- Email: [email protected]
Biofilm thickness measurements by variance analysis of optical images
ELSEVIER
JOURNALOF MICROBIOLOGICAL METHODS Journal of Microbiological Methods 20 (1994) 219-224
Biofilm thickness measurements by variance analysis of optical images Terje Lauvvik 1, Rune Bakke* Rogaland University Centre, P.O. Box 2557 Ullandhaug, 4004 Stavanger, Norway
Received 20 September 1993; revision received 23 February 1994; accepted 24 February 1994
Abstract An approach to automating biofilm thickness measurements by light microscopy based on variance analysis of optical images is described in this article. This new in situ method is tested and the results are consistent with manually determined thickness measurements. The method's main advantage is in its efficiency in, for instance, acquiring large quantities of data in long term biofilm experiments. The method is based on the hypothesis that the variance of a series of images in a biofilm is a function of the image's vertical position within the biofilm at a fixed horizontal position. The method was tested on a 40 #m thick biofilm for which a variance maximum at 38 + 5 am was observed. Key words: Biofilm thickness; Image processing
I. Introduction Biofilm thickness is an essential parameter in analyzing and predicting biofilm behaviour [e.g., 1,2], but it is also a s o m e w h a t elusive parameter. The 'Biofilm thickness measurements by light microscopy' [3] m e t h o d has been widely adapted [4-7], but it is subject to error due to subjective interpretation. Locating the biofilm-liquid interface t h r o u g h the microscope is not always a trivial endeavour. Image analysis methods are presently being developed to a u t o m a t e optical methods for biofilm analysis, including biofilm thickness measurement procedures. The main motivation to a u t o m a t e biofilm thickness measurement procedures is to obtain *Corresponding author. 1Present address: Allianse, Box 369, 4001 Stavanger, Norway. 0167-7012/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 1 6 7 - 7 0 1 2 ( 9 4 ) 0 0 0 2 0 - 8 0 0 0 2 0 - 8
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
220
increased efficiency in biofilm analysis. Manual biofilm thickness analysis is labour intensive and interesting changes in biofilm morphology 'typically' happen while nobody is around to observe the changes. Biofilm images obtained by microscopy are collected through a video camera mounted on the microscope and connected to a computer. Images can then be acquired and processed in several ways. Series of images can be analyzed to discover differences which are hardly visible to the eye, enabling us to analyze features previously not studied. The goal of this study was to automate the biofilm thickness measurements by a light microscopy method to obtain a more efficient method for in situ biofilm thickness measurements.
2. Theory A digitized image consists of a matrix of picture elements, called pixels. These pixels will have different ranges of values depending on how many bits the computer uses to store each pixel. If, as in our case, the computer applies 8 bits to store the value of one pixel, the values can range from 0 to 255. Each row in the matrix can be considered a separate series, or each column can be treated as one series. More complex techniques can also be applied based on two dimensional signal processing. One commonly applied parameter extracted from the pixel matrix is the variance, as defined in Eq. 1: m
1 Variance a2(x)= (~-~--~) E
(Xi--J2) 2
(1)
i=0
where m = the number of pixels analyzed x = the pixel series xi = the pixel being processed kt = the mean value of the pixels The variance, as defined in Eq. 1, can be interpreted as the sum of the squared differences between each element and the mean value, #. Now, given a set of elements being the pixels of an image. The variance will be small if the majority of the elements have pixel values close to the mean value. An image containing both very dark areas and bright areas, on the other hand, will yield a higher variance. Variance can, therefore, be considered a measure of the contrast of an image. The biofilm-liquid interface will be more or less rough depending on biofilm type, morphology, history etc. [6]. It was, therefore, assumed that images acquired from this surface layer, also termed surface film [6] will yield more contrast than images acquired from the base film (Fig. 1). We expected a maximum variance at the biofilm-liquid interface. Based on this assumption we stated the following hypothesis: The variance of a series of images in a biofilm is a function of the image's vertical position within the biofilm, at a fixed horizontal position. If this is true, then it is
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
221
Light source
Liquid phase Focal planes
Surface film Big- "~ Base film I film
Lens
Fig. 1. Sketch of a biofilm with a relatively rough surface film indicating biofilm thickness measurements by light microscopy.
possible to derive the biofilm thickness from the variance data, given, of course, the same need for correction factors as manual optical thickness measurements [3].
