Changes in the Absorption and Scattering Properties in theNear-Infrared Region During the Growth of Bacillus subtilis inLiquid Culture

ELITSA DZHONGOVA, COLIN R. HARWOOD, and SURESH N. THENNADIL*School of Chemical Engineering and Advanced Materials (E.D., S.N.T.), and Institute for Cell and Molecular Biosciences, Newcastle University,Newcastle upon Tyne, United Kingdom (C.R.H.)

Multiple scattering of light by cells poses a significant challenge in the

development of near-infrared-based methodologies to reliably extract

chemical and physical information contained in the spectra collected

during the bacterial growth cycle. The extent of information that can be

obtained from NIR spectra could, in principle, be vastly improved if the

scattering and absorption effects can be effectively separated. This study

focuses on the methodology for extracting the bulk optical properties over

the course of the bacterial growth cycle and investigates the nature and

extent of changes in the optical properties with time. By inverting the

radiative transfer equation (RTE) using three measurements, total diffuse

reflectance, total diffuse transmittance, and collimated transmittance, the

bulk absorption coefficient (la), the bulk scattering coefficient (ls), and the

anisotropy factor (g) are extracted and their changes during the course of

the growth cycle are investigated. In this study, a simple bacterial growth

system consisting of Bacillus subtilis growing in an aqueous solution

(minimum medium) was investigated. The changes in the optical

properties of this system during bacterial growth, stationary, and decline

phases were investigated by inverting the measurements using the adding-

doubling method to solve the RTE in the wavelength region of 950–1850

nm. This study shows that during growth in liquid culture, the absorption

and scattering property changes can be consistently extracted from

measurements under multiple light scattering conditions. The estimation

of the anisotropy factor was not reliable beyond 1200 nm at low bacterial

cell counts, but reliability increased with increasing biomass concentra-

tion. At all stages in the growth cycle, the anisotropy factor could not be

reliably extracted in the first overtone region. However, this does not

appear to adversely affect the estimation of the absorption and scattering

coefficients.

Index Headings: Multiple light scattering; Optical properties; Radiative

transfer theory; Fermentation; Bacillus subtilis.

INTRODUCTION

During the last two decades, there has been considerableinterest in utilizing near-infrared (NIR) spectroscopy formonitoring microbial fermentation processes since this tech-nique has the potential to provide information about both thechemical and physical state of a system. The fact that NIRmeasurements could be made with minimum or no samplepreparation, coupled with the availability of robust, easy tooperate instruments with high signal-to-noise characteristics,has made this technique a promising tool for at-line and on-linemonitoring of microbial growth.1,2

Several research groups have investigated the utility of NIRspectroscopy as an analysis technique for various fermenta-tion processes such as wine3 and beer4 fermentation and

batch, fed-batch, and continuous cultivations5–8 in combina-tion with chemometric techniques. Multiple scattering of lightby the cells poses a significant challenge in the developmentof NIR-based methodologies to extract reliable chemical andphysical information contained in the spectra of growingsuspension of microbial cells. The extent of information thatcan be obtained from NIR spectra could, in principle, bevastly improved if the scattering and absorption effects can beeffectively separated.

In this paper, we investigate an approach to separate theabsorption and scattering effects using the radiative transferequation (RTE) to account for multiple scattering of light.9,10

By inverting the RTE, the bulk transport coefficients, i.e., thebulk absorption (la) and scattering (ls) coefficients and theanisotropy factor (g), can be extracted. The changes in theabsorption and scattering properties can then be separatelymonitored during the microbial growth cycle. The bulkscattering coefficient will be predominantly related to changesin properties such as cell size and biomass concentration,whereas information regarding non-scattering constituents,such as glucose, and product concentrations will be containedin the bulk absorption coefficient. Thus, by extracting la andls, it may be possible to obtain more information formonitoring microbial growth than could be obtained usingonly the transmittance or reflectance data. This is because thela and ls data discriminates better between variations in theconstituents of the cells and growth medium by takingadvantage of the different information content of the twocoefficients. Further, from the point of view of buildingcalibration models for estimating the concentrations of productand nutrients, the removal of the confounding effects due tomultiple light scattering from the absorption effects could leadto simpler and more robust models.

