A new method for the detection of microorganisms in blood cultures: Part I. Theoretical analysis and simulation of blood culture processes.
Methods to detect the presence of microorganisms in blood cultures have been in existence for many decades and serve as a very important diagnostic tool. Sepsis, defined as the presence of pathogens in the blood stream, is currently the 10th leading cause of death in the United States and the number of reported cases has been steadily increasing with an ageing population (Angus et al., 2001). Early detection and identification of pathogens in blood is critical to the selection of proper therapies and, thus, patient outcome (Brindley et al., 2006).
Blood culturing systems available today are based on creating optimal conditions for microbial growth under aerobic and anaerobic environments coupled with the detection of microbial metabolic products and gases resulting from the growth of microorganisms (Berndt, 1995, 1998). The presence of metabolic gases, C[O.sub.2] in particular, can be detected in several ways: by measuring changes in the gas pressure of the head space of the blood culture vial, by measuring the differences in the colour of an indicator added to the blood culture bottle for this purpose, and/or by labelling the carbon in the growth media such that metabolic C[O.sub.2] becomes easily detectable in the headspace of the culture bottle. Measurement of the changes in the optical properties of the immobilized indicators induced by changes in C[O.sub.2] is done directly through the culture bottles using spectrophotometric techniques (reflection, transmission, fluorescence, etc.) at a small number of discrete wavelengths. The production of metabolic gases can be measured via pressure-sensitive methods and/or spectrometric measurements particular to the type of label used for the carbon (i.e., scintillation, radiometric, etc.) (Schrot et al., 1973). Other methods based on spectrophotometric measurements are aimed at the direct comparison of the spectral features of organisms grown in standard media and in blood culture bottles (Cross and Latimer, 1972). Other approaches have included the measurement of the properties of back-scattered light from dissolved indicator dyes in blood culture froths (Berndt, 1998).
All of the methods described above are limited by the rate of growth of the microorganisms and have sensitivities that depend on the particular measurement technique and the following factors:
1. The rate of production of metabolic C[O.sub.2] or other metabolic gases.
2. The transport of the metabolic products to an indicator dye. Typically the dyes are immobilized in a solid matrix that is integrated with the culture bottle for ease of detection.
3. The time constant associated with reaction of metabolic products and the indicator dyes.
4. The transport of metabolic gases from the liquid culture media to the bottle headspace.
The time to detection of microorganisms depends on the sensitivity of the measurement technique, the time required to reach the minimum detectable metabolic gas concentration (primarily C[O.sub.2]), and on the transport and reaction time constants. The rate of microbial growth, and therefore the rate of production of metabolic gases, depends on the initial concentration of organisms (CFU/mL blood) and on the incubation conditions (growth media, temperature, etc.). The detection systems described in the literature typically require between [10.sup.8]-[10.sup.9] CFU/mL for positive detection with an incubation, or amplification time, corresponding to the specific growth rate of each organism.
In a series of three papers a new approach for the detection of microorganisms in blood cultures is reported. The proposed approach uses the changes induced by the presence of microorganisms on the physical and chemical properties of the blood sample for the detection of microbial pathogens. Part I of this series reports on the theoretical analysis and computer simulation of the changes in the physical and chemical properties of blood expected as a result of the presence of microorganisms and explores the possibilities of the direct application of spectrophotometric systems for the early detection of pathogens. Part II reports on the quantitative evaluation of multi-wavelength reflectance spectra of blood (Serebrennikova et al., in preparation). Part III combines the work of Part I and II and applies the quantitative interpretation to experimental blood culture data (Huffman et al., in preparation).
Blood culturing systems are bio-reactors and as such they can be analyzed using the standard mass and energy balances used for the description of other types of chemical and biological reactors (Levenspiel, 1972a,b; Senfield and Lapidus, 1973; Fogler, 1992). In this context, blood culture vials fall in the categories of batch or semi-batch reactors, with the reagents being introduced in two steps. In the first step the growth media is introduced into the vial under sterile conditions and the composition of the headspace is adjusted depending of whether the culture is targeting aerobic or anaerobic microorganisms. In the second stage, blood containing microorganisms is added to the vial through a septum and the vial is incubated at constant temperature, typically 37[degrees]C until a positive sample is detected. In several commercial systems some form of agitation is provided. The growth media contains the necessary nutrients for microbial growth. Typically, the nutrients are in excess such that they do not become a limiting reagent to the growth process. In most situations the concentration of microorganisms in blood, at the time of inoculation, is very low (1-10 CFU/mL of blood; Kellogg et al., 1984) and therefore below the detection level of most sensing systems. The presence of microorganisms has a negligible effect on the physical and chemical properties of the blood sample at the time of addition to the blood culture bottle due to their low concentrations.
Because blood culture systems are generally closed, the metabolic products from the organisms accumulate in the vial and distribute between the vapour (head space), the liquid (culture media and plasma), and the solid (immobilized indicator, particulates) phases present. The particulates in this case are primarily the red blood cells (RBCs), although initially there will also be white blood cells, platelets, and microorganisms which are capable of respiration (Daland and Isaacs, 1927; Kitchens and Newcomb, 1968; Andersen and Vonmeyenburg, 1980). As time evolves the number of contaminant organisms will increase and give rise to increasing concentrations of their metabolic products which interact with different blood components. Figure 1 shows a schematic of a blood culture vial with an immobilized indicator system.
At time t = [0.sup.-], prior to inoculation with the blood sample, the blood culture vial with sterile nutrient broth is assumed to be in equilibrium (i.e., the composition of the head space is in thermodynamic equilibrium with the liquid phase at room temperature and pressure). At time t = [0.sup.+] all the blood sample has been introduced into the vial initiating the adjustment of physical and chemical parameters of blood to the physical and chemical environment of the vial (i.e., temperature, osmolarity, composition, pH). The possible physical adjustments include changes in shape, volume (swelling, contraction), and number density (hemolysis) of erythrocytes and other blood components. Simultaneously, changes in the chemical composition also occur in the [O.sub.2]-C[O.sub.2] state of the vial which in turn dictates the chemical form of haemoglobin.
