Comparison of three mathematical models to estimate lactation performance in dairy cows

Milk yield dynamics and production performance reflect how dairy cows cope with their environment. To optimize farm management, time-series of individual cow milk yield have been studied in the context of precision livestock farming, and many mathematical models have been proposed to translate raw data into useful information for the stakeholders of the dairy chain. To gain better insights on the topic, this study aimed at comparing 3 recent methods that allow to estimate individual cow potential lactation performance, using daily data recorded by the automatic milking systems of 14 dairy farms (7 Holstein, 7 Italian Simmental) from Belgium, the Netherlands, and Italy. An iterative Wood model (IW), a perturbed lactation model (PLM), and a quantile regression (QR) were compared in terms of estimated total unperturbed (i.e., expected) milk production and estimated total milk loss (relative to unperturbed yield). The IW and PLM can also be used to identify perturbations of the lactation curve and were thus compared in this regard. The outcome of this study may help a given end-user in choosing the most appropriate method according to their specific requirements. If there is a specific interest in the post-peak lactation phase, IW can be the best option. If one wants to accurately describe the perturbations of the lactation curve, PLM can be the most suitable method. If there is need for a fast and easy approach on a very large data set, QR can be the choice. Finally, as an example of application, PLM was used to analyze the effect of cow parity, calving season, and breed on their estimated lactation performance.

Milk yield residuals and their link with the metabolic status of dairy cows in the transition period

The transition period is one of the most challenging periods in the lactation cycle of high-yielding dairy cows. It is commonly known to be associated with diminished animal welfare and economic performance of dairy farms. The development of data-driven health monitoring tools based on on-farm available milk yield development has shown potential in identifying health-perturbing events. As proof of principle, we explored the association of these milk yield residuals with the metabolic status of cows during the transition period. Over 2 yr, 117 transition periods from 99 multiparous Holstein-Friesian cows were monitored intensively. Pre- and postpartum dry matter intake was measured and blood samples were taken at regular intervals to determine β-hydroxybutyrate, nonesterified fatty acids (NEFA), insulin, glucose, fructosamine, and IGF1 concentrations. The expected milk yield in the current transition period was predicted with 2 previously developed models (nextMILK and SLMYP) using low-frequency test-day (TD) data and high-frequency milk meter (MM) data from the animal's previous lactation, respectively. The expected milk yield was subtracted from the actual production to calculate the milk yield residuals in the transition period (MRT) for both TD and MM data, yielding MRTTD and MRTMM. When the MRT is negative, the realized milk yield is lower than the predicted milk yield, in contrast, when positive, the realized milk yield exceeded the predicted milk yield. First, blood plasma analytes, dry matter intake, and MRT were compared between clinically diseased and nonclinically diseased transitions. MRTTD and MRTMM, postpartum dry matter intake and IGF1 were significantly lower for clinically diseased versus nonclinically diseased transitions, whereas β-hydroxybutyrate and NEFA concentrations were significantly higher. Next, linear models were used to link the MRTTD and MRTMM of the nonclinically diseased cows with the dry matter intake measurements and blood plasma analytes. After variable selection, a final model was constructed for MRTTD and MRTMM, resulting in an adjusted R2 of 0.47 and 0.73, respectively. While both final models were not identical the retained variables were similar and yielded comparable importance and direction. In summary, the most informative variables in these linear models were the dry matter intake postpartum and the lactation number. Moreover, in both models, lower and thus also more negative MRT were linked with lower dry matter intake and increasing lactation number. In the case of an increasing dry matter intake, MRTTD was positively associated with NEFA concentrations. Furthermore, IGF1, glucose, and insulin explained a significant part of the MRT. Results of the present study suggest that milk yield residuals at the start of a new lactation are indicative of the health and metabolic status of transitioning dairy cows in support of the development of a health monitoring tool. Future field studies including a higher number of cows from multiple herds are needed to validate these findings.