3. Methods
A biofilm, grown in a rectangular transparent tube (Wale apparatus co., RT2540; 0.4 x 4.0 mm internal dimensions and length 400 mm), was analyzed to test the hypothesis. The tube was operated as a once through plug flow reactor with a glucose (20 mg/ 1) nutrient solution feed. The tube was inoculated with an undefined mixed bacterial culture. A biofilm developed and the biofilm thickness, measured according to Bakke and Olsson [3], stabilized after a few weeks. The tube was mounted on a servo-controlled stage, to enable accurate sample positioning on the microscope (Olympus, IMT-2 inverted microscope) (Fig. 2). A video camera (Panasonic F10 CCD) was also mounted to the microscope and connected to a computer (IBM compatible 80386/33 MHz) via a video-interface card (FG/ALU-8, Analogic Corporation, MA, USA). An image analysis program (IMAGINE, Analogic Corp.) in the computer was used to acquire, store and process the images. The images were acquired though the following procedure: Biofilm thickness was measured at a 'randomly' picked location according to Bakke and Olsson [3], by measuring the vertical distance between the biofilm-substratum interface focal plane and the biofilm-liquid interface focal plane. The microscope was then fo-
222
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
, /
,- . . . . . . . .
i-~---
£-i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
~----,
x
I I
I I I
Lens
,I, Fig. 2. Sample positioning for image acquisition by microscopy.
cused on the substratum-biofilm interface. An image was acquired. The microscope micrometer screw was then used to manually move the sample vertically, 10/zm at the time, acquiring new images at each vertical position. This procedure continued well past the biofilm-liquid interface and it was also applied in the glass substratum. The image series was stored in the PC. Then the reactor was moved slightly ( < 100 #m) in the horizontal plane, to study a neighbouring section of the biofilm, and a new series of images was acquired. A total of five such image series were acquired, each series consisting of 17 images.
4. Results
The optical biofilm thickness at the five locations analyzed, measured according to Bakke and Olsson [3], was approximately 40 #In ( + 5). The variance was calculated for each image and is plotted as a function of sample location in Fig. 3. Each curve represents one image series. Common for all the series is that the variance gradually increases towards a maximum, and then decreases. One series reaches maximum at 30 #m while the other series peaks at 40 #m, yielding an average optical thickness of 38 /~m ( + 5), corresponding to the optical thickness measured manually.
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
223
Variance /
240
\
/
\
II
\x
I I
\
!
,,
\
//
200
\~,,
I!
~\x
/I
160
xx x
iI
120
80
P
:,-.:o
'-2o
'
oo
'
2o
'
,'o
'
Oo
'
8o
'
loo
Depth [pm]
liquid
Fig. 3. Variance as a function of depth through the biofilm, including data from the liquid phase and the transparent substratum, is presented here. Each curve represents variance data calculated from individual images at seventeen locations, ten micrometersapart, in the vertical direction (depth).
5. Discussion The correlation between biofilm optical thickness and the point at which the variance reaches a m a x i m u m is good, implying that this method for automated biofilm thickness measurements has potential. The results also, however, suggest that there are some constraints in applying this method, depending somewhat on the need for accuracy in the measurements. It is not possible to determine whether this new method is more accurate than the manual optical method [3]. Its main advantages are the 'objectivity', the capacity to work continuously 24 h a day, and the reduced strain on laboratory personnel for whom manual biofilm thickness determination is unpleasant work. We do not, however, recommend that manual measurements are abandoned all together, because visual inspections are very useful in qualitative biofilm analysis. Also, with the image analysis hardware installed and the images displayed on a nice big screen, manual observations and measurements is a joy. The variance increases through the substratum glass approaching the biofilm as the biofilm gets into focus. The slope of the increase appears to get steeper entering the biofilm. This change is, however, not well defined, implying that this variance analysis is not an accurate method to detect the biofilm-substratum interface. This is normally not a limitation in applying this method for biofilm thickness measurements, however, since the vertical position of the substratum is typically 'fixed' while
224
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
the biofilm-liquid interface is the 'variable'. The substratum's vertical position is fixed in the sense that the computer always knows its exact position through a predefined, fixed, reference point on the substratum for the automated image analysis to 'recalibrate' against on a regular basis. We are presently applying such a reference point in a 3-dimensional image analysis of a biofilm system allowing exact 3-D relocation any time. The computer guides the microscope through a sequence of biofilm locations and the reference point, continuously, to monitor biofilm spatial distribution in long term (several weeks) experiments. This method is restricted to biofilms grown on transparent substrata. There are probably also restrictions on applications of the method on very thick biofilm, as is also the case for manual analysis. Thicker biofilms absorb more light which will, probably, reduce the variance difference between adjacent images. If a biofilm under surveillance has large areas of bare substratum, the images aquired at the substratum would probably yield high variance, in which case the variance might not have a distinct maximum value. It is, therefore, important also to observe biofilm morphology in order to properly interpret the variance data. This method can be further evolved to cope with this challenge by adjusting the size of the image area analyzed to the size of biofilm morphological features of interest. We might, through such an image analysis approach, end up with a method which can yield significantly more information than just biofilm thickness.
