hemoglobin isosbestic point

et al. Analysis of complex mixture containing three or more components represented a challenge for analysts. Disclaimer. NIR-based Sensing System for Non-invasive Detection of Hemoglobin for [2] The reason for this is that it would be very unlikely for three compounds to have extinction coefficients linked in a linear relationship by chance for one particular wavelength. They were also successfully applied to commercial pharmaceutical formulations without interference from other dosage form additives. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Schematic of phantoms representing (a) epi/subdural, (b) subarachnoid, and (c) intracerebral hematomas. A study of different novel and smart spectrophotometric techniques for resolution of severely overlapping spectra were presented in this work utilizing isosbestic points present in different absorption spectra . hematoma detection; lighttissue interaction; near-infrared spectroscopy; standardization; tissue phantoms; traumatic brain injury. Merck and Co Inc, Whitehouse Station, Sweetman SC (2009) Martindale: the complete drug reference, 33rd edn. The maximum lateral detection area for the single-emitter/single-collector device studied here appears elliptical and decreases strongly with inclusion depth. -, Thurman D., Guerrero J., Trends in hospitalization associated with traumatic brain injury, JAMA 282(10), 954957 (1999).JAMAAP10.1001/jama.282.10.954 12b. The word derives from two Greek words: "iso", meaning "equal", and "sbestos", meaning "extinguishable". Initially centered with the source and detector fibers, inclusions were repositioned either (a)along the SD axis (, Repeatability of hematoma detector OD measurements (. Anaesthesia UK : Principles of pulse oximetry - FRCA Productive sensors develop more than eight wavelengths to compute hemoglobin concentration and four wavelengths to display only Hb-index (trending of hemoglobin) either in disposable adhesive or reusable cliptype sensor's configuration. 2020 Jul 29;7:100246. doi: 10.1016/j.ejro.2020.100246. eCollection 2021. Biochem Pharmacol 56:12291236, Article government site. A: There are several conditions that can affect A1C results because hemoglobin A1C is dependent on both the glucose levels over the last 2 to 3 months and the lifespan of the red blood cell. Results are presented for a 5-cm-diameter intracerebral hematoma located at depths of 0 and 0.55cm below the CSF. Isosbestic | definition of isosbestic by Medical dictionary sharing sensitive information, make sure youre on a federal Magnetophoretic and spectral characterization of oxyhemoglobin and PLoS One. Continuous monitoring method of cerebral subdural hematoma based on MRI guided DOT. The -curve for conjugated bilirubin is obtained by subtracting the absorbance of hemoglobin and turbidity from native sera with a high concentration of conjugated bilirubin. Para-aminophenol was purchased from Sigma Aldrich, Germany. They are also sensitive and selective and could be used for routine analysis of complex most of the binary, ternary and quaternary mixtures and even more complex mixtures. Results: The same procedures were applied for determination of CAF where the absorption spectrum of the mixture was divided by the absorption spectrum of the normalized spectra of PCT as divisor and the difference between the amplitude at the two selected isosbestic points (233.8 and 273.7nm) between DRO and PCT was corresponding to CAF concentration only as shown in Fig. Isosbestic points are wavelengths at which both oxyhemoglobin and deoxyhemoglobin absorption is similar which is 808 nm, and the absorbance at this point depends only on the hemoglobin concentration. While the proposed novel spectrophotometric methods showed wider range. First order absorption spectra of 10g/mL DRO (solid line), 10g/mL PCT (dotted line), 10g/mL CAF (dashed line) and 10g/mL PAP (dashed dotted line), Zero order absorption spectra of DRO in mixtures (2, 6, 10, 12, and 20g/mL). Society of Photo-Optical Instrumentation Engineers. Google Scholar, Hegazy MA, Eissa MS, Abd El-Sattar OI, Abd El-Kawy MM (2014) Determination of a novel ACE inhibitor in the presence of alkaline and oxidative degradation products using smart