As a first step towards achieving reliable models forpredicting the concentrations of components in a culturemedium by separating the absorption and scattering effects, thisstudy focuses on the methodology for extracting the bulkoptical properties and investigates the nature and extent ofchanges in the optical properties over the course of bacterialgrowth cycles. For this purpose a simple culture system wasestablished consisting of Bacillus subtilis growing in anaqueous solution (minimum medium). The changes in theoptical properties of this system during growth, stationary, anddecline phase were studied using measurements in thewavelength region of 950–1850 nm.

MATERIALS AND METHODS

Inversion of the Radiative Transfer Equation to ExtractOptical Properties. The radiative transfer equation (RTE),

Received 21 August 2008; accepted 15 October 2008.* Author to whom correspondence should be sent. E-mail: suresh.thennadil@strath.ac.uk. Current Address: Department of Chemicaland Process Engineering, University of Strathclyde, Glasgow, UnitedKingdom.

Volume 63, Number 1, 2009 APPLIED SPECTROSCOPY 250003-7028/09/6301-0025$2.00/0

� 2009 Society for Applied Spectroscopy

which describes the transport of light through a mediumcontaining particles, is given by9

dIðk; r!; sÞds

¼� ltðkÞIðk; r!; sÞ þltðkÞIðk; r!; sÞ

4p

3

Z4p

pðs; s0ÞIðk; r!; sÞ dx0 ð1Þ

where I(k, r!, s) is the specific intensity of light of wavelength kat point r! with radiation incident along direction s, lt(k)[¼ls(k)þla(k)] is the bulk extinction coefficient, ls (mm�1) isthe bulk scattering coefficient, la (mm�1) is the bulk absorptioncoefficient, and p(s, s0) is the phase function, which is ameasure of the angular distribution of scattered light and isusually approximated as a function of the anisotropy factor g.The bulk scattering and absorption coefficients are related tothe individual species i present in a sample as follows:

laðkÞ ¼X

qira;iðkÞ ð2Þ

and

lsðkÞ ¼X

qirs;iðkÞ ð3Þ

where qi is the number density (concentration) of species i, andra,i and rs,i are the absorption and scattering cross-sections,respectively, of species i. The phase function is usuallyapproximated as a function of the scattering angle h andanisotropy factor g (¼hcos hi). One of the widely usedfunctions is the Henyey–Greenstein approximation:9–11

pðcoshÞ ¼ 0:5ð1� g2Þð1� g2 þ 2coshÞ1:5 ð4Þ

Thus, for describing the propagation of light of wavelengthk through a suspension using Eq. 1 along with appropriateboundary conditions, the three transport parameters la, ls, andg are needed. In the context of the inverse problem, thismeans that the information content of the suspension iscontained in these three parameters, and in order to extract theparameters at least three measurements have to be made ateach wavelength. The absorption (la) and scattering (ls)parameters are of particular interest because they are sensitiveto changes in the physical and chemical state of thesuspension.

In this study, the optical parameters were extracted using aninversion method based on the adding-doubling method fornumerically solving the RTE including the boundary effectsdue to the glass cuvette.11–13 In the adding-doubling method,the total diffuse reflectance (Rd) and total diffuse transmittance(Td) from a very thin layer having the same optical propertiesas the sample is calculated using, for example, the singlescattering theory or the diamond-initialization method.12,14 Ithas been shown that the diamond initialization method is moreaccurate than using the single scattering theory14 and thereforethe former was used in this work. Once Td and Rd for the initialthin layer has been calculated, the values for a layer double thethickness can be obtained by invoking the principle ofinvariance.10 This process of doubling the layers is continueduntil the desired thickness (i.e., the sample thickness) isreached. Since in this work the sample is placed in a glasscuvette, the (specular) reflection and transmission at the air–glass and the glass–sample boundaries must be taken intoaccount. This is done by first computing the reflectance and

transmittance from the glass and then as before invoking theprinciple of variance to ‘‘add’’ the sample and glass layers toobtain the total diffuse reflectance and transmittance from theentire glass–sample–glass entity. The calculation of thecollimated transmission is straightforward and is given byBeer’s law:

TcðkÞ ¼ exp½�ltðkÞ‘� ð5Þ

where lt(k) is the bulk extinction coefficient and ‘ is thesample thickness (i.e., the cuvette path length). The mathe-matical and the implementation details of the adding-doublingmethod can be found in the literature cited.10–14

To use the adding-doubling method as part of an inversionscheme to extract the bulk absorption and scattering properties,the three measurements needed are the total diffuse transmit-tance (Td), total diffuse reflectance (Rd), and collimatedtransmittance (Tc). The total diffuse transmittance andreflectance measurements are obtained using an integratingsphere setup. It should be noted that the total diffusetransmittance includes the collimated portion of the transmittedlight and the total diffuse reflectance includes the specularreflectance from the boundaries. These are taken into accountin the adding-doubling calculations. Due to the correlationbetween Td and Tc measurements, there is an inherentinstability in the inversion, which could lead to problems withconvergence under some circumstances such as when theabsorbance is very high. A schematic of the three measurementconfigurations is shown in Fig. 1.

In addition to the three measurements, to invert the RTEfor the system (glass–suspension–glass) using the adding-doubling method, the refractive index of the glass cuvette andthe suspension are required as inputs. The refractive index ofthe glass cuvette was taken to be 1.523 (given by themanufacturer). The refractive index of the sample was takenas the average refractive index, 1.3362, estimated bymeasuring the refractive index of several samples with arefractometer.

The inversion algorithm starts by taking as inputs therefractive index of sample and glass and the thickness of thesample, i.e., the cuvette path length (‘). In addition, initialguess values of the bulk absorption albedo (a), optical depth(s), and the anisotropy factor (g0) of the sample have to beprovided. The albedo and the optical depth are given by:

a ¼ ls

ðls þ laÞð6bÞ

and

s ¼ ðls þ laÞ‘ ð6bÞ

The reason for using the albedo and optical depth as theparameters for the inversion instead of directly using la and ls

is because the algorithm is much more stable when the formertwo parameters are used. Further the adding-doubling equa-tions are naturally cast in terms of albedo and optical depth andonce these are extracted the scattering and absorptionparameters can be obtained using Eq. 6. The calculated totaldiffuse reflectance (Rdcalc) and total diffuse transmittance(Tdcalc) obtained from the adding-doubling routine and thecollimated transmittance obtained from using Beer’s law(Tccalc) for the input guess values of albedo and optical depth

26 Volume 63, Number 1, 2009

are then compared with the corresponding measured values:

n ¼ absðRd � RdcalcÞ þ absðTd þ TdcalcÞ þ absðTc � TccalcÞ ð7Þ

The guess values are then updated and the iterations carriedout until convergence (n � 1.0 3 10�7) is achieved. Thisiteration was carried out using the function ‘‘fmincon’’ of theMATLABt Optimization toolbox to minimize Eq. 7.

Experimental Details. The growth studies were conductedusing the Gram-positive bacterium Bacillus subtilis strain 168,which was obtained from the Institut Pasteur, Paris. The strainwas cultivated in 100 mL Spizizen’s minimal medium andtrace element solution15 in a 250 mL Erlenmeyer flask. All thebacterial growth cycle experiments were carried out with theculture at an initial pH of the media of 7 6 0.5. Thetemperature was controlled during the entire bacterial growthcycle at 37 8C 6 0.5, and the agitation rate was set at 220 rpm.In this study, data from the growth, stationary, and declinephases were collected from separate cultivations. A total of

nine growth cycles were performed. For the first three cultures,data was collected during the growth phase. For cultures 4–6,data was collected only during the stationary phase, and forcultures 7–9, data was collected during the decline phase. Sinceall the growth cycle runs were performed under the sameconditions, each of the sets of three runs for each phase(growth, stationary, and decline) are essentially replicate runs.For all these cultures, during the data collection phase, a totalof five samples were taken at approximately 2 hour intervals.The progress of the cultivations was also followed by makingoptical density measurements, which provided informationregarding the stage of the growth cycle, which, in turn, ensuredthat the samples were collected at the appropriate growthphase. All measurements for optical density were made using aCARY 5000 UV-Vis NIR spectrophotometer in absorptionmode at a 600 nm wavelength with a 1 cm path length cuvette.