The number density of microorganisms increases over the incubation period of the blood culture. The microbial metabolic respiratory activity produces changes in the chemical composition in the blood culture vial, for example, a reduction in the partial pressure of [O.sub.2] and a corresponding increase the partial pressure of C[O.sub.2]. These chemical changes drive the haemoglobin equilibrium from oxy-haemoglobin (Hb[O.sub.2]) toward deoxy- (Hb) and carbamino-haemoglobin (HbC[O.sub.2]). In the absence of microorganisms, the red blood cells will age slowly, eventually lysing and the haemoglobin present converting to met-haemoglobin (metHb) over a few days. If hemolysis occurs as a result of the fragility of the red blood cells, and/or as a result of the production of hemolysins by certain bacteria (i.e., Clostridium perfringens), two effects will be observed; a decrease in the red blood cell density, and an increase in the concentration of free haemoglobin in the liquid phase. It is noteworthy that the physical and chemical changes occurring in blood as a result of the presence of microorganisms, as well as the growth behaviour or microorganisms, can be quantitatively measured using spectrophotometric methods (Mendelson, 1992; Flewelling, 2000; Alupoaei and Garcia-Rubio, 2004, 2005; Alupoaei et al., 2004).
[FIGURE 1 OMITTED]
Like most bio-reactors, blood culturing systems are rather complex. To make the problem tractable a series of assumptions and approximations have been made:
* The bio-reactor is assumed to be well-mixed, each phase being homogeneous, and to operate under isothermal conditions.
* Nutrients are in excess such that their concentration can be assumed to remain constant.
* The buffering capacity of the growth media enables the pH to remain approximately constant.
* Only three forms of haemoglobin are considered: oxy-, deoxy-, and carbamino-haemoglobin.
* The initial equilibration between blood and the environment of blood culture is assumed to occur instantaneously at t = 0.
* The reactivity of haemoglobin to microbial metabolic products is greater than the time step of the model.
* Haemoglobin composition is always in chemical equilibrium with the state of the blood culture vessel.
* Of all the possible impacts on haemoglobin composition due to metabolic activity, only the transitions amongst oxy-, deoxy-, and carbamino-haemoglobin are considered.
* The consumption of one mole of [O.sub.2] in respiration produces one mole of C[O.sub.2].
Under the above assumptions it is possible to provide a general mathematical description of the processes occurring within aerobic blood culture vials. This description can then be used for the quantitative evaluation of the cultures.
The physical dimensions of the blood components, primarily the erythrocyte population, have an effect on the optical measurements of blood. The detailed discussion of these effects is the subject of a forthcoming publication (Part II of this series, Serebrennikova et al., in preparation). An example of the physical changes to the erythrocytes can be expressed by the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [V.sub.rbc,0] corresponds to the initial or physiological red cell volume, [[DELTA].sub.0] is the maximum volume increase, and [k.sub.sw] is the swelling rate constant in ([min.sup.-1]). Both, [[DELTA].sub.0] and [k.sub.sw] are functions of the particular blood sample, temperature, osmolarity, composition, and pH of the growth media.
Swelling implies that fluid is being drawn into red blood cells causing the mean corpuscular haemoglobin concentration to decrease. The volume fraction of haemoglobin in the erythrocytes can be estimated as:
[f.sub.Hb](t) = [f.sub.Hb,0] ([V.sub.rbc,0]/[V.sub.rbc](t)) (2)
These effects become important in Equation (10) and are manifest in the macroscopic scattering cross-sections (Eqs. 11-12).
At each time step in the model the state of cell populations and haemoglobin in the blood sample is a function of the physical and chemical environment of the blood culture vial. For the cases studied in this paper we assume that the environmental parameters such as osmolarity, pH, and temperature of incubation remain constant throughout the experiment as set at time zero. Therefore, the only temporal changes we consider are the changes in the chemical composition in the blood culture vial. Those chemical changes include changing gas composition ([O.sub.2] and C[O.sub.2]) within the vial as a result of metabolism of blood components and microorganisms. The primary effect of these chemical changes is on haemoglobin composition, that is, conversion between its forms. For example, the depletion of [O.sub.2] in the system leads to the dissociation of oxy-haemoglobin producing deoxyhaemoglobin and liberated [O.sub.2]. The reaction of deoxyhaemoglobin with C[O.sub.2] produces carbamino-haemoglobin as shown in Equation (3). Total haemoglobin in the modelled system is the sum of three forms of haemoglobin and is assumed to be conserved (Eq. 4). Further, reaction of haemoglobin with certain reagents and/or microbial metabolic products might lead to formation of other haemoglobin forms such as methemoglobin, carboxy-haemoglobin, sulfa-haemoglobin (Stadie, 1921; Pauling, 1952; Park and Nagel, 1984). The specific model cases for such scenarios require additional terms in haemoglobin balance equations and will be discussed in subsequent publications. In this paper we focus on the three main forms of haemoglobin
HbC[O.sub.2] [left and right arrow] Hb [left and right arrow] Hb[O.sub.2] (3)
[[Hb.sub.T]] = [Hb] + [Hb[O.sub.2]] + [HbC[O.sub.2]] (4)
The equilibrium between Hb, Hb[O.sub.2], and HbC[O.sub.2] is governed by the partial pressures of [O.sub.2] and C[O.sub.2] in the system and is assumed to occur instantaneously since the gas exchange through the erythrocyte membrane is relatively fast due to its high surface area (Constantine et al., 1965) and, therefore, the Hb[O.sub.2]-Hb-HbC[O.sub.2] equilibrium reflects the chemical composition of the blood culture vial. The dynamics of the reactions between haemoglobin, [O.sub.2] and C[O.sub.2] is well understood and there is a large body of mathematical models addressing the [O.sub.2]-C[O.sub.2] exchange with blood and the main variables affecting its equilibrium (Mendelson, 1992; Flewelling, 2000). These models can be readily adapted for the description of the equilibration processes taking place in the blood cultures. For the simulations reported herein the model proposed by Dash and Bassingthwaighte (2004, 2006) is used for the equilibrium binding of [O.sub.2] and C[O.sub.2] with haemoglobin inside red blood cells. This model has the advantage of including the effect of the gas composition as well as the effects of temperature, pH, and osmolarity.