Sensor-based behavioral patterns can identify heat-sensitive lactating dairy cows

Heat stress impairs the health and performance of dairy cows, yet only a few studies have investigated the diversity of cattle behavioral responses to heat waves. This research was conducted on an Italian Holstein dairy farm equipped with precision livestock farming sensors to assess potential different behavioral patterns of the animals. Three heat waves, defined as at least five consecutive days with mean daily temperature-humidity index higher than 72, were recorded in the farm area during the summer of 2021. Individual daily milk yield data of 102 cows were used to identify "heat-sensitive" animals, meaning the cows that, under a given heat wave, experienced a milk yield drop that was not linked with other health events (e.g., mastitis). Milk yield drops were detected as perturbations of the lactation curve estimated by iteratively using Wood's equation. Individual daily minutes of lying, chewing, and activity were retrieved from ear-tag-based accelerometer sensors. Semi-parametric generalized estimating equations models were used to assess behavioral deviations of heat-sensitive cows from the herd means under heat stress conditions. Heat waves were associated with an overall increase in the herd's chewing and activity times, along with an overall decrease of lying time. Heat-sensitive cows spent approximately 15 min/days more chewing and performing activities (p < 0.05). The findings of this research suggest that the information provided by high-frequency sensor data could assist farmers in identifying cows for which personalized interventions to alleviate heat stress are needed.

Association between management practices and estimated mastitis incidence and milk losses on robotic dairy farms

This study aims to describe the relation between farm-level management factors and estimated farm-level mastitis incidence and milk loss traits (MIMLT) at dairy farms with automated milking systems. In this observational study, 43 commercial dairy farms in Belgium and the Netherlands were included and 148 'management and udder health related variables' were obtained during a farm visit through a farm audit and survey. The MIMLT were estimated from milk yield data. Quarter-level milk yield perturbations that were caused by presumable mastitis cases (PMC) were selected based on quarter-level milk yield and electrical conductivity. On average, 57.6 ± 5.4% of the identified milk yield perturbations complied with our criteria. From these PMC, 3 farm-level MIMLT were calculated over a one-year period around the farm visit date: (1) the 'average number of PMC per cow per year', (2) the 'absolute milk loss per cow per day', calculated as the farm-level sum of all milk losses during PMC in one year, divided by the average number of lactating cows and the number of days, and (3) the 'relative milk loss', calculated as the farm-level sum of milk losses during PMC in one year, divided by the estimated total production in the absence of PMC. The 'average number of PMC per cow per year' was on average 1.81 ± 0.47. The PMC caused an average milk loss of 0.77 ± 0.26 kg per lactating cow per day, which corresponded to an average production loss of 2.38 ± 0.82% of the expected production in the absence of PMC. We performed a principal component regression (PCR) analysis to link the 3 MIMLT to the 'management and udder health related variables', whilst reducing the multicollinearity and the number of dimensions. The first principal component was mainly related to 'milking system brand, maintenance and settings'. The second component mainly linked to average productivity and somatic cell counts, whereas the third component mainly contained variables linked with mastitis management, treatment, and biosecurity. The 3 PCR models had R² ranging from 0.46 (for absolute milk loss per cow per day) to 0.57 (for relative milk loss). For all models, the second PC had the largest effect size. This analysis raises awareness of the impact of management factors on a factual basis and provides handles to take management actions to improve udder health.

Short communication: Predicting blood plasma non-esterified fatty acid and beta-hydroxybutyrate concentrations from cow milk-addressing systematic issues in modelling

Negative energy status in early lactation is linked to a variety of metabolic disorders, reduced fertility, and decreased milk production. To improve the energy status of cows by breeding and management, the identification of negative energy status is crucial. While biomarkers such as non-esterified fatty acid (NEFA) concentration and beta-hydroxybutyrate (BHB) in blood plasma could be used to identify a negative energy state, measuring them directly from blood is both invasive and expensive. In this work, we developed prediction equations for blood plasma NEFA and BHB levels based on mid-IR spectral measurements of milk. The models were fitted using partial least squares regression and evaluated using both cross-validation and independent-herd validation. A total of 3 183 spectral records from 606 lactations originating from three different herds were utilised. R2 values of 0.53 (RMSE = 0.206 mmol/l, RMSE of cross-validation (RMSECV) 0.217 mmol/l) for NEFA and 0.63 (RMSE = 0.326 mmol/l, RMSECV = 0.353 mmol/l) for BHB were obtained. Furthermore, relatively similar prediction accuracies were found for BHB (RMSE of prediction (RMSEP) 0.411 mmol/l and 0.422 mmol/l) and NEFA (RMSEP = 0.186 mmol/l and 0.221 mmol/l) when model training was done using two herds and validated on the third herd. The results from the model fits confirm that it is possible to build blood plasma BHB and NEFA models based on mid-IR spectra that are sufficiently accurate for practical use.

