosensitivity with precise localization of matrix components at the molecular level.     

The combination of chemical fixation procedures with high pressure freezing and freeze substitution preserves highly labile tissue ultrastructure for electron tomography applications

The emergence of electron tomography as a tool for three dimensional structure determination of cells and tissues has brought its own challenges for the preparation of thick sections. High pressure freezing in combination with freeze substitution provides the best method for obtaining the largest volume of well-preserved tissue. However, for deeply embedded, heterogeneous, labile tissues needing careful dissection, such as brain, the damage due to anoxia and excision before cryofixation is significant. We previously demonstrated that chemical fixation prior to high pressure freezing preserves fragile tissues and produces superior tomographic reconstructions compared to equivalent tissue preserved by chemical fixation alone. Here, we provide further characterization of the technique, comparing the ultrastructure of Flock House Virus infected DL1 insect cells that were (1) high pressure frozen without fixation, (2) high pressure frozen following fixation, and (3) conventionally prepared with aldehyde fixatives. Aldehyde fixation prior to freezing produces ultrastructural preservation superior to that obtained through chemical fixation alone that is close to that obtained when cells are fast frozen without fixation. We demonstrate using a variety of nervous system tissues, including neurons that were injected with a fluorescent dye and then photooxidized, that this technique provides excellent preservation compared to chemical fixation alone and can be extended to selectively stained material where cryofixation is impractical.     

Ligand orientation of oxyproto- and oxymesocobalt porphyrin-substituted myoglobin by single crystal EPR spectroscopy

Single crystals of oxyproto- and oxymesocobalt myoglobin have been examined by electron paramagnetic resonance spectroscopy at ambient and cryogenic temperatures in order to determine the principal values and eigenvectors of g tensors and the hyperfine coupling tensors. The Co--O--O bond angle was determined to be 125 degrees +/- 5 degrees for oxyprotocobalt myoglobin, and 153 degrees +/- 5 degrees for oxymesocobalt myoglobin at ambient temperature. This result suggests that differences in stereochemical interactions of the modified 2,4-side chains of porphyrin with protein contribute to the ligand orientations as well as the altered ligand-binding behavior in these hemoproteins. Upon freezing, two unequivalent orientations of the O--O axis (species I and II) were found in both oxycobalt myoglobin single crystals. Shifts of the resonance spectra of these species were observed below the freezing point of the crystals. The signal intensities of two paramagnetic species in oxyprotocobalt myoglobin were approximately equivalent (I congruent to II), whereas those in oxymesocobalt myoglobin were quite different (I greater than II) at 77 K. The present electron paramagnetic resonance studies demonstrate that changes in the bonding structure of Co--O2 are induced upon freezing the biological macromolecule, including the movement of the residues of the heme environment.     

Measurement of water transport during freezing in mammalian liver tissue: Part II--The use of differential scanning calorimetry.

There is currently a need for experimental techniques to assay the biophysical response (water transport or intracellular ice formation, IIF) during freezing in the cells of whole tissue slices. These data are important in understanding and optimizing biomedical applications of freezing, particularly in cryosurgery. This study presents a new technique using a Differential Scanning Calorimeter (DSC) to obtain dynamic and quantitative water transport data in whole tissue slices during freezing. Sprague-Dawley rat liver tissue was chosen as our model system. The DSC was used to monitor quantitatively the heat released by water transported from the unfrozen cell cytoplasm to the partially frozen vascular/extracellular space at 5 degrees C/min. This technique was previously described for use in a single cell suspension system (Devireddy, et al. 1998). A model of water transport was fit to the DSC data using a nonlinear regression curve-fitting technique, which assumes that the rat liver tissue behaves as a two-compartment Krogh cylinder model. The biophysical parameters of water transport for rat liver tissue at 5 degrees C/min were obtained as Lpg = 3.16 x 10(-13) m3/Ns (1.9 microns/min-atm), ELp = 265 kJ/mole (63.4 kcal/mole), respectively. These results compare favorably to water transport parameters in whole liver tissue reported in the first part of this study obtained using a freeze substitution (FS) microscopy technique (Pazhayannur and Bischof, 1997). The DSC technique is shown to be a fast, quantitative, and reproducible technique to measure dynamic water transport in tissue systems. However, there are several limitations to the DSC technique: (a) a priori knowledge that the biophysical response is in fact water transport, (b) the technique cannot be used due to machine limitations at cooling rates greater than 40 degrees C/min, and (c) the tissue geometric dimensions (the Krogh model dimensions) and the osmotically inactive cell volumes Vb, must be determined by low-temperature microscopy techniques.     