In addition to haemoglobin, the gas composition of a blood culture system is affected by the respiration of other blood components such as leukocytes and platelets, and when contaminated, microorganisms. Respiration rates under specific conditions have been measured and rigorous models accounting for the electron transport chain, the biomass, and the energy available from the environment have been developed (Jin and Bethke, 2007). Since these models are general and provide the links between substrates and metabolic products, they are to be deployed in the cases when the effects of metabolic products are considered. Here we have chosen to represent the [O.sub.2] consumption and C[O.sub.2] production with a simple approximation (Eq. 5), that is, for each molecule of [O.sub.2] consumed one molecules of C[O.sub.2] is produced. It is a reasonable assumption for the substrate-rich environment such as that in the blood culture vials (Andersen and Vonmeyenburg, 1980; Jin and Bethke, 2007)
[C.sub.6][H.sub.12] + 6[O.sub.2] [??] 6[H.sub.2]O + 6C[O.sub.2] (5)
In the model the changes in the amounts of total [O.sub.2] and C[O.sub.2] in the vials are assumed to be strictly due to respiration of the cell populations present. Equation (6) describes the general respiration structure of the model that assumes the total [O.sub.2] loss to be a sum of the [O.sub.2] consumption by J cell populations and being functions of the population number density [N.sub.j] and assigned respiration rate [k.sub.rj],
d[O.sub.2]/dt = [J.summation over (j=1)] [k.sub.rj][N.sub.j](t) = dC[O.sub.2]/dt (6)
Typically contaminating microorganisms dominate [O.sub.2] consumption in the blood culture vials due to their high metabolic respiration rates. Yet, in the cases of leukemia or thrombocytosis leukocytes or platelets, respectively, might utilize most of the available [O.sub.2] (Qian et al., 2001; Mehta et al., 2008) especially when microbial counts are low.
In the model the evolution of the number density of the jth cell population, [N.sub.j](t), as a function of time was approximated using a logistic growth model (Madigan et al., 2000):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
The growth/decay rate constants [k.sub.Dj], and typical values of [N.sub.[infinity]j], and [N.sub.0j], for modelled cell populations are given in Table 1. The models for cell growth and respiration present an interesting possibility for a preliminary classification of microorganisms. The growth/decay constant, [k.sub.Dj], and the respiration rate, [k.sub.rj], vary among organisms and, depending upon how they cluster over a wide range of species, hold the potential to discriminate among various groups of pathogens. The magnitudes of these parameters dictate the time to detection. For example, Yebenes et al. (2006) demonstrate the principle of varying growth rates on the time to detection. The fast-growing bacterium E. coli had a typical time to detection of 10 h while the slower growing fungus Candida albicans was approximately 24 h for an inoculum of [10.sup.3] organisms.
The modelled consumption of [O.sub.2] and production of C[O.sub.2] are proportional to the number of cells, which, in turn, changes as cells grow (microorganisms) or decay (leukocytes, platelets). At each time point, [O.sub.2] and C[O.sub.2] are distributed between the gas and liquid phases of the modelled blood culture vials and affect the chemical form of haemoglobin (Eq. 3). The modelled C[O.sub.2] equilibrium also includes the pH-dependant dissociation of carbonic acid (Dash and Bassingthwaighte, 2004). Given that the rates of the gas transport between vapour and liquid phases are much greater than the rates of C[O.sub.2] production and [O.sub.2] consumption, we assumed the overall equilibrium of gases distribution in the blood culture vials to be achieved instantaneously
[[O.sub.2T]](t) = [[O.sub.2vap]](t) + [[O.sub.2liq]](t) + [[O.sub.2HB]](t)
= [[O.sub.2T]]t = 0 - [J.summation over (j=1)] [k.sub.rj][N.sub.j](t) (8)
Further assumptions made in the model include ideal gas behaviour for the vapour phase of the blood culture vials and applicability of Henry's law for the liquid phase. From this and the haemoglobin [O.sub.2]-C[O.sub.2] dynamics discussed above, the distribution of gases between the vapour phase, the liquid phase, and haemoglobin is evaluated with standard vapour-liquid equilibrium calculations (Dash and Bassingthwaighte, 2004).
Observation and measurement methods
The state of the blood culture system can be evaluated using a variety of measurements that reflect the changes in [O.sub.2] and C[O.sub.2] concentrations. The most commonly used techniques have been described in the introduction section. However, spectroscopic measurements of blood have great appeal due to distinct differences in optical properties among the forms of haemoglobin (Steuer et al., 1999). Herein we propose the use of diffuse reflectance measurements. We find it to be the most suitable since reflectance is sensitive to both absorptive and scattering properties of blood and thus allows for simultaneous changes in the chemical and physical characteristics of blood invoked by metabolic activities.