Milk losses linked to mastitis treatments at dairy farms with automatic milking systems

Mastitis-associated milk losses in dairy cows have a massive impact on farm profitability and sustainability. In this study, we analyzed milk losses from 4 553 treated mastitis cases as recorded via treatment registers at 41 AMS dairy farms. Milk losses were estimated based on the difference between the expected and the actual production. To estimate the unperturbed lactation curve, we applied an iterative procedure using the Wood model and a variance-dependent threshold on the milk yield residuals. We calculated milk losses both in a fixed window around the first treatment day of each mastitis case and in the perturbations corresponding to this day, at the cow level as well as at the quarter level. In a fixed time window of day -5 to 30 around the first treatment, the absolute median milk losses per case were 101.5 kg, highly dependent on the parity and the lactation stage with absolute milk losses being highest in multiparous cows and at peak lactation. Relative milk losses expressed in percentage were highest on the first treatment day, and full recovery was often not reached within 30 days from treatment onset. In 62 % of the cases, we found a perturbation in milk yield at the cow level at the time of treatment. On average, perturbations started 8.7 days before the first treatment and median absolute milk losses increased to 128 kg of milk per perturbation. Mastitis is not expected to have equal effects on the four quarters so this study additionally investigated losses in the individual udder quarters. We used a data-based method leveraging milk yield and electrical conductivity to project the presumably inflamed quarter. Next, we compared losses with the average of presumably non-inflamed quarters. Median absolute losses in a fixed 36-day window around treatment varied between 50.2 kg for front and 59.3 kg for hind inflamed quarters compared to respectively 24.7 and 26.3 kg for the median losses in the non-inflamed quarters. Also here, these losses differed between lactation stages and parities. Expressed proportionally to expected yield, the relative median milk losses in inflamed quarters on the treatment day were 20 % higher in inflamed quarters with a higher variability and slower recovery. In 86 % of the treated mastitis cases, at least one perturbation was found at the quarter level. This analysis confirms the high impact of mastitis on milk production, and the large variation between quarter losses illustrates the potential of quarter analysis for on-farm monitoring at farms with an automated milking system.

Microbial profile during fermentation and aerobic stability of ensiled mixtures of maize stover and banana pseudostem in South Ethiopia

AIMS

This study evaluated pH reduction and microbial growth during fermentation of maize stover (MS) mixed with banana pseudostem (BPS) under South Ethiopian conditions.

MATERIALS AND RESULTS

The MS and BPS were chopped and mixed into six treatments (T): 80% BPS plus 20% DMS (T1), 70% BPS plus 30% DMS (T2), 40% BPS plus 60% FMS (fresh MS) (T3), 20% BPS plus 80% FMS (T4), 100% FMS (T5), and 95% BPS plus 5% molasses (T6). At 0, 7, 14, 30, 60, and 90 days, pH and dry matter were determined. Microbiological quality was assessed using plate counts and Illumina MiSeq sequencing. On day 60 and 90, aerobic stability was investigated. The results showed a significant reduction in pH in all mixtures, except in T1 and T2. Lactic acid bacteria counts reached a maximum in all treatments within 14 days. Sequencing showed marked changes in dominant bacteria, such as Buttiauxella and Acinetobacter to Lactobacillus and Bifidobacterium.

CONCLUSIONS

The fresh MS and BPS mixtures and fresh maize showed significant pH reduction and dominance of desirable microbial groups.

SIGNIFICANCE AND IMPACT OF THE STUDY

The study enables year-round livestock feed supplementation to boost milk and meat production in South Ethiopia.

Bridging the gap between measurement-based and simulation-based metamodels for deriving bulk optical properties from spatially-resolved reflectance profiles: effect of illumination and detection geometry

Non-invasive determination of the optical properties is essential for understanding the light propagation in biological tissues and developing optical techniques for quality detection. Simulation-based models provide flexibility in designing the search space, while measurement-based models can incorporate the unknown system responses. However, the interoperability between these two types of models is typically poor. In this research, the mismatches between measurements and simulations were explored by studying the influences from light source and the incident and detection angle on the diffuse reflectance profiles. After reducing the mismatches caused by the factors mentioned above, the simulated diffuse reflectance profiles matched well with the measurements, with R2 values above 0.99. Successively, metamodels linking the optical properties with the diffuse reflectance profiles were respectively built based on the measured and simulated profiles. The prediction performance of these metamodels was comparable, both obtaining R2 values above 0.96. Proper correction for these sources of mismatches between measurements and simulations thus allows to build a simulation-based metamodel with a wide range of desired optical properties that is applicable to different measurement configurations.