On each sample the following spectroscopic measurementswere made: total diffuse reflectance (Rd), total diffuse

FIG. 1. Experimental setup for measuring (a) total diffuse transmittance, (b) total diffuse reflectance, and (c) collimated transmittance.

APPLIED SPECTROSCOPY 27

transmittance (Td), and collimated transmittance (Tc). Thesemeasurements were made using a UV-Vis-NIR spectropho-tometer (Cary 5000, Varian Scientific Instruments) equippedwith an integrating sphere (diffuse reflectance accessory, DRA2500) by placing the samples in a special optical glass cuvettewith a path length of 4 mm. The measurements were made overthe wavelength range of 95–1850 nm with an averageintegration time of 0.4 s, an average signal band-width ofabout 15 nm, and wavelength interval 4 nm.

For these samples, biomass was measured gravimetrically.Aliquots of 5 mL of suspension were filtered without washingthrough pre-weighed Millipore filters (pore size 0.45 lm).After the culture suspension was filtered, the filters were thendried at 50 8C to a constant weight, cooled down in a vacuumdesiccator, and then weighed again. The difference between thedried and pre-weighed filter was expressed as weight of the drycells per sample volume.

RESULTS AND DISCUSSION

Figure 2 shows the optical density curves during thecultivation for the different phases and the points on thecurves indicate when the samples for measurements weredrawn from the flask. While the same recipe was used for allthe cultivations, it is seen that for the three runs in each of thegrowth phases, there are small but distinctive variations in theoptical density curves and the points where the samples weredrawn are not exactly at the same time point on the curves.

Figures 3a through 3c show the raw spectra, plotted inabsorbance units, of the samples collected during all thecultivations using the different measurement configurations,i.e., total diffuse reflectance (Rd), total diffuse transmittance(Td), and collimated transmittance (Tc). Both Tc and Td arenoisy around the 1450 nm water absorption peak (Figs. 3b and3c). In the case of Rd, the spectra appear to flatten out beyond1400 nm. The reason is that in this region, the amount of lightreflected from the sample is small compared to the specularreflectance contribution from the glass cuvette. However, theinformation regarding changes in the sample is embedded inthe spectrum and can be extracted by accounting for thespecular reflectance as is done when extracting the opticalproperties.

The extracted optical properties, i.e., the bulk scatteringcoefficient ls(k), bulk absorption coefficient la(k), andanisotropy factor g(k), for the samples collected during thegrowth phase are shown in Figs. 4a through 4c. In these plots,the gaps in the wavelength region 1360–1550 nm are becausethe inversion using the adding-doubling method does notconverge due to the high absorbance in this region. To obtainthe optical properties in this region, sample thickness wouldhave to be reduced by using cuvettes with path lengths smallerthan 4 mm. It can be seen that the relative change in ls(k) ishigh compared to the relative changes in la(k) over theduration of the growth phase. This is expected since, in thecultivation system considered here, the largest variation is dueto the increase in biomass. While the biomass also affectsla(k), the absorption due to biomass in the NIR region is smallcompared to the absorption due to water; therefore, the relativechanges due to an increase in biomass are small.

The extracted anisotropy factor also exhibits changes duringthe growth phase. In the early stage of the growth phase, acrossthe wavelength region 950–1350 nm, g(k) drops sharplytowards zero beyond 1200 nm or flattens out in this region.

FIG. 2. Bacillus subtilis growth profiles for three cultivations: (a) growthphase, (b) stationary phase, and (c) decline phase.