In this paper we present the expected changes in the spectral features of a blood sample contained within a blood culture vial as it can be measured with diffuse reflectance. To model the diffuse reflectance spectra of blood any number of relevant mathematical/numerical methods can be used, for instance, Monte-Carlo simulations, Kubelka-Munk theory, Photon diffusion models, etc. (Reynolds et al., 1976; Molenaar et al., 1999; Zonios and Dimon, 2006). We choose to simulate the diffuse reflectance spectra with a photon diffusion approximation.
Here we would like to note that we use an effective solution for diffusely reflected intensity ([R.sub.x]([lambda])) for an arbitrary detector aperture ([r.sub.x]) concentric with the source of radius a and separated from the source by distance [r.sub.b] as following those reported in literature (Reynolds, 1975; Ishimaru, 1978) and is expressed as:
[R.sub.x] ([lambda]) = [r.sup.2.sub.x]/[r.sup.2.sub.2] + [r.sup.2.sub.1] ([R.sub.x]([r.sub.2]) - [R.sub.x]([r.sub.1])) (9)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
The terms of the Equations (9) and (10) are defined as:
[r.sub.1] [r.sub.b] - b [r.sub.2] [r.sub.b] + b [D.sub.f] photon diffusion constant [D.sub.f] = 1/3 ([[mu]. sub.st] + [[mu].sub.a]) [I.sub.0], [K.sub.0], Zeroth and first-order modified Bessel [I.sub.1], [K.sub.1] functions of first and second kind, respectively [k.sub.n] the nth eigenvalue of the Green's function defined by tan([k.sub.n]d) = -2.142[D.sub. f][k.sub.n] [N.sub.n] eigenvalue normalization constant [N.sub.n] = (2[k.sub.n]d + sin 2[[gamma].n] - sin(2 [k.sub.n]d + 2[[gamma].sub.n])) /4[k.sub.n] r radius of observation d thickness of the sample [z.sub.n] the nth term of the dependence series of distance along the axis of incident light [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [[gamma].sub.n] phase function [[gamma].sub.n] = arctan(2. 142[D.sub.f][k.sub.n]) [[zeta].sub.n] Bessel function parameter of the nth order [[zeta.sup.2.sub.n] = [k.sup.2.sub.n] + [[mu].sub.a] ([lambda])/[D.sub.f] [[mu.sub.t]([lambda]) total (absorption + scattering) macroscopic cross-section [[mu].sub.t]([lambda]) = [[mu] .sub.s]([lambda])+ [[mu].sub.a]([lambda]) [[mu].sub.st]([lambda]) reduced macroscopic scattering cross-section [[mu].sub.st]([lambda]) = (1 - <[mu]>) [[mu] .sub.s]([lambda]) <[mu>] asymmetry parameter defined as the average cosine of the scattering angle.
The absorption and scattering macroscopic cross-sections are defined as follows:
[[mu].sub.a] ([lambda]) = [N.sub.p][C.sub.abs](m([lambda]),D) (11)
[[mu].sub.s] ([lambda]) = [N.sub.p] (1 - [N.sub.p][V.sub.p])[C.sub.sca](m([lambda]),D) (12)
In these equations, [N.sub.p] is the cell density, [C.sub.abs], and [C.sub.sca] are the microscopic absorption and scattering cross-sections and are functions of the particle sizes (D) and of the wavelength dependent complex refractive indices of the particles (m([lambda])). The microscopic cross-sections were calculated using Mie scattering theory (Kerker, 1969). Yet, other scattering theories such as Rayleigh-Debye-Gans, Fraunhofer, anomalous diffraction theories, etc., can be used (van de Hulst, 1957; Wiscombe, 1979).
Model testing and validation
The basic elements of the model, cell respiration and equilibrium considerations, have been tested against experimental data obtained in our laboratories and at Los Alamos National Laboratories (Claro Scientific, 2008, unpublished data). The logistic growth model is well accepted in the literature (Madigan et al., 2000) and has been successfully tested against measured particle count data from pure culture batch experiments (Alupoaei, 2001; Alupoaei et al., 2001, 2002a,b; Garcia-Rubio et al., 2005). The respiration rates of leukocytes and platelets used in our model are consistent with those reported in literature. The Mie scattering algorithm used in the model has been evaluated previously for the estimation of the distributions of particle sizes (Alupoaei, 2001) and tested extensively against available computer codes and published tables (Wiscombe, 1979; Bohren and Huffman, 1983). The refractive index of water and haemoglobin forms are from the literature (Thormahlen et al., 1985; Nonoyama, 2004). The complete reflectance model has been successfully used in the analysis of blood culture data and is described in detail in Claro Scientific (2007). The model parameters and blood characterization data used in this study are reported in Table 1.
To demonstrate the capabilities of the integrated process-measurement model and the sensitivity of the reflectance spectroscopy model for the detection of bacterial growth, three case studies addressing key process and measurement variables are reported:
* Case I demonstrates the results from the model for the reference data shown in Table 1 for both a control and a contaminated sample.
* Case II reports on the effect of the blood sample volume, an important parameter for current blood culture technology.
* Case III demonstrates an example where the blood composition is changed with increased white blood cell counts. This case is representative of septic and leukaemic patients and is a possible cause of false positives with current detection methods.