6. Conclusion
A new method for in situ biofilm thickness measurements through variance analysis of optical biofilm images has been developed, tested and found applicable. The method gives results that are consistent with manual optical thickness measurements and has significant advantages in systematic data acquisition.
References [1] Wanner, O. and Gujer, W. (1990) Modeling mixed population biofilms. In Biofilms (Characklis and Marshall, Eds.), Wiley. [2] Stewart, P.S. (1993) A model of biofilm detachment. Biotech. Bioeng. 41, 111-117. [3] Bakke, R. and Olsson, P.Q. (1986) Biofilm thickness measurements by light microscopy. J. Microbiol. Methods 5, 93-98. [4] Trulear, M.G. and Characklis, W.G. (1992) Dynamics of biofilm prosesses. J. WPCF, 54,1288-1301. [5] Shieh, W.K. and Mulcahy, L.T. (1985) Experimental determination of intrinsic kinetic coefficients for biological wastewater treatment systems. IAWPCR Specialized seminar; Modelling of Biological Wastewater Treatment, pp. 7-16. [6] Characklis, W.C. and Marshall, K. (Eds.) (1990) Biofilms. Wiley. [7] Bakke, R., Salte, K., Tengberg-Hansen, H. and Ingsy P. (1990) Xanthan degradation by biofilm in porous media. Biofouling, 2, 311-321.
JOURNALOF MICROBIOLOGICAL METHODS Journal of Microbiological Methods 20 (1994) 219-224
Biofilm thickness measurements by variance analysis of optical images Terje Lauvvik 1, Rune Bakke* Rogaland University Centre, P.O. Box 2557 Ullandhaug, 4004 Stavanger, Norway
Received 20 September 1993; revision received 23 February 1994; accepted 24 February 1994
Abstract An approach to automating biofilm thickness measurements by light microscopy based on variance analysis of optical images is described in this article. This new in situ method is tested and the results are consistent with manually determined thickness measurements. The method's main advantage is in its efficiency in, for instance, acquiring large quantities of data in long term biofilm experiments. The method is based on the hypothesis that the variance of a series of images in a biofilm is a function of the image's vertical position within the biofilm at a fixed horizontal position. The method was tested on a 40 #m thick biofilm for which a variance maximum at 38 + 5 am was observed. Key words: Biofilm thickness; Image processing
I. Introduction Biofilm thickness is an essential parameter in analyzing and predicting biofilm behaviour [e.g., 1,2], but it is also a s o m e w h a t elusive parameter. The 'Biofilm thickness measurements by light microscopy' [3] m e t h o d has been widely adapted [4-7], but it is subject to error due to subjective interpretation. Locating the biofilm-liquid interface t h r o u g h the microscope is not always a trivial endeavour. Image analysis methods are presently being developed to a u t o m a t e optical methods for biofilm analysis, including biofilm thickness measurement procedures. The main motivation to a u t o m a t e biofilm thickness measurement procedures is to obtain *Corresponding author. 1Present address: Allianse, Box 369, 4001 Stavanger, Norway. 0167-7012/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 1 6 7 - 7 0 1 2 ( 9 4 ) 0 0 0 2 0 - 8 0 0 0 2 0 - 8
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
220
increased efficiency in biofilm analysis. Manual biofilm thickness analysis is labour intensive and interesting changes in biofilm morphology 'typically' happen while nobody is around to observe the changes. Biofilm images obtained by microscopy are collected through a video camera mounted on the microscope and connected to a computer. Images can then be acquired and processed in several ways. Series of images can be analyzed to discover differences which are hardly visible to the eye, enabling us to analyze features previously not studied. The goal of this study was to automate the biofilm thickness measurements by a light microscopy method to obtain a more efficient method for in situ biofilm thickness measurements.
