Modeling

Algae Growth Model

Biomass Measurements in the Home Laboratory. Conventionally, the relative biomass of an algae culture is estimated using OD (Optical Density), which is a measurement of the absorbance of a given wavelength of light through a translucent medium. However, this requires the use of specially calibrated laboratory equipment and controlled conditions that are unlikely to be found at home. [1]

Thus, we experimented with image analysis, using software and math models to accomplish the same measurement task. This made it possible for our home algae cultures to yield meaningful data at a scale we would otherwise find difficult to reach. This growth data and the model it generated is crucial as a basic measure of our algae chassis product.

You can find our developed code tools and the data set used, for use in replicating our results.

Baseline ///

To provide a baseline, we used standard equipment to measure OD of a culture in our laboratory. We used OD₇₅₀, meaning we measured the absorbance of 750nm short infrared light. By plotting OD₇₅₀ against the approximate time of culture (given in days due to the slow nature of algae growth), we are able to graph algae growth. It is apparent that OD₇₅₀ measurements present a relatively consistent indication of the algae culture biomass, and we observe linear growth in the culture. The goal will be to duplicate this consistency using the tool of image analysis.

Image Analysis ///

Image analysis refers to the use of computerized tools to pull information from digital images. This method would allow us to read data from cellphone photos rather than professional equipment, greatly simplifying our task in quantifying algae growth. This improved scientific accessibility is important not only for our team of students, allowing us to make scientific measurements at home with our culture flasks, but also to the broader world of commercial and industrial algae cultivation.

In this case, we use the reference of RGB (Red, Green, Blue) values for color. If we directly graph these RGB values, we obtain data that is directly visually understandable but difficult to quantitatively analyze. Thus, we introduced HSI (Hue, Saturation, Intensity) analysis [2], which is another way of quantifying color, and can be calculated from RGB data.

We paid particular attention to intensity, from which it is possible to calculate absorbance according to the Beer-Lambert Law:

With the assumption that lighting conditions I₀ are consistent across input images, we can obtain an estimation of absorbance that is at least consistent relative to the rest of the dataset. To normalize the estimate and create OD_approx, we shift the datapoints upwards, moving the intercept of the regression line to the origin. The linear regression model is then able to predict algae growth.

Results

Using image analysis software with additional HSI processing, we were able to extract a regression coefficient representing rate of growth. This growth rate approximation was inferior in consistency to OD measurements, as expected (r²=0.72 and r²=0.98, respectively), but still within acceptable margins. While not perfect, the correlation between the image analysis approximation and measured OD values was r²=0.890.

This tells us that our image analysis method is an effective replacement for traditional OD measurements, smartphone images giving approximately 90% of the accuracy of professional equipment. Proving the robustness of this analysis method enabled us to confidently collect data from our home laboratories as growth modeling. For example, here is the same modeling program run on 14 images (taken over 30 days) collected by our team member Helen in her home fishtank lab.

There are some drawbacks to not having an absolute measurement, but the same flaw is in any optical test, including OD. In this case, relative growth is also sufficient for our cultivation and quantification needs.