Milk losses and dynamics during perturbations in dairy cows differ with parity and lactation stage

Milk yield dynamics during perturbations reflect how cows respond to challenges. This study investigated the characteristics of 62,406 perturbations from 16,604 lactation curves of dairy cows milked with an automated milking system at 50 Belgian, Dutch, and English farms. The unperturbed lactation curve representing the theoretical milk yield dynamics was estimated with an iterative procedure fitting a model on the daily milk yield data that was not part of a perturbation. Perturbations were defined as periods of at least 5 d of negative residuals having at least 1 day that the total daily milk production was below 80% of the estimated unperturbed lactation curve. Every perturbation was characterized and split in a development and a recovery phase. Based hereon, we calculated both the characteristics of the perturbation as a whole, and the duration, slopes, and milk losses in the phases separately. A 2-way ANOVA followed by a pairwise comparison of group means was carried out to detect differences between these characteristics in different lactation stages (early, mid-early, mid-late, and late) and parities (first, second, and third or higher). On average, 3.8 ± 1.9 (mean ± standard deviation) perturbations were detected per lactation in the first 305 d after calving, corresponding to an estimated 92.1 ± 135.8 kg of milk loss. Only 1% of the lactations had no perturbations. On average, 2.3 kg of milk was lost per day in the development phase, while the recovery phase corresponded to an average increase in milk production of 1.5 kg/d, and these phases lasted an average of 10.1 and 11.6 d, respectively. Perturbation characteristics were significantly different across parity and lactation stage groups, and early and mid-early perturbations in higher parities were found to be more severe with faster development rates, slower recovery rates, and higher milk losses. The method to characterize perturbations can be used for precision phenotyping purposes that look into the response of cows to challenges or that monitor applications (e.g., to evaluate the development and recovery of diseases and how these are affected by preventive actions or treatments).

Silage making of maize stover and banana pseudostem under South Ethiopian conditions: evolution of pH, dry matter and microbiological profile

The study was conducted to evaluate the microbial dynamics during silage of maize stover and banana pseudostem in the environmental conditions of southern Ethiopia. To meet this objective, microsilos containing either maize stover or banana pseudostem, both with and without molasses, were prepared. Subsequently, samples were analysed on day 0, 7, 14, 30, 60 and 90 of the fermentation process. As a result, on day 7, all treatments except banana pseudostem without molasses showed a significant reduction in pH. It was also this silage type that supported the growth of Enterobacteriaceae longer than three other silage types, i.e. until 30 days. The yeasts and moulds and the Clostridum endospore counts also showed a reducing trend in early fermentation and afterwards remained constant until day 90. Illumina MiSeq sequencing revealed that Leuconostoc, Buttiauxella species and Enterobacteriaceae were the most abundant bacteria in the initial phases of the fermentation. Later on, Buttiauxella, Lactobacillus, Weissella and Bifidobacterium species were found to be dominant. In conclusion, silage of the two crop by-products is possible under South Ethiopian conditions. For banana pseudostem, the addition of molasses is crucial for a fast fermentation, in contrast to maize. Upscaling needs to be investigated for the two by-products.

Mid-infrared spectroscopic analysis of raw milk to predict the blood nonesterified fatty acid concentrations in dairy cows