Case Study I
Figure 2 contrasts microbial growth with the decay of platelet and leukocyte populations for venous blood using the reference data shown in Table 1 (10 ml, blood; pp[O.sub.2] = 30 mmHg; PPC[O.sub.2] = 50 mmHg). Both the parameter values selected and the cell densities are typical of what is encountered in practical situations. The doubling time for the microorganism is within the range of aerobic bacteria grown in nutrient rich media. Figure 3 shows the fractional consumption of oxygen by each of the cell populations.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
The respiration of white blood cells and platelets initially dominate the [O.sub.2] consumption causing a corresponding decrease in the oxygen partial pressure. Note that although platelets are more numerous, the specific respiration rate of the white blood cells is such that the oxygen consumption is approximately the same for each population. The microorganisms are the most active population with a relatively high metabolic rate and have continuously increasing numbers. The microbial growth results in a high rate of oxygen consumption which is clearly evident during the log phase of the growth (~4-G h). The distribution of [O.sub.2] and C[O.sub.2] between the liquid and gaseous phases present in the culture bottles is shown in Figure 4 as a function of time for a control sample and a sample contaminated with 100 microbial CFU/mL of blood. The pressure in the vial is that resulting from the contributions of water, oxygen and carbon dioxide (the system is under vacuum). In the case of the control (no microorganisms), the pressure stabilizes once the populations of white blood cells and platelets become inactive. In the case of a contaminated sample, the decrease in [O.sub.2] partial pressure continues unabated at a rate proportional to the bacterial growth: a function of its specific growth rate and respiration rate. The point at which the two lines separate can be used to detect the presence of microorganisms.
[FIGURE 4 OMITTED]
The changes in the chemical composition of haemoglobin are shown in Figure 5. The variation in the concentrations of oxy-, deoxy-, and carbamino-haemoglobin are the result of the changes in the partial pressures of oxygen and carbon dioxide throughout the evolution of the process. The ratio of deoxy- to oxy-haemoglobin (Hb]/[Hb[O.sub.2]) is sensitive to changes in partial pressures and is shown in Figure G. Note that the ratio (Hb]/[Hb[O.sub.2]) can be obtained directly from reflectance measurements.
The reflectance spectra, as described in Equations (9)-(12), are functions of the cell densities (Eqs. 11-12), the changes in the physical and chemical properties of blood (Eqs. 1-4), and the absorption and scattering properties of the cell populations present in the mixture (Eqs. 11-12). In addition, the effect of the chemical composition is introduced directly through the additive properties of the complex refractive index (Alupoaei and Garcia-Rubio, 2004, 2005; Alupoaei et al., 2004). The reflectance model is comprehensive relative to the measurement variables. The results reported herein focus on the variables relevant to changes in the chemical composition of haemoglobin. Figure 7 shows the reflectance spectra for the blood properties listed in Table 1 for each of the two principal forms of haemoglobin for reference (oxy- and deoxy-haemoglobin). Notice the distinct spectra features characteristic of each haemoglobin species; in the measurement mode, these distinct features enable an accurate quantitative spectral deconvolution. Using the properties of the blood included in Table 1, the physical and chemical changes represented by Equations (1)-(4), and the changes in chemical composition shown in Figure 7, it is possible to quantitatively predict the evolution of the reflectance spectra as a function of time. Figure 8 shows the spectra over the complete time course of the experiment.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
Case Study II
The volume of blood inoculated into the blood culture bottles constitutes an important parameter for two reasons. For the low pathogen numbers, an increase in the blood volume leads to a higher likelihood that the sample contains the pathogen (Mermel and Maki, 1993). From the measurement sensitivity point of view, different blood volumes result in different distributions of oxygen and carbon dioxide between the liquid and vapour phases. Since the liquid phase acts as a capacitor for C[O.sub.2] and the vapour phase acts as a capacitor for [O.sub.2], changes in the amount of blood injected can be expected to affect the partial pressure of [O.sub.2]. The optimal sample has the largest concentration of microorganisms in the smallest blood volume.
The effect of the addition of different volumes of blood (2, 5, 10, and 20 mL; pp[O.sub.2] = 30 mmHg, PPC[O.sub.2] = 50 mmHg) on the [O.sub.2] and C[O.sub.2] partial pressures is shown in Figure 9. As the volume of blood increases not only do the partial pressures increase substantially, but the baseline for the determination of bacterial growth becomes less distinguishable. As a consequence, indication as to whether or not there is bacterial growth present is delayed until the organisms are in the log phase.
An advantage of spectrophotometric measurements is that they are self-calibrating in the sense that a spectral deconvolution yields quantitative information on the hematocrit and the relative concentration of deoxy- and oxy-haemoglobin during the early stages of the blood culture. Figure 10 shows the corrected ratio of [Hb]/[Hb[O.sub.2]] obtained in this manner. As expected, an increased volume of the blood sample provides a larger initial concentration of microorganisms and as a result, a shorter time to detection.
Case Study III
When blood culture detection systems are based only on the production of C[O.sub.2] as a measure of microbial growth, the respiration of other cells (leukocytes and platelets) may become a confounding factor especially if it results in a false positive culture. This is of particular importance in the case of septic and leukaemic patients who have elevated concentrations of leukocytes. While only the effects of normal respiration are being considered in this case, leukocytes can also react to the presence of pathogens and are known to generate a respiratory burst in which [O.sub.2] consumption can increase by two- to threefold in the process of destroying the microorganisms (Lee, 1999).
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
Using the parameters of blood from Case I, Figures 11 and 12 illustrate the changes the partial pressures of C[O.sub.2] and [O.sub.2] in the headspace of an infected blood culture for both normal (5000 WBC/[micro]L blood) and elevated leukocyte levels (50 000 and 250 000 WBC/[micro]L blood). It becomes more difficult to uniquely distinguish the contribution of microbial metabolism from the respiratory processes of the blood itself from the perspective of a direct total pressure or partial pressure measurement. On the other hand, spectrophotometric measurements of the reflectance spectra and their deconvolution, in terms of oxy- and deoxy-haemoglobin, reveal unique changes that can be linked directly to the presence of bacterial growth. Furthermore, the haemoglobin composition can be readily corrected to enable the detection of microorganisms by use of the quantitative information pertaining to the hematocrit and the relative concentration of oxy- and deoxy-haemoglobin during the early stages of the blood culture. Figure 13 shows the evolution of the haemoglobin composition (Hb]/[Hb[O.sub.2]) in a blood culture as function of time for the three leukocyte concentrations under consideration.