2. Theory A digitized image consists of a matrix of picture elements, called pixels. These pixels will have different ranges of values depending on how many bits the computer uses to store each pixel. If, as in our case, the computer applies 8 bits to store the value of one pixel, the values can range from 0 to 255. Each row in the matrix can be considered a separate series, or each column can be treated as one series. More complex techniques can also be applied based on two dimensional signal processing. One commonly applied parameter extracted from the pixel matrix is the variance, as defined in Eq. 1: m
1 Variance a2(x)= (~-~--~) E
(Xi--J2) 2
(1)
i=0
where m = the number of pixels analyzed x = the pixel series xi = the pixel being processed kt = the mean value of the pixels The variance, as defined in Eq. 1, can be interpreted as the sum of the squared differences between each element and the mean value, #. Now, given a set of elements being the pixels of an image. The variance will be small if the majority of the elements have pixel values close to the mean value. An image containing both very dark areas and bright areas, on the other hand, will yield a higher variance. Variance can, therefore, be considered a measure of the contrast of an image. The biofilm-liquid interface will be more or less rough depending on biofilm type, morphology, history etc. [6]. It was, therefore, assumed that images acquired from this surface layer, also termed surface film [6] will yield more contrast than images acquired from the base film (Fig. 1). We expected a maximum variance at the biofilm-liquid interface. Based on this assumption we stated the following hypothesis: The variance of a series of images in a biofilm is a function of the image's vertical position within the biofilm, at a fixed horizontal position. If this is true, then it is
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
221
Light source
Liquid phase Focal planes
Surface film Big- "~ Base film I film
Lens
Fig. 1. Sketch of a biofilm with a relatively rough surface film indicating biofilm thickness measurements by light microscopy.
possible to derive the biofilm thickness from the variance data, given, of course, the same need for correction factors as manual optical thickness measurements [3].
3. Methods
A biofilm, grown in a rectangular transparent tube (Wale apparatus co., RT2540; 0.4 x 4.0 mm internal dimensions and length 400 mm), was analyzed to test the hypothesis. The tube was operated as a once through plug flow reactor with a glucose (20 mg/ 1) nutrient solution feed. The tube was inoculated with an undefined mixed bacterial culture. A biofilm developed and the biofilm thickness, measured according to Bakke and Olsson [3], stabilized after a few weeks. The tube was mounted on a servo-controlled stage, to enable accurate sample positioning on the microscope (Olympus, IMT-2 inverted microscope) (Fig. 2). A video camera (Panasonic F10 CCD) was also mounted to the microscope and connected to a computer (IBM compatible 80386/33 MHz) via a video-interface card (FG/ALU-8, Analogic Corporation, MA, USA). An image analysis program (IMAGINE, Analogic Corp.) in the computer was used to acquire, store and process the images. The images were acquired though the following procedure: Biofilm thickness was measured at a 'randomly' picked location according to Bakke and Olsson [3], by measuring the vertical distance between the biofilm-substratum interface focal plane and the biofilm-liquid interface focal plane. The microscope was then fo-
222
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
, /
,- . . . . . . . .
i-~---
£-i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
~----,
x
I I
I I I
Lens
,I, Fig. 2. Sample positioning for image acquisition by microscopy.
cused on the substratum-biofilm interface. An image was acquired. The microscope micrometer screw was then used to manually move the sample vertically, 10/zm at the time, acquiring new images at each vertical position. This procedure continued well past the biofilm-liquid interface and it was also applied in the glass substratum. The image series was stored in the PC. Then the reactor was moved slightly ( < 100 #m) in the horizontal plane, to study a neighbouring section of the biofilm, and a new series of images was acquired. A total of five such image series were acquired, each series consisting of 17 images.
4. Results
The optical biofilm thickness at the five locations analyzed, measured according to Bakke and Olsson [3], was approximately 40 #In ( + 5). The variance was calculated for each image and is plotted as a function of sample location in Fig. 3. Each curve represents one image series. Common for all the series is that the variance gradually increases towards a maximum, and then decreases. One series reaches maximum at 30 #m while the other series peaks at 40 #m, yielding an average optical thickness of 38 /~m ( + 5), corresponding to the optical thickness measured manually.