Evaluation of the impedance technique for cryosurgery in a theoretical model of the head

Bioimpedance is a noninvasive technique that produces information on the electrical characteristics of tissue inside the body from currents injected and electrical potentials measured on the surface of the body. Because freezing causes a large increase in tissue electrical impedance we thought that it may also cause significant changes in the surface electrical potential making the bioimpedance technique suitable for noninvasive monitoring and imaging of cryosurgery. To evaluate the feasibility of the bioimpedance technique in cryosurgery we examined, as a case study, a theoretical model for the electrical potentials during brain cryosurgery. A three-dimensional spherical model was used to calculate the change in the electrical potential distribution in the head as a function of the current source location and the size of the frozen lesion in the brain. The numerical calculations were executed using the finite volume method and the iterative successive over relaxation method. The results demonstrate that, indeed, freezing inside the head produces measurable changes in the electrical potential on the outer surface-the scalp.     

Automated computer evaluation of time-varying cryomicroscopical images

A system has been developed to perform automatic computerized recognition, tracking, and quantitative morphological analysis of viable cells in freezing solutions. Cryomicroscopical image sequences of freezing cells are digitized and analyzed by computer. Image-processing techniques are used which are insensitive to contrast fluctuations from image to image, and which perform well even in noisy, cluttered images. The generalized Hough transform is used for shape detection, and a heuristic graph-search boundary completion algorithm is applied for shape extraction. The extracted cell shape may be analyzed for changes in cross-sectional area, perimeter length, shape deformation, and other metrics of interest. Knowledge from the shapeextraction phase is used to form a prediction of what shape the cell will be in the next image frame, and thus what to look for in the next shape-detection phase. This combination of knowledge-feedback with a powerful shape-detection technique produces an automatic, dynamic shape-recognition scheme capable of accurate recognition and analysis of the cells regardless of how deformed they may become during the freezing sequence. Example performance of the system is illustrated for a series of micrographs of freezing granulocytes.     

Reactive complexes in myoglobin and nitric oxide synthase

In this overview some of our crystallographic and spectroscopic studies on reactive complexes in myoglobin and nitric oxide synthase are summarised. Myoglobin and nitric oxide synthase are both haemoproteins with some similar reaction intermediates. For myoglobin we have studied different intermediates generated in the reaction with hydrogen peroxide by X-ray diffraction, single-crystal microspectrophotometry, electron paramagnetic resonance spectroscopy, Mössbauer spectroscopy, resonance Raman spectroscopy and quantum refinement. Several of these myoglobin states are quite susceptible to radiation-induced changes during crystallographic data collection, and we have observed a radiation-induced change of the ferric resting myoglobin to aqua ferrous myoglobin, of myoglobin compound II to a proposed intermediate H, and of myoglobin compound III to peroxy myoglobin. For the myoglobin compound II/ intermediate H we observe a single-bonded Fe^IV-O species, which is probably protonated. The long Fe-O bond seen in the crystal structure can be supported by the observation of a new ¹⁸O-sensitive resonance Raman mode at 687 cm⁻¹. For nitric oxide synthase we detected with cryobiochemical methods in electron paramagnetic resonance spectra the first biopterin radical serving as electron donor to the ferrous-oxy complex, and that biopterin serves as a proton donor as well, in addition we could observe formation of the Fe(NO) complex with a amino-pterin cofactor capable to form a reactive radical.     

On the role of myoglobin in muscle respiration

The presence of myoglobin in red muscle tissue has a marked effect on its respiration because it combines reversibly with oxygen and hence gives rise to facilitated diffusion. In this paper we consider the role of myoglobin in facilitating oxygen diffusion and give quantitative results for the oxygen concentration within a typical muscle fibre. Simple expressions are derived for the critical metabolism for the onset of oxygen debt and the growth and size of the region in oxygen debt when the muscle metabolism exceeds this critical value.The general principle, enunciated by Murray &; Wyman (1971), that the macromolecule, myoglobin here, can only function as a carrier if it is unsaturated in some region of the system is again shown to hold.A singular perturbation procedure is used to analyze the model, the effect of which is to reduce the mathematical problem to that of trivially solving a quadratic algebraic equation for the oxygen concentration in the muscle fibre. Physically one condition which causes this phenomenon to be singular in the mathematical sense is that the relaxation times of the myoglobin-oxygen reaction are small compared with the diffusion time of the myoglobin-oxygen complex.     