spectrophotometric and chemometric methods. Layer thicknesses: 3mm for scalp, 5mm for skull, and 3mm for CSF. official website and that any information you provide is encrypted Table4 showed statistical comparisons of the results obtained by the proposed methods and reported method for DRO [23], and official methods for CAF [24] and PCT [25]. Kinetic and Equilibrium Properties of Hemoglobin Kansas The main disadvantage of this method is the restriction in the choice of the selected wavelengths which are restricted to those wavelengths with constant absorbance of the interfering substance. Paracetamol (PCT) N-(4-hydroxyphenyl) acetamide, also known as acetaminophen PAR is widely used as analgesic and antipyretic for the relief of fever, headaches and minor pains. Early diagnosis of traumatic intracranial hematomas. Schematic of phantoms representing (a)epi/subdural, (b)subarachnoid, and (c)intracerebral hematomas. Derivative transformation [12], spectrum subtraction [13], amplitude factor [14], advanced absorbance subtraction method (AAS) [15], advanced amplitude modulation method (AAM) [15] and simultaneous derivative ratio (S1DD) [16] are well developed method that were successfully adopted for resolution of overlapped spectra of binary mixtures. A probe is placed on the finger, toe, ear lobe or nose. R. G. Ratcliffe. Isosbestic points are used in medicine in a laboratory technique called oximetry to determine hemoglobin concentration, regardless of its saturation. The standards used include potassium dichromate (isosbestic points at 339 and 445 nm), bromothymol blue (325 and 498 nm) and congo red (541 nm). doi: 10.1093/tropej/fmaa111. Phantom-based evaluation of near-infrared intracranial hematoma Visualization of NIR light in the phantom during hematoma detector operation, as acquired from (a)above and to the side of the phantom; as well as directly below the hematoma layer for a 5-cm-diameter intracerebral hematoma [Fig. The point of this is to be able to then correct the other absorption data (from the non-isosbestic points, for the other species of haemoglobin). Principles of pulse oximetry | Deranged Physiology Disclaimer. Ekram H. Mohamed. 4. 2022 Mar 7;43(2). Spectrochim Acta A Mol Biomol Spectrosc 148:328337, Lamie NT, Yehia AM (2015) Development of normalized spectra manipulating spectrophotometric methods for simultaneous determination of dimenhydrinate and cinnarizine binary mixture. By using this website, you agree to our Biomed Res Int. Abstract: Background: Hemoglobin is an essential biomolecule for the transportation of oxygen, therefore, its assessment is also important to be done frequently in numerous clinical practices. The aim of this work was to develop novel spectrophotometric methods based on smart original mathematical techniques for resolving the quaternary mixture of DRO, CAF, PCT and PAP with spectral interfering problems. To cancel the contribution of PCT at both selected wavelengths, induced dual wave length method was adopted by calculating an equality factor for pure PCT at two selected wave lengths of CAF \(\left( {{\text{F}} \; = \; \left[ {{\text{P}}_{ 2 6 5} /{\text{P}}_{ 2 9 5} } \right] \; = \; 5. This can be summarized in the following equations. Point-of-Care Testing Using Invasive and Non-Invasive Hemoglobinometers: Reliable and Valid Method for Estimation of Hemoglobin among Children 6-59 Months. The absorbance difference A (AisoA231.5) between two selected wavelengths on the mixture spectra is directly proportional to the concentration of CAF; while for PCT the absorbance difference inherently equals to zero. 2021 Jan 29;67(1):fmaa111. The isosbestic point of the HB/HbO2 absorption spectrum is circled in white . The obtained constants of DRO are then subtracted from the total ratio spectra of the mixture obtaining the ratio spectra of binary mixtures of both CAF and PCT divided by normalized spectra of DRO as shown in Fig. When carrying out the standard addition technique, different known concentrations of pure standard of each drug were added to the pharmaceutical dosage form before proceeding in the previously mentioned procedure. a Ratio spectra of three binary mixtures of CAF and PAP in different concentrations using the sum of normalized spectra of CAF and PAP as double divisor showing the obtained constant region. Working standard solutions(50 g/mL) working solutions for DRO, CAF, PCT and PAP were prepared from (1mg/mL) stock solutions by appropriate dilutions with methanol. 