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
223
Variance /
240
\
/
\
II
\x
I I
\
!
,,
\
//
200
\~,,
I!
~\x
/I
160
xx x
iI
120
80
P
:,-.:o
'-2o
'
oo
'
2o
'
,'o
'
Oo
'
8o
'
loo
Depth [pm]
liquid
Fig. 3. Variance as a function of depth through the biofilm, including data from the liquid phase and the transparent substratum, is presented here. Each curve represents variance data calculated from individual images at seventeen locations, ten micrometersapart, in the vertical direction (depth).
5. Discussion The correlation between biofilm optical thickness and the point at which the variance reaches a m a x i m u m is good, implying that this method for automated biofilm thickness measurements has potential. The results also, however, suggest that there are some constraints in applying this method, depending somewhat on the need for accuracy in the measurements. It is not possible to determine whether this new method is more accurate than the manual optical method [3]. Its main advantages are the 'objectivity', the capacity to work continuously 24 h a day, and the reduced strain on laboratory personnel for whom manual biofilm thickness determination is unpleasant work. We do not, however, recommend that manual measurements are abandoned all together, because visual inspections are very useful in qualitative biofilm analysis. Also, with the image analysis hardware installed and the images displayed on a nice big screen, manual observations and measurements is a joy. The variance increases through the substratum glass approaching the biofilm as the biofilm gets into focus. The slope of the increase appears to get steeper entering the biofilm. This change is, however, not well defined, implying that this variance analysis is not an accurate method to detect the biofilm-substratum interface. This is normally not a limitation in applying this method for biofilm thickness measurements, however, since the vertical position of the substratum is typically 'fixed' while
224
T. Lauvvik, R. Bakke/Journal of Microbiological Methods 20 (1994) 219-224
the biofilm-liquid interface is the 'variable'. The substratum's vertical position is fixed in the sense that the computer always knows its exact position through a predefined, fixed, reference point on the substratum for the automated image analysis to 'recalibrate' against on a regular basis. We are presently applying such a reference point in a 3-dimensional image analysis of a biofilm system allowing exact 3-D relocation any time. The computer guides the microscope through a sequence of biofilm locations and the reference point, continuously, to monitor biofilm spatial distribution in long term (several weeks) experiments. This method is restricted to biofilms grown on transparent substrata. There are probably also restrictions on applications of the method on very thick biofilm, as is also the case for manual analysis. Thicker biofilms absorb more light which will, probably, reduce the variance difference between adjacent images. If a biofilm under surveillance has large areas of bare substratum, the images aquired at the substratum would probably yield high variance, in which case the variance might not have a distinct maximum value. It is, therefore, important also to observe biofilm morphology in order to properly interpret the variance data. This method can be further evolved to cope with this challenge by adjusting the size of the image area analyzed to the size of biofilm morphological features of interest. We might, through such an image analysis approach, end up with a method which can yield significantly more information than just biofilm thickness.
6. Conclusion
A new method for in situ biofilm thickness measurements through variance analysis of optical biofilm images has been developed, tested and found applicable. The method gives results that are consistent with manual optical thickness measurements and has significant advantages in systematic data acquisition.
References [1] Wanner, O. and Gujer, W. (1990) Modeling mixed population biofilms. In Biofilms (Characklis and Marshall, Eds.), Wiley. [2] Stewart, P.S. (1993) A model of biofilm detachment. Biotech. Bioeng. 41, 111-117. [3] Bakke, R. and Olsson, P.Q. (1986) Biofilm thickness measurements by light microscopy. J. Microbiol. Methods 5, 93-98. [4] Trulear, M.G. and Characklis, W.G. (1992) Dynamics of biofilm prosesses. J. WPCF, 54,1288-1301. [5] Shieh, W.K. and Mulcahy, L.T. (1985) Experimental determination of intrinsic kinetic coefficients for biological wastewater treatment systems. IAWPCR Specialized seminar; Modelling of Biological Wastewater Treatment, pp. 7-16. [6] Characklis, W.C. and Marshall, K. (Eds.) (1990) Biofilms. Wiley. [7] Bakke, R., Salte, K., Tengberg-Hansen, H. and Ingsy P. (1990) Xanthan degradation by biofilm in porous media. Biofouling, 2, 311-321.