28 Volume 63, Number 1, 2009

This is physically inconsistent. It is noticed that the wavelengthbeyond which it falls in this manner increases as the growthcycle progresses. It could be concluded that this effect is due tothe fact that the low biomass in the initial stages of thecultivation and the resulting low scattering, which character-istically falls off at higher wavelengths, could be a factor in theinversion not being effective in extracting the anisotropy factor

under such conditions. This effect has previously been

evidenced in a polystyrene–water system12 where a sample

with 0.15% polystyrene particles by weight was considered. In

that study it was shown that while the estimated values of the

anisotropy factor were unreliable in the region where it falls off

sharply, it did not affect the estimation of la(k) and ls(k). As

FIG. 3. Spectra of samples taken at different stages of the growth cycle(growth phase, stationary phase, decline phase). (a) Total diffuse reflectance,(b) total diffuse transmittance, and (c) collimated transmittance.

FIG. 4. Estimated optical properties and anisotropy factor during the growthphase for three cultivations; (solid line) Run 1, (dashed line) Run 2, (dottedline) Run 3. (a) Scattering coefficient ls, (b) absorption coefficient la, and (c)anisotropy factor g.

APPLIED SPECTROSCOPY 29

the growth cycle progresses, the estimates of g(k) becomestable over a larger span of wavelengths. Beyond 1500 nm,g(k) stays around 0.8, which is the initial guess value input tothe inverse adding-doubling program and thus cannot beexpected to be a reliable estimate. Changing the initial guessvalues (0.7 and 0.9 were tried) resulted in g(k) over thiswavelength range converging to a value close to those guess

values, thus reinforcing the conclusion that the estimate of theanisotropy factor in this region is not reliable, although thisdoes not affect the estimation of the bulk absorption andscattering coefficients.

Examining Fig. 4, it can be seen that the extracted opticalproperties are consistent over the three cultivations for thegrowth stage. Since the samples were taken at approximatelythe same point in the growth cycle during each of the threecultivations, which all used the same culture medium andanalytical protocol, we would expect, if the inversion method isstable, to obtain similar optical properties at these time points.The optical properties corresponding to similar time points areindeed similar. The small differences in the magnitude can beattributed to small variations in the synchrony of cultures.

Figures 5a through 5c show the evolution of the opticalproperties during the stationary phase. As would be expected,due to the fact that there is very little change in the biomassconcentration, the optical properties show a much smallervariation compared to the growth phase. As in the case of thegrowth stage, the extracted optical properties are consistentover the three cultivations, indicating the reliability of theinversion method. Figures 6a through 6c show the changes inthe optical properties during the decline phase. The variationsin the optical properties are smaller compared to the growthphase.

In order to have a closer look at the ‘‘direction’’ of variationsin the optical properties over the course of a cultivation, theextracted values are plotted for two wavelengths, 1050 nm and1602 nm. These two wavelengths were chosen to examine thebehavior of the optical properties in a scattering-dominatedregion and an absorption-dominated region, respectively. InFig. 7, the optical properties at 1050 nm are plotted against thebiomass concentration. It is seen from Fig. 7a that during thegrowth phase ls(k) varies approximately linearly with thebiomass except for one point with very low biomassconcentration. This could be due to the low biomassconcentration resulting in a combination of measurementerrors and the low scattering levels exacerbating errors in theinversion since the numerical method employed is based onmultiple scattering effects being dominant. In the stationaryphase, the bulk scattering coefficient does not show strongtrends. This is due to the fact that the changes in biomassduring this period are not large; trends if any will be swampedby the errors in the measurement of biomass. This character-istic is also seen in the decline phase. Overall, for the samelevels of biomass, the values of ls(k) in the decline phase areless than those observed in the stationary phase, possiblyindicating differences in the biomass characteristics such as themorphology of viable and non-viable cells, clumping, etc.

In the case of la(k) (Fig. 7b), the relationship with biomassindicates a slight nonlinearity with a curvature observable atthe lower end (around the region of 0.5 lg/mL) of the biomassconcentration. Again, samples at the lower cell densities aremore likely to be outliers for reasons mentioned above whilediscussing the bulk scattering coefficient in the last paragraph.The values of la(k) in the stationary and decline phase do notshow any clear-cut clustering that was similar to that seen whenexamining ls(k). This could be due to the lack of significantchanges in the concentration of the cellular components overthese periods.