9a. These wavelength . Federal government websites often end in .gov or .mil. What is the concentration when the transmission is 40 % in a cuvette of 2 cm? Optical Properties and Fluence Distribution in Rabbit Head Tissues at Selected Laser Wavelengths. Oxyhaemoglobin and deoxyhaemoglobin have (not exclusively . This is the point at which two substances absorb a certain wavelength of light to the same extent. Firstly, they were divided by the sum of normalized spectrum of DRO and CAF, to construct a calibration graph was constructed between the amplitude differences at 311 and 318nm versus the corresponding PAP concentrations. The light absorbed by non-pulsatile tissues is constant (DC). Isosbestic_point - chemeurope.com Download scientific diagram | The absorbance of blood samples at 800 nm (A 800 , isosbestic point), normalised to the same haemoglobin concentration as a function of blood pH. The non-constant absorption (AC) is the result of pulsatile blood pulsations. With this purpose, reusable finger probe assembly is facilitated in transmittance mode based on the newly offered sliding mechanism to block ambient light. A remarkable amplitude difference between the two selected wavelengths in the ratio spectra of pure X should be present. FOIA A pair of substances can have several isosbestic points in their spectra. Robertson C. S., et al. Salinas et al. Dark-shaded regions in (a) and (c)represent blood, light-shaded region in (b)represents bloodCSF mixture; hashed regions represent CSF layer. Injury. Isosbestic points are also used in clinical chemistry, as a quality assurance method, to verify the accuracy . 3). Spectrophotometry at that wavelength measures total concentration of hemoglobin, . Google Scholar, Gilman AC, Rall TW, Nies AS, Tayor P (2001) Goodman and Gilmans the pharmacological basis of therapeutics, 10th edn. The amplitudes difference of the obtained ratio spectrum at 263.6nm (iso) and 240nm were recorded (Pm). J AOAC Int 90:391404, Belal FF, Sharaf El-Din MK, Tolba MM, Elmansi H (2015) Determination of two ternary mixtures for migraine treatment using HPLC method with ultra violet detection. The prepared solutions were found to be stable without any degradation when stored in the dark in the refrigerator at 4C for 1week except for PAP which should be freshly prepared. Calibration graphs were constructed by plotting (a) the difference between the amplitudes at [263.6 and 291.8nm], (b) the constant values measured from 310400nm, (c) the difference between the amplitudes at [315 and 336nm] versus the corresponding DRO concentrations, respectively. Chemistry Central Journal Different applications of isosbestic points, normalized spectra and dual wavelength as powerful tools for resolution of multicomponent mixtures with severely overlapping spectra, $${\text{P}}_{ 1} = \left[ {{\text{C}}_{\text{x}} } \right]\; + \;\left[ {{\text{C}}_{\text{Y}} } \right]\; + \;\left[ {{\text{a}}_{\text{z1}} {\text{C}}_{\text{z}} } \right]/{\text{a}}_{\text{x}}$$, $${\text{P}}_{ 2} = \;\left[ {{\text{C}}_{\text{x}} } \right]\; + \;\left[ {{\text{C}}_{\text{Y}} } \right]\; + \;\left[ {{\text{a}}_{\text{z2}} {\text{ C}}_{\text{z}} } \right]/{\text{a}}_{\text{x}}$$, $${\text{P}}_{ 1} - {\text{P}}_{ 2} = \left( {\frac{{a_{z} C_{z} }}{{a_{x} }}} \right)1 - \left( {\frac{{a_{z} C_{z} }}{{a_{x} }}} \right)2$$, $${\text{Pm}}_{ 1} = {\text{P}}_{\text{X1}} \; + \;{\text{P}}_{\text{Y1}} \quad {\text{at }}\lambda_{ 1}$$, $${\text{Pm}}_{ 2} = {\text{P}}_{\text{X2}} \; + \;{\text{P}}_{\text{Y2}} \quad {\text{at }}\lambda_{ 2}$$, $${\text{F}}_{\text{Y}} = {\text{P}}_{\text{Y1}} /{\text{P}}_{\text{Y2}}$$, $$\therefore {\text{P}}_{\text{Y1}} = {\text{F}}_{\text{Y}} {\text{P}}_{\text{Y2}}$$, $${\text{Pm}}_{ 1} = {\text{P}}_{\text{X1}} \; + \;{\text{F}}_{\text{Y}} {\text{P}}_{\text{Y2}}$$, $${\text{F}}_{\text{Y}} {\text{Pm}}_{ 2} = {\text{F}}_{\text{Y}} {\text{P}}_{\text{X2}} \; + \;{\text{F}}_{\text{Y}} {\text{P}}_{\text{Y2}}$$, $$\Delta {\text{P }}\left( {{\text{Pm}}_{ 