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
An experimental data set was generated to test the robustness of the model. Two blood culture bottles (BacT/Alert BPA, bioMerieux, Durham, NC) were inoculated with 10 ml, of normal healthy blood containing approximately 25 CFU of E. coli (ATTC strain #25922; Manassas, VA). One of the seeded bottles was placed into the BacT/ALERT 3D system for comparison. A control bottle, inoculated with 10 ml, of blood from the same donor, was run as well. The bottles were incubated at 37[degrees]C and reflectance measurements were taken every 2 min over a period of 11 h. Figure 14 shows representative reflectance spectra of the seeded bottle taken at select time points over the course of the experiment. Similar to Figure 8, the reflectance spectra progress from oxyhaemoglobin to deoxy-haemoglobin in the presence of actively respiring and reproducing bacteria.
[FIGURE 13 OMITTED]
[FIGURE 14 OMITTED]
As demonstrated in Figure 15 the ratio of [Hb]/[Hb[O.sub.2]] from the bottle containing bacteria diverges from the control between hours 9 and 10, which is at least 2 h prior to the positive call for the bottle placed in the BacT/ALERT 3D system (12.2 h). Figure 16 reports the corresponding pressures in the headspace over the duration of the experiment. In agreement with the simulation (Figure 9), both the total pressure and the partial pressure of oxygen decline dramatically as the bacterial respiration exerts its influence on the chemical equilibrium. The high solubility of C[O.sub.2] results in a less pronounced shift in the partial pressure of C[O.sub.2] in the headspace.
[FIGURE 15 OMITTED]
[FIGURE 16 OMITTED]
The theoretical and computer simulation of the changes in the physical and chemical properties of blood expected as a result of the presence of microorganisms in blood culture bottles has been conducted to explore the possibilities of spectrophotometric systems for the early detection of pathogens in sepsis cases. Observable changes such as the conversion between oxy-, deoxy-, and carbamino-haemoglobin are accessible through the measurement of the reflectance spectra of blood culture vials. Among the advantages of reflectance measurements are the fact that they are non-destructive and can be easily configured for real-time monitoring of blood culture vials. Haemoglobin is also present in large concentrations and is well dispersed through the culture media either contained within intact erythrocytes or free in solution (from lysed erythrocytes). Exploiting haemoglobin as an intrinsic indicator of the presence of organisms eliminates the need for immobilized indicators, thus simplifying manufacturing costs without a loss in sensitivity. Furthermore, use of the quantitative theoretical deconvolution of the initial data provides a self-calibration feature that eliminates the need for external calibrations and results in a superior interpretation of the data. The three cases presented in combination with experimental data highlight the main features of the proposed approach and demonstrate the robustness of the model's skill in detecting changes in key variables that may result in false positives using conventional measurement techniques. Future model enhancements will account for additional changes in the blood culture system such as additional forms of haemoglobin (e.g., met-haemoglobin) and other physical changes occurring to the erythrocyte population (e.g., swelling, lysis, and crenation).
The authors would like to acknowledge the support of Claro Scientific LLC, Florida Blood Services, and the College of Marine Science, University of South Florida. We would also like to recognize the thoughtful suggestions of the reviewer.
Manuscript received March 18, 2008; revised Manuscript received Jime 9, 2008; accepted for publication June 17, 2008.
Alupoaei, C. E., "Modeling of the Transmission Spectra of Microorganisms," Master of Science Thesis, University of South Florida, Tampa (2001).
Alupoaei, C. E. and L. H. Garcia-Rubio, "Growth Behaviour of Microorganisms Using UV-Vis Spectroscopy: Escherichia coli," Biotechnol. Bioeng. 86, 163-167 (2004).
Alupoaei, C. E. and L. H. Garcia-Rubio, "An Interpretation Model for the UV-VIS Spectra of Microorganisms," Chem. Eng. Commun. 192, 198-218 (2005).
Alupoaei, C. E., J. A. Olivares and L. H. Garca-Rubio, "An Interpretation Model for the UV-vis Spectra of Microorganisms: Applications to the Analysis of Bacterium Vegetative Cells and Spores," Rep. LA-UR015529, Los Alamos National Laboratory, Los Alamos, New Mexico (2001).
Alupoaei, C. E., J. A. Olivares and L. H. Garca-Rubio, "Growth Behaviour of Microorganisms using UV-vis Spectroscopy: E. coli and P. agglomerans," Rep. LA-UR026721, Los Alamos National Laboratory, Los Alamos, New Mexico (2002a).
Alupoaei, C. E., J. A. Olivares and L. H. Garca-Rubio, "Quantitative Analysis of Prokaryotic Cells: Vegetative Cells and Spores," Rep. LA-UR026586, Los Alamos National Laboratory, Los Alamos, New Mexico (2002b).
Alupoaei, C. E., J. A. Olivares and L. H. Garcia-Rubio, "Quantitative Spectroscopy Analysis of Prokaryotic Cells: Vegetative Cells and Spores," Biosens. Bioelectron. 19, 893-903 (2004).
Andersen, K. B. and K. Vonmeyenburg, "Are Growth Rates of Escherichia coli in Batch Cultures Limited by Respiration?" J. Bacteriol. 144, 114-123 (1980).
Angus, D. C., W T. Linde-Zwirble, J. Lidicker, G. Clermont, J. Carcillo and M. R. Pinsky, "Epidemiology of Severe Sepsis in the United States: Analysis of Incidence, Outcome, and Associated Costs of Care," Crit. Care Med. 29, 1303-1310 (2001).
Berndt, K. W, Blood culture sensor station utilizing two distinct light sources, United States Patent June 6, 1995.