Amino Acid Sequence, Spectral, Oxygen-Binding, and Autoxidation Properties of Indoleamine Dioxygenase-Like Myoglobin from the Gastropod Mollusc Turbo cornutus

Myoglobin was isolated from the radular muscle of the archaeogastropod mollusc Turbo cornutus (Turbinidae). This myoglobin is a monomer carrying one protoheme group; the molecular mass was estimated by SDS–PAGE to be about 40 kDa, 2.5 times larger than that of usual myoglobin. The cDNA-derived amino acid sequence of 375 residues was determined, of which 327 residues were identified directly by chemical sequencing of internal peptides. The amino acid sequence of Turbo myoglobin showed no significant homology with any other usual 16-kDa globins, but showed 36% identity with the myoglobin from Sulculus diversicolor (Haliotiidae) and 27% identity with human indoleamine 2,3-dioxygenase, a tryptophan-degrading enzyme containing heme. Thus, the Turbo myoglobin can be counted among the myoglobins which evolved from the same ancestor as that of indoleamine 2,3-dioxygenase. The absorbance ratio of γ to CT maximum (γ/CT) of Turbo metmyoglobin was 17.8, indicating that this myoglobin probably possesses a histidine residue near the sixth coordination position of heme iron. The Turbo myoglobin binds oxygen reversibly. Its oxygen equilibrium properties are similar to those of Sulculus myoglobin, giving P ₅₀ = 3.5 mm Hg at pH 7.4 and 20°C. The pH dependence of autoxidation of Turbo oxymyoglobin was quite different from that of mammalian myoglobin, suggesting a unique protein folding around the heme cavity of Turbo myoglobin. A kinetic analysis of autoxidation indicates that the amino acid residue with pK _a = 5.4 is involved in the reaction. The autoxidation reaction was enhanced markedly at pH 7.6, but not at pH 5.5 and 6.3 in the presence of tryptophan. We suggest that a noncatalytic binding site for tryptophan, in which several dissociation groups with pK _a ≥ 7.6 are involved, remains in Turbo myoglobin as a relic of molecular evolution.     

DEVELOPMENT AND EVALUATION OF A FREEZE-ETCH,FREEZE-FRACTURE TECHNIQUE APPLIED TO DEVELOPING WHEAT ENDOSPERM

A technique was developed and evaluated whereby differentiating wheat endosperm tissue could be processed for the freeze-etch, freeze-fracture technique without the use of chemical fixatives. Field grown, developing hard red winter wheat (cv. Newton) caryopses were infiltrated with glycerol prior to freezing in liquid nitrogen-cooled Freon-22. Frozen samples were placed in cryogenic vials and stored in liquid nitrogen until needed. Freeze-fracture was carried out under standard conditions. Evaluation of replicas from glycerol-imbibed endosperm was made by comparing them to replicas obtained from freshly frozen untreated endosperm, and endosperm that had been prefixed in glutaraldehyde and paraformaldehyde. Other evaluations were made by comparing replicas of glycerol-treated endosperm to thin sections obtained from wheat that had been imbibed with glycerol, fixed, dehydrated, and infiltrated and embedded in epoxy resin for routine electron microscopy. The results indicate that if the unfixed glycerol-treated wheat endosperm is handled carefully, replicas can be obtained which show few artifacts due to glycerol and freezing. Typical artifacts such as vesiculation of RER, ice crystal damage, production of fusion intermediates, and membrane particle segregation can be nearly eliminated when this technique is applied to developing wheat endosperm.     