1} \;{-}\;{\text{F}}_{\text{Y}} {\text{Pm}}_{ 2} } \right) = {\text{A}}_{\text{X1}} \; - \;{\text{F}}_{\text{Y}} {\text{A}}_{\text{X2}}$$, $${\text{Pm}} = \frac{{a_{X} C_{X} }}{{a_{Z} + a_{W} }}\; + \,\frac{{a_{Y} C_{Y} }}{{a_{Z} + a_{W} }}\; + \;{\text{constant}}$$, $${\text{P}}_{ 1} = \frac{{a_{X} C_{X} }}{{[a_{Z} + a_{W} ]1}} + \frac{{a_{Y} C_{Y} }}{{[a_{Z} + a_{W} ]1}} + {\text{constant}}$$, $${\text{P}}_{ 2} = \frac{{a_{X} C_{X} }}{{[a_{Z} + a_{W} ]2}} + \frac{{a_{Y} C_{Y} }}{{[a_{Z} + a_{W} ]2}} + {\text{constant}}$$, $$\frac{{a_{Y} C_{Y} }}{{[a_{Z}\,+\,a_{W} ]1}} = \frac{{a_{Y} C_{Y} }}{{[a_{Z}\,+\,a_{W} ]2}}$$, $${\text{P}}_{ 1} - {\text{P}}_{ 2} = \left( {\frac{{a_{X} C_{X} }}{{a_{Z + } a_{W} }}} \right)1 - \left( {\frac{{a_{X} C_{X} }}{{a_{Z + } a_{W} }}} \right)2$$, \(\left( {{\text{F}} \; = \; \left[ {{\text{P}}_{ 2 6 5} /{\text{P}}_{ 2 9 5} } \right] \; = \; 5. MAH revised the manuscript and the data, collected the data, and put the theoretical background. When a 1-to-1 (one mole of reactant gives one mole of product) chemical reaction (including equilibria) involves a pair of substances with an isosbestic point, the absorbance of the reaction mixture at this wavelength remains invariant, regardless of the extent of reaction (or the position of the chemical equilibrium). Since that publication the noteworthy advance has been made by Nahas who utilized the isosbestic point of hemoglobin for the determination of oxygen saturation of blood and designed a I.ucite cuvette of short light path (2). New smart spectrophotometric methods have been recently evolved with no limitation. Semi-idealized phantom geometries are designed to represent epidural/subdural, subarachnoid, and intracerebral hemorrhages. Kirschen MP, Myers SR, Neuman MI, Grubenhoff JA, Mannix R, Stence N, Yang E, Woodford AL, Rogers T, Nordell A, Vossough A, Zonfrillo MR. West J Emerg Med. Diagnostic properties of a portable near-infrared spectroscopy to detect intracranial hematoma in traumatic brain injury patients. The wavelength of the isosbestic point determined does not depend on the concentration of the substance used, and so it becomes a very reliable reference. 1. Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, The British University in Egypt, El-Sherouk City, 11837, Egypt, Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Cairo University, Kasr El-Aini Street, Cairo, 11562, Egypt, Pharmaceutical Chemistry Department, Faculty of Pharmaceutical Science & Pharmaceutical Industries, Future University, Cairo, 12311, Egypt, Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Helwan University, Ein Helwan, Cairo, 11795, Egypt, You can also search for this author in Yuksen C, Sricharoen P, Puengsamran N, Saksobhavivat N, Sittichanbuncha Y, Sawanyawisuth K. Eur J Radiol Open. It considered as one of the new applications of double divisor [19] and an extension to the double divisor-ratio difference method (DD-RD) [20] by coupling it with dual wavelength method. To cancel the contribution of Y at the two selected wavelengths upon obtaining the ratio difference, the equality factor of pure ratio spectra of Y at these wavelengths (FY) is calculated. Aliquots equivalent to 10260g DRO, 15260g CAF, 10240g PCT and 10300g PAP were accurately transferred from their working standard solutions into four separate series of 10-mL volumetric flasks then completed to volume with the same solvent. Privacy At the isosbestic point the total absorbance of a solution of the two ions is independent of their . The validity of the proposed methods was further assessed by applying the standard addition technique as presented in Table3. Two light-emitting diodes produce beams at red and infrared frequencies (660 nm and 940 nm, respectively). Progressive evaluation in spectroscopic sensors for non-invasive blood haemoglobin analysis-a review. The first one related the absorbance at 263.6nm versus the corresponding CAF concentrations. Federal government websites often end in .gov or .mil. Non-invasive hemoglobin measurement using embedded platform Different applications of isosbestic points, normalized spectra and EHM collected the data, wrote the manuscript, made the practical work in the lab, and put the theoretical