Berndt, K. W, Method and apparatus for detecting bacteria using a blood culture froth, United States Patent June 23, 1998.
Bohren, C. F. and D. R. Huffman, "Absorption and Scattering of Light by Small Particles," John Wiley and Sons, New York (1983).
Brindley, P. G., N. Zhu and W Sligl, "Best Evidence in Critical Care Medicine--Early Antibiotics and Survival from Septic Shock: It's about Time," Can. J. Anaesth. 53, 1157-1160 (2006).
Claro, S., United States Patent protection pending (2007).
Constantine, H. P., M. R. Craw and R. E. Forster, "Rate of Reaction of Carbon Dioxide with Human Red Blood Cells," Am. J. Physiol. 208, 801 (1965).
Cross, D. A. and P. Latimer, "Angular Dependence of Scattering from Escherichia coli Cells," Appl. Opt. 11, 1225 (1972).
Daland, G. A. and R. Isaacs, "Cell Respiration Studies. II. A Comparative Study of the Oxygen Consumption of Blood from Normal Individuals and Patients with Increased Leucocyte Counts," J. Exp. Med. 46, 53-563 (1927).
Dash, R. K. and J. B. Bassingthwaighte, "Blood Hb[O.sub.2] and HbC[O.sub.2] Dissociation Curves at Varied [O.sub.2], C[O.sub.2], pH, 2,3-DPG and Temperature Levels," Ann. Biomed. Eng. 32, 1676-1693 (2004).
Dash, R. K. and J. B. Bassingthwaighte, "Simultaneous Blood-Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion," Ann. Biomed. Eng. 34, 1129-1148 (2006).
Flewelling, R., Noninvasive Optical Monitoring, in "The Biomedical Engineering Handbook," J. D. Bronzino, Ed., CRC Press LLC (2000), pp. 86-81-85-11.
Fogler, S. H., "Elements of Chemical Reaction Engineering," Prentice Hall, Englewood Cliffs, NJ (1992).
Garcia-Rubio, L. H., C. E. Alupoaei, D. E. Huffman, T. Berg and A. Brooke, "Novel Spectroscopy Methods for Identification and Discrimination of Microorganisms, Final Report," Rep. Grant No: DAAD13-02-C-0080, University of South Florida Center for Biological Defense (2005).
Huffman, D. E., J. M. Smith, Y. M. Serebrennikova and L. R. Garcia-Rubio, "A New Method for the Detection of Microorganisms in Blood Cultures: Application of the Quantitative Interpretation to Blood Cultures," (in preparation).
Ishimaru, A., "Wave Propagation and Scattering in Random Media," Academic Press, New York (1978).
Jin, Q. and C. M. Bethke, "The Thermodynamics and Kinetics of Microbial Metabolism," Am. J. Sci. 307, 643-677 (2007), 10.2475/04.2007.01.
Kellogg, J. A., J. P. Manzella and J. H. McConville, "Clinical Laboratory Comparison of the 10-ml, Isolator Blood Culture System with BACTEC Radiometric Blood Culture Media," J. Clin. Microbiol. 20, 618-623 (1984).
Kerker, M., "The Scattering of Light, and Other Electromagnetic Radiation," Academic Press, New York (1969).
Kitchens, C. S. and T. F. Newcomb, "Human Platelet Respiration," J. Appl. Physiol. 25, 581-585 (1968).
Lee, G. R., "Wintrobe's Clinical Hematology," 10th ed., Williams & Wilkins, Baltimore (1999).
Levenspiel, O., "Chemical Reaction Engineering," Wiley, New York (1972a).
Levenspiel, O., "The Chemical Reactor Omnibook," OSU Bookstores, Corvallis, Oregon (1972b).
Madigan, M. T., J. M. Martinko and J. Parker, "Brock Biology of Microorganisms," 9th ed., Prentice Hall, (2000).
Marlowe, E. M., L. Gibson, J. Hogan, S. Kaplan and D. A. Bruckner, "Conventional and Molecular Methods for Verification of Results Obtained with BacT/Alert Nonvent Blood Culture Bottles," J. Clin. Microbiol. 41, 1266-1269 (2003).
Mehta, A., A. E. Lichtin, A. Vigg and J. G. Parambil, "Platelet Larceny: Spurious Hypoxaemia due to Extreme Thrombocytosis," Eur. Resp. J. 31, 469-472 (2008), 10.1183/0903 1936.00039607.
Mendelson, Y., "Pulse Oximetry: Theory and Applications for Non-Invasive Monitoring," Clin. Chem. 38, 1601-1607 (1992).
Mermel, L. A. and D. G. Maki, "Detection of Bacteremia in Adults: Consequences of Culturing an Inadequate Volume of Blood," Ann. Inter. Med. 119, 270-272 (1993).
Molenaar, R., J. J. ten Bosch, and J. R. Zijp, "Determination of Kubelka-Munk Scattering and Absorption Coefficients by Diffuse Illumination," Appl. Opt. 38, 2068-2077 (1999).
Nonoyama, A., "Using multiwavelength UV-visible spectroscopy for the characterization of red blood cells," Ph.D. dissertation, University of South Florida, Tampa, Florida (2004).
Park, C. M. and R. L. Nagel, "Sulfhemoglobinemia: Clinical and Molecular Aspects," N. Engl. J. Med. 310, 1579-1584 (1984).
Pauling, L., The hemoglobin molecule in health and disease, paper presented at Proceedings of the American Philosophical Society (1952).
Qian, Q. F., Y W Tang, C. P. Kolbert, C. A. Torgerson, J. G. Hughes, E. A. Vetter, W S. Harmsen, S. O. Montgomery, F. R. Cockerill and D. H. Persing, "Direct Identification of Bacteria from Positive Blood Cultures by Amplification and Sequencing of the 16S rRNA Gene: Evaluation of BACTEC 9240 Instrument True-Positive and False-Positive Results," J. Clin. Microbiol. 39, 3578-3582 (2001).