In high-yielding dairy cattle, severe postpartum negative energy balance is often associated with metabolic and infectious disorders that negatively affect production, fertility, and welfare. Mobilization of adipose tissue associated with negative energy balance is reflected through an increased level of nonesterified fatty acids (NEFA) in the blood plasma. Earlier, identification of negative energy balance through detection of increased blood plasma NEFA concentration required laborious and stressful blood sampling. More recently, attempts have been made to predict blood NEFA concentration from milk samples. In this study, we aimed to develop and validate a model to predict blood plasma NEFA concentration using the milk mid-infrared (MIR) spectra that are routinely measured in the context of milk recording. To this end, blood plasma and milk samples were collected in wk 2, 3, and 20 postpartum for 192 lactations in 3 herds. The blood plasma samples were taken in the morning, and representative milk samples were collected during the morning and evening milk sessions on the same day. To predict plasma NEFA concentration from the milk MIR spectra, partial least squares regression models were trained on part of the observations from the first herd. The models were then thoroughly validated on all other observations of the first herd and on the observations of the 2 independent herds to explore their robustness and wide applicability. The final model could accurately predict blood plasma NEFA concentrations <0.6 mmol/L with a root mean square error of prediction of <0.143 mmol/L. However, for blood plasma with >1.2 mmol/L NEFA, the model clearly underestimated the true level. Additionally, we found that morning blood plasma NEFA levels were predicted with significantly higher accuracy using MIR spectra of evening milk samples compared with MIR spectra of morning samples, with root mean square error of prediction values of, respectively, 0.182 and 0.197 mmol/L, and R² values of 0.613 and 0.502. These results suggest a time delay between variations in blood plasma NEFA and related milk biomarkers. Based on the MIR spectra of evening milk samples, cows at risk for negative energy status, indicated by detrimental morning blood plasma NEFA levels (>0.6 mmol/L), could be identified with a sensitivity and specificity of, respectively, 0.831 and 0.800. As this model can be applied to millions of historical and future milk MIR spectra, it opens an opportunity for regular metabolic screening and improved resilience phenotyping.

Validation of a novel milk progesterone-based tool to monitor luteolysis in dairy cows: Timing of the alerts and robustness against missing values

Automated monitoring of fertility in dairy cows using milk progesterone is based on the accurate and timely identification of luteolysis. In this way, well-adapted insemination advice can be provided to the farmer to further optimize fertility management. To properly evaluate and compare the performance of new and existing data-processing algorithms, a test data set of progesterone time-series that fully covers the desired variability in progesterone profiles is needed. Further, the data should be measured with a high frequency to allow rapid onset events, such as luteolysis, to be precisely determined. Collecting this type of data would require a lot of time, effort, and budget. In the absence of such data, an alternative was developed using simulated progesterone profiles for multiple cows and lactations, in which the different fertility statuses were represented. To these, relevant variability in terms of cycle characteristics and measurement error was added, resulting in a large cost-efficient data set of well-controlled but highly variable and farm-representative profiles. Besides the progesterone profiles, information on (the timing of) luteolysis was extracted from the modeling approach and used as a reference for the evaluation and comparison of the algorithms. In this study, 2 progesterone monitoring tools were compared: a multiprocess Kalman filter combined with a fixed threshold on the smoothed progesterone values to detect luteolysis, and a progesterone monitoring algorithm using synergistic control, PMASC, which uses a mathematical model based on the luteal dynamics and a statistical control chart to detect luteolysis. The timing of the alerts and the robustness against missing values of both algorithms were investigated using 2 different sampling schemes: one sample per cow every 8 h versus 1 sample per day. The alerts for luteolysis of the PMASC algorithm were on average 20 h earlier compared with the ones of the multiprocess Kalman filter, and their timing was less sensitive to missing values. This was shown by the fact that, when 1 sample per day was used, the Kalman filter gave its alerts on average 24 h later, and the variability in timing of the alerts compared with simulated luteolysis increased with 22%. Accordingly, we postulate that implementation of the PMASC system could improve the consistency of luteolysis detection on farm and lower the analysis costs compared with the current state of the art.

Estimation of Particle Size Distribution from Bulk Scattering Spectra: Validation on Monomodal Suspensions

A particle size distribution (PSD) estimation method based on light-scattering properties was validated on experimental visible/near-infrared scattering spectra of polystyrene suspensions, with a nominal particle size ranging from 0.1 to 12 μm in diameter. On the basis of μ_s and g spectra extracted from double integrating sphere measurements, good PSD estimates were obtained for particles ≥1 μm. The particle volume fraction estimates in the case of μ_s were close to the target concentrations, although influenced by small baseline fluctuations on the spectra. For submicrometer particles, on the other hand, the non-oscillating μ_s spectra lack discriminating power, resulting in erroneous PSD estimates. The reduced scattering coefficient spectra (μ_s') were found less useful for particle size estimation as they lack a characteristic shape, causing an over- or underestimation of the distribution width. In summary, the estimation routine proved to deliver PSD estimates in line with the reference measurements for micrometer-sized or larger particles based on their μ_s and g scattering spectra. Additional validation on more polydisperse samples forms the next step before going to bimodal PSD estimates.