background. Epub 2023 Mar 12. Comparison of time-resolved and -unresolved measurements of - PubMed The obtained D0 of PAP was successively subtracted from the D0 spectrum of the resolved ternary mixture to get the D0 spectrum of binary mixture of CAF and PCT. Zero order absorption spectra of 10g/mL DRO (solid line), 10g/mL PCT (dotted line), 10g/mL CAF (dashed line) and 10g/mL PAP (dashed dotted line). A study of different novel and smart spectrophotometric techniques for resolution of severely overlapping spectra were presented in this work utilizing isosbestic points present in different absorption spectra, normalized spectra as a divisor and dual wavelengths. Iron Deficiency Anemia: Guidelines from the American In Soumadril Compound, Carisopradol which is an open aliphatic structure doesnt show any interference, therefore the mixture acts as a binary mixture of CAF and PCT. eCollection 2020. Talanta 48:11451157, Article CAF and PCT were kindly supplied by Minapharm Pharmaceutical Company, Cairo, Egypt. The authors declare that they have no competing interests. Oxyhaemoglobin and deoxyhaemoglobin have isosbestic points at 590 nm and near 808 nm. 3, but it was difficult to accurately measure the amplitude of DRO at its extended region due to its low absorptivity, so derivative transformation was adopted to overcome this problem. 6a). The magnetic properties of hemoglobin (Hb) and its derivative forms have been documented since the 1930's . 2019 Feb;24(5):1-10. doi: 10.1117/1.JBO.24.5.051411. Two distinguishable light emitting sources (810 nm and 1300 nm) are utilized at isosbestic points with a single photodetector (800-1700 nm). The microprocessor analyses the changesin light absorption during the arterial pulsatile flow and ignores the non-pulsatile component of the signal (which results from the tissues and venous blood). 8600 Rockville Pike HHS Vulnerability Disclosure, Help government site. Then the difference between the amplitudes at the two selected isosbestic points between CAF and PCT (263.6 and 291.8nm) was directly proportional to DRO concentration only. PDF Rapid Determination of Oxygen Saturation and Vascularity - ResearchGate 11a. The ratio spectra obtained using the normalized spectrum of the more extended component Z as a divisor generated a constant value of its concentration along the whole spectra that can be measured from the extended region parallel to the X axis. Intracranial Traumatic Hematoma Detection in Children Using a Portable Near-infrared Spectroscopy Device. cm-1. Initially centered with the, Effect of hemoglobin oxygenation level ( S t O 2 )as measured by, Repeatability of hematoma detector OD measurements ( n = 5 ) for four, Visualization of NIR light in the phantom during hematoma detector operation, as acquired, Effect of CSF layer presence on system sensitivity to 5- and 8.5-cm-diameter intracerebral, NIRS system sensitivity to epi/subdural and subarachnoid hematomas over a range of hematoma, Effect of volume/thickness and depth on detectability in intracerebral hematoma phantoms. USA: University Science Books, 2005. Results indicated high sensitivity to epidural/subdural and subarachnoid hematomas. These reports proposed spectrophotometric [8, 9], TLC [9] and high performance liquid chromatography (HPLC) [8, 10, 11]. First derivative of ratio spectra of CAF (226g/mL) using normalized PCT spectrum as a divisor. Figure 4: An example of isosbestic point (CC BY-4.0; Heesung . (ETH Zurich): A/D-corrin-ring closure by the photochemical A/D-seco-corrin corrin cycloisomerization). The (D0) spectra of CAF were divided by the normalized spectrum of PCT, and then two calibration graphs were constructed. eCollection 2022 Dec 1. 