Reynolds, L. O., "Optical diffuse reflectance and transmission from an anisotropically scattering finite blood medium," Ph.D. Thesis, University of Washington, Seattle (1975).
Reynolds, L., C. Johnson and A. Ishimaru, "Diffuse Reflectance from a Finite Blood Medium: Applications to the Modeling of Fiber Optic Catheters," Appl. Opt. 15, 2059-2067 (1976).
Schrot, J. R., W C. Hess and G. V Levin, "Method for Radiorespirometric Detection of Bacteria in Pure Culture and in Blood," Appl. Microbiol. 26, 867-873 (1973).
Senfield, L. and J. H. Lapidus, "Chemical Reactor Theory," Edward Arnold Ltd., London (1973).
Serebrennikova, Y. M., J. M. Smith, D. E. Huffman, G. F. Leparc and L. H. Garcia-Rubio, Quantitative Interpretations of Visible-NIR Reflectance Spectra of Blood (in preparation).
Snyder, J. W, G. K. Munier, G. D. Bostic, P. S. B[O.sub.2]igar and R. Hanna, "Evaluation of a Plastic Nonvented Aerobic Blood Culture Bottle for Use with the BacT/ALERT Microbial Detection System," J. Clin. Microbiol. 40, 4757-4759 (2002).
Stadie, W C., "Studies on Blood Changes in Pneumococcus Infections. An Experimental Study of the Formation and Fate of Methemoglobin in the Blood," J. Exp. Med. 33, 627-640 (1921).
Steuer, R. R., D. A. Bell and L. L. Barrett, "Optical Measurement of Hematocrit and Other Biological Constituents in Renal Therapy," Adv. Renal Replacement Ther. 6, 217-224 (1999).
Thormahlen, I., J. Straub and U. Grigull, "Refractive Index of Water and Its Dependence on Wavelength, Temperature, and Density," J. Phys. Chem. Reference Data 14, 933-946 (1985).
van de Hulst, H. C., "Light Scattering by Small Particles," Wiley, New York (1957).
Wiscombe, W J., "Mie scattering calculations: Advances in technique and fast, vector-speed computer codes," Rep. NCAR/TN--140 + STR, National Center for Atmospheric Research, Boulder, Colorado (1979).
Yebenes, J. C., M. Serra-Prat, G. Miro, G. Sauca and J. A. Capdevila, "Differences in Time to Positivity Can Affect the Negative Predictive Value of Blood Cultures Drawn Through a Central Venous Catheter," Intensive Care Med. 32, 1442-1443 (2006).
Zonios, G. and A. Dimon, "Modeling Diffuse Reflectance from Semi-Infinite Turbid Media: Application to the Study of Skin Optical Properties," Opt. Express 14, 8661-8674 (2006).
Jennifer M. Smith, (1) Yulia M. Serebrennikova, (1,2) Debra E. Huffman, (1) German F. Leparc (3) and Luis H. Garcia-Rubio (1) *
(1.) Claro Scientific, LLC., 10100 Dr. Martin Luther King Jr. St. N., St. Petersburg, FL 33716, U.S.A.
(2.) College of Marine Science University of South Florida, 140 Seventh Avenue S, St. Petersburg, FL 33701, U.S.A.
(3.) Florida Blood Services, 10100 Dr. Martin Luther King Jr. St. N., St. Petersburg, FL 33716, U.S.A.
* Author to whom correspondence may be addressed. E-mail address: firstname.lastname@example.org
Table 1. Parameters and values used in the simulations Vessel parameters and experimental conditions Total volume of the culture bottle ([cm.sup.3]) 76.8 Volume of culture media (mL) 40 Culture preparation temperature ([degrees]C) 25 Incubation temperature ([degrees]C) 37 (a) pH of the media 7.24 (a) Inert gas ([N.sub.2]) partial pressure (mmHg) 0.0 Initial [O.sub.2] partial pressure (mmHg) 80 (b) Initial C[O.sub.2] partial pressure (mmHg) 20 (b) Blood parameters Volume of blood (mL) 2-20 Hematocrit (erythrocyte volume fraction) 0.45 (c) Total haemoglobin (g/dL) 15.0 (c) Erythrocyte mean corpuscular volume (fL) 90.0 (c) Mean corpuscular haemoglobin concentration 0.33 (c) Leukocyte concentration (k/[mu]L blood) 5 (c) Platelet concentration (k/[mu]L blood) 326 (c) Blood [O.sub.2] partial pressure (mmHg) 35-100 (c) Blood C[O.sub.2] partial pressure (mmHg) 30-60 (c) Cell population metabolism Rate constant for leukocyte decay (1/h) -1.3946 (d) Leukocyte respiration rate constant 4.534 x (gmol/(min-[O.sub.2]-[N.sub.WBC])) [10.sup.-12] (e) Rate constant for platelet decay (1/h) -1.3946 (d) Platelet respiration rate constant 6.45 x (gmol/(min-[O.sub.2]-[N.sub.PLT])) [10.sup.-14] (d) Microorganism inoculum ([N.sub.ORG]/mL blood) 100 Microbial doubling time (min) 20 Microbial respiration rate constant 6.06 x (gmol/(min-[O.sub.2]-[N.sub.ORG])) [10.sup.-9] (e) Limiting no. of organisms 1.0 x [10.sup.8] ([N.sub.ORG]/mL-culture) (a) Dash and Bassingthwaighte (2004). (b) Snyder et al. (2002). (c) Lee (1999). (d) Kitchens and Newcomb (1968). (e) Schrot et al. (1973).