OPTIMAL FREEZING CONDITIONS FOR CEREBRAL METABOLITES IN RATS

Abstract— Optimal freezing conditions for metabolites were evaluated in 250-450 g rats. As a standard procedure, the brains were frozen in such a way that the blood pressure and arterial oxygenation were upheld during the freezing. The progression of the freezing front was determined by means of implanted thermocouples, and the interruption of the circulation by means of injections of carbon particles into the blood stream. The freezing gave rise to a rapid interruption of the circulation in the superficial cortical layer first reached by the freezing front well before the temperature reached 0°C. In deeper regions the progression of the freezing front was slower and interruption of the circulation occurred simultaneously with the freezing of the tissue. Measurements of labile cerebral metabolites, including phosphocreatine, ATP, ADP, AMP and lactate, failed to show signs of autolysis in the part of cortex which became unperfused at temperatures above zero. Since the energy state was identical in superficial cortical areas and in areas that did not freeze until after 40–90 s, it is concluded that the freezing technique gives optimal conditions for metabolites also in deep cerebral structures. Decapitation of unanaesthetized animals gave rise to large autolytic changes in the cerebral cortex. In unanaesthetized animals that were immersed in liquid nitrogen the changes were less marked and mainly affected the concentrations of phosphocreatine, ADP and lactate. When paralysed animals that were anaesthetized with N₂O were immersed in liquid nitrogen the only significant change from the control was a decrease in phosphocreatine content. The virtual absence of autolytic changes in this group of animals was not related to the anaesthesia since more pronounced changes were observed in phenobarbitone-anaesthetized rats immersed in the coolant. These differences could be explained by the fact that spontaneously breathing animals immersed in liquid nitrogen developed arterial hypoxia much faster than paralysed animals. It is concluded that an optimal metabolite pattern can only be obtained in anaesthetized animals, frozen with a method that was described by Kerr almost 40 years ago (Kerr , 1935). If unanaesthetized animals must be used, greater attention should be paid to the oxygenation of the blood during the freezing than to such factors as speed of freezing or depth of anaesthesia.     

Mechanics of proteins with a focus on atomic force microscopy

The capacity of proteins to function relies on a balance between molecular stability to maintain their folded state and structural flexibility allowing conformational changes related to biological function. Among many others, four different examples can be chosen. The giant protein titin is stretched and can unfold during muscle contraction providing passive elasticity to muscle tissue; myoglobin adsorbs and releases oxygen molecules thank to conformational changes in its structure; the outer membrane protein G (OmpG) is a bacterial porin with a long and flexible loop that modulates gating; and the proton pump bacteriorhodopsin adapts its cytosolic half to allow proton pumping. All these conformational changes triggered either by chemical or by physical cues, require mechanical flexibility or elasticity of certain protein domains. While the methods to determine protein structure, X-ray crystallography above all, have been dramatically improved over the last decades, the number of tools that directly measure the mechanical flexibility of proteins and protein domains is still limited. In this tutorial, after a brief introduction to protein structure, we present some of the available techniques to estimate protein flexibility, then focusing on atomic force microscopy (AFM). We describe the principles of the technique and its various imaging and force spectroscopy modes of operation that allow probing the elasticity of proteins, protein domains and their surrounding environment.     

Multiple freezing points as a test for viability of plant stems in the determination of frost hardiness

A technique is presented for a simple, rapid, and reliable means of determining the viability of plant tissue subjected to freezing temperatures. Freezing curves of excised stems of Cornus stolonifera Michx., and several other genera were studied. Tissue temperature was recorded during freezing of plant stem sections. The heat of crystallization deflected the resultant freezing curves at points where tissue froze. Living stem sections of all genera studied revealed 2 freezing points, while dead tissue exhibited only 1. The influence of variables such as moisture content, sample size, thermocouple placement, and cooling rate on freezing curves was analyzed. Stem samples wrapped in moisture-proof film with a thermocouple inserted into the pith were frozen to a predetermined test temperature, thawed, and subjected to a second freezing cycle. The presence or absence of 2 freezing points in the second freezing cycle was used as a criterion for establishing viability. The results were immediately available and identical to results from regrowth tests which took about 20 days.     

Freezing tolerance in Draba chionophila,a ‘miniature’ caulescent rosette species

Summary Freezing tolerance as a cold resistance mechanism is described for the first time in a plant growing in the tropical range of the Andean high mountains. Draba chionophila, the plant in which freezing tolerance was found, is the vascular plant which reaches the highest altitudes in the Venezuelan Andes (approximately 4700m). Night cycles of air and leaf temperature were studied in the field to determine the temperature at which leaf freezing began. In the laboratory, thermal analysis and freezing injury determinations were also carried out. From both field and laboratory experiments, it was determined that freezing of the leaf tissue, as well as root and pith tissue, initiated at a temperature of approximately-5.0°C, while freezing injury occurred at approximately-12.0°C for the pith, and below-14.0°C for roots and leaves. This difference in temperature suggests that the plant still survives freezing in the-5.0 to-14.0°C range. Daily cycles of leaf osmotic potential and soluble carbohydrate concentration were also determined in an attempt to explain some of the changes occurring in this species during the nighttime temperature period. A comparison between Andean and African high mountain plants from the point of view of cold resistance mechanisms is made.