9b. The concentration of PCT was progressively determined by subtraction of the obtained CAF concentration from the total concentration at isosbestic point (iso 263.6nm) recorded before derivatization. -. Continuous (CW) and pulsed light were used for the noninvasive measurement of hemoglobin oxygenation in tissues. Traditionally, a wavelength of 700 nm is used to detect the peak for deoxygenated hemoglobin (Hb R), 800 nm as measure for total hemoglobin (isosbestic point, Hb T), and 850 nm for oxygenated hemoglobin (HbO 2). Serum ferritin testing is . US FDA, Federal Register (1997), Jain J, Patadia R, Vanparia D, Chauhan R, Shah S (2010) Dual wavelength spectrophotometric method for simultaneous estimation of drotaverine hydrochloride and aceclofenac in their combined tablet dosage form. There is a photo detector on the other side. Sep Sci Tech 50:592603, Issa YM, Hassoun ME, Zayed AG (2012) Simultaneous determination of paracetamol, caffeine, domperidone, ergotamine tartrate, propyphenazone, and drotaverine HCl by high performance liquid chromatography. We developed a ratiometric method capable of estimating total hemoglobin concentration from optically measured diffuse reflectance spectra. Interpreting A1C: Diabetes and Hemoglobin Variants The site is secure. Intracerebral hematomas are detectable to a maximum depth of 2.5 cm, depending on thickness and diameter. Scans were carried out in the range from 200 to 400nm at 0.1nm intervals. In this work more than eight novel and smart spectrophotometric methods were developed and validated for the resolution of the quaternary mixtures either successively or progressively. Isosbestic point. [3] The isosbestic points provide proof for a direct conversion of the seco-corrin complex to the metal-free corrin ligand without intermediary or side products (within the detection limits of UV/VIS spectroscopy). The absorption coefficient of a glycogen-iodine complex is 0.20 at light of 450 nm. By John W. Moore, Learn how and when to remove this template message, A/D variant of the total syntheses of vitamin B, https://en.wikipedia.org/w/index.php?title=Isosbestic_point&oldid=1137892749, This page was last edited on 6 February 2023, at 23:40. Cite this article. Talanta 75:258265, El-Gindy A, Emara S, Shaaban H (2010) Validation and application of chemometrics-assisted spectrophotometry and liquid chromatography for simultaneous determination of two ternary mixtures containing drotaverine hydrochloride. Structural formulae for a drotaverine, b caffeine, c paracetamol, d para-aminophenol. For determination of X, two wave lengths were selected in the ratio spectra of the resolved binary mixture. Then their first derivative spectra (D1) were recorded using scaling factor=10 and =8 and a calibration graph was constructed relating the amplitude of the obtained (D1) spectra of PAP at 314.5nm versus the corresponding concentrations. and transmitted securely. 8600 Rockville Pike Chang, Raymond. Eur J Pediatr. While PAP was determined adopting two methods; first derivative spectrophotometric method and double divisor-ratio difference-dual wavelength. Spectrochim Acta A Mol Biomol Spectrosc 150:142150, Lotfy HM, Hegazy MA (2013) Simultaneous determination of some cholesterol-lowering drugs in their binary mixture by novel spectrophotometric methods. The concentration of Y is calculated using the same procedure after calculating the equality factor of pure X (FX) at the two chosen wavelengths for Y. Two wavelengths are selected (iso of CAF 263.6nm and 2=231.5nm) where PCT shows equal absorbance at these wavelengths. By screening the ratio spectra of pure CAF divided by the normalized spectra of DRO, two wavelengths were selected, 265 and 295nm, where 265nm showed the maximum peak in order to obtain maximum sensitivity. Currently, various techniques are underway in the allied domain, and scanty products are also feasible in the market. By scanning the absorption spectra of DRO, CAF, PCT and PAP in the solution of dosage forms in methanol, severely overlapped spectral bands were observed in the wavelength region of 200300nm; which hindered their direct determination (Fig. However, due to the low satisfaction rate, invasive solutions are still assumed as the gold standard. Thus, ratios other than 1-to-1 are possible. , Clinical evaluation of a portable near-infrared device for detection of traumatic intracranial hematomas, J. Neurotrauma 27(9), 15971604 (2010).JNEUE410.1089/neu.2010.1340 What is the significance of the isosbestic point? sharing sensitive information, make sure youre on a federal Irwin H. Segel, Biochemical Calculations (How to Solve Mathematical Problems in General Biochemistry), 2nd edition, John Wiley & Sons, 1975.

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