The variation of the anisotropy factor g(k) with biomass isshown in Fig. 7c. It is seen that during the growth phase, g(k)

FIG. 5. Optical properties during the stationary phase for three cultivations;(solid line) Run 4, (dashed line) Run 5, (dotted line) Run 6. (a) Scatteringcoefficient ls, (b) absorption coefficient la, and (c) anisotropy factor g.

30 Volume 63, Number 1, 2009

rises sharply and stabilizes around 0.9, where it remains during

the stationary phase. In the decline phase, g(k) takes on slightly

lower values than observed for the stationary phase. The sharp

increase in g(k) initially could be due to the rapid increase in

rate of cell divisions creating a larger population of freshly

divided cells (of smaller size) compared to the cells yet to

divide into smaller cells. However, more investigation is

needed to verify this explanation.

In Fig. 8, the optical properties at 1602 nm are plotted

against biomass concentration. The values for g(k) are not

shown since, as discussed earlier, they were not reliable in this

region. It is seen in Fig. 8a that ls(k) shows a nonlinear

FIG. 6. Estimated optical properties and anisotropy factor during the declinephase for three cultivations; (solid line) Run 7, (dashed line) Run 8, (dottedline) Run 9. (a) Scattering coefficient ls, (b) absorption coefficient la, and (c)anisotropy factor g.

FIG. 7. Estimated optical properties at 1050 nm during growth, stationary, anddecline phase for three cultivations [(gray symbols) growth phase, (solid blacksymbols) stationary phase, (open symbols) decline phase] versus biomass. (a)Scattering coefficient ls, (b) absorption coefficient la, and (c) anisotropy factor g.

APPLIED SPECTROSCOPY 31

relationship in contrast to the trend seen at 1050 nm, remainingflat initially, and then rising rapidly with biomass concentra-tion. There are two outliers observed in this region. These aremore likely to be due to convergence problems in the inversionrather than to any physical characteristics in the system. As wasthe case for 1050 nm, there are no discernible trends in the bulkscattering coefficient with respect to biomass in the stationaryand the decline phase. Compared to the decline phase, ls(k)appears to be slightly higher in the stationary phase. For thebulk absorption coefficient, it is seen that the relationshipbetween la(k) and the biomass in the growth phase is weakercompared to that at 1050 nm. Thus, while the absorption andscattering properties change with the biomass concentration,the extent of this variation depends on wavelength.

CONCLUSION

This study shows that the absorption and scattering propertychanges during the cultivation of a bacterium can beconsistently extracted from measurements under multiplescattering conditions. The cultivation system considered herewas a simple one in which the major change during thecultivation process was the increase in biomass. This isreflected by the fact that the greatest relative change was seenin the scattering properties during the growth phase. Since thewavelength range used in this study (950–1850 nm) spans twodifferent regimes, that is, the absorption-dominated andscattering-dominated regions, the path length of the cuvetteused may not be optimal for extracting the optical propertieswith sufficient accuracy over the entire wavelength range. Theextreme example occurs around the water peak at the 1400–1500 nm region. In the context of using this approach toseparate absorption and scattering effects so that effectivemodels can be built for monitoring concentrations of nutrients,biomass, etc., further studies must be conducted to establish theeffect of sample thickness on the extracted optical properties.We must also determine how reliable the extraction methodwill be at higher biomass concentrations, i.e., at levels that areusually encountered in industrial situations. This is because at

high biomass concentrations the collimated transmittancesignal will be adversely affected. This issue has to besuccessfully overcome for this approach to be used as a meansof correcting scattering effects when building calibrationmodels for estimating concentrations of (e.g., glucose, product,etc.) analytes.

ACKNOWLEDGMENTS

This work was funded by Marie Curie FP6 (INTROSPECT) and by EPSRCgrants GR/S50441/01 and GR/S50458/01.

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FIG. 8. Optical properties at 1602 nm during growth, stationary, and decline phase for three cultivations [(gray symbols) growth phase, (solid black symbols)stationary phase, (open symbols) decline phase] versus biomass. (a) Scattering coefficient ls, and (b) absorption coefficient la.

32 Volume 63, Number 1, 2009