Short communication: Validation of a novel milk progesterone-based tool to monitor luteolysis in dairy cows using cost-effective, on-farm measured data

The progesterone (P4) monitoring algorithm using synergistic control (PMASC) uses luteal dynamics to identify fertility events in dairy cows. This algorithm employs a combination of mathematical functions describing the increasing and decreasing P4 concentrations during the development and regression of the corpus luteum and a statistical control chart that allows identification of luteolysis. The mathematical model combines sigmoidal functions from which the cycle characteristics can be calculated. Both the moment at which luteolysis is detected and confirmed by PMASC, as well as the model features themselves, can be used to inform the farmer on the fertility status of the cows.

Estimation of particle size distributions from bulk scattering spectra: sensitivity to distribution type and spectral noise

A shape dependent method for particle size distribution (PSD) estimation based on bulk scattering properties was elaborated. This method estimates the parameters of a particle size distribution with predefined shape from the bulk scattering spectra. The estimation routine was validated on simulated data of polystyrene in water suspensions. To investigate the effect of measurement errors on PSD estimates, a sensitivity analysis was performed. The influence of spectral resolution and range was rather limited. Good PSD estimations were obtained on noise-free spectra, spectra with limited random noise and for estimations on μs or μs' in case of a multiplicative baseline. However, the PSD estimation deteriorated if an incorrect value for the refractive index of the particle relative to the medium was used as input parameter. Deviations caused by an incorrect distribution type were smaller for more narrow PSDs than for broader ones. Overall, this study showed the potential to estimate PSDs from bulk scattering spectra and indicated the factors affecting the accuracy.

Anisotropic light propagation in bovine muscle tissue depends on the initial fiber orientation, muscle type and wavelength

The effects of fiber orientation on vis/NIR light propagation were studied in three bovine muscles: biceps brachii, brachialis and soleus. Broadband light was focused onto the sample and the diffuse reflectance spot was captured using a hyperspectral camera (470-1620 nm), after which rhombuses were fitted to equi-intensity points. In samples with fibers running parallel to the measurement surface, the rhombus' major axis was oriented perpendicular to the fiber direction close to the point of illumination. However, at larger distances from the illumination spot, the major axis orientation aligned with the fiber direction. This phenomenon was found to be muscle dependent. Furthermore, the rhombus orientation was highly dependent on the sample positioning underneath the camera, especially when the muscle fibers ran parallel to the measurement surface. The bias parameter, indicating the deviation from a circular shape, was higher for samples with the fibers running parallel to the measurement surface. Moreover, clear effects of wavelength and distance from the illumination point on this parameter were observed. These results show the importance of fiber orientation when considering optical techniques for measurements on anisotropic, fibrous tissues. Moreover, the prediction of muscle fiber orientation seemed feasible, which can be of interest to the meat industry.

Near-infrared bulk optical properties of goat wound tissue and human serum: consequences for an implantable optical glucose sensor

Near-infrared (NIR) spectroscopy offers a promising technological platform for continuous glucose monitoring in the human body. Moreover, these measurements could be performed in vivo with an implantable single-chip based optical sensor. However, a thin tissue layer may grow in the optical path of the sensor. As most biological tissues are highly scattering, they only allow a small fraction of the collimated light to pass, significantly reducing the light throughput. To quantify the effect of a thin tissue layer in the optical path, the bulk optical properties of serum and tissue samples grown on implanted dummy sensors were characterized using double integrating sphere and unscattered transmittance measurements. The estimated bulk optical properties were then used to calculate the light attenuation through a thin tissue layer. The combination band of glucose was found to be the better option, relative to the first overtone band, as the absorptivity of glucose molecules is higher, while the reduction in unscattered transmittance due to tissue growth is less. Additionally, as the wound tissue was found to be highly scattering, the unscattered transmittance of the tissue layer is expected to be very low. Therefore, a sensor configuration which measures the diffuse transmittance and/or reflectance instead was recommended. (a) Dummy sensor; (b) explanted dummy sensor in tissue lump; (c) removal of dummy sensor from tissue lump; and (d) 900 µm slices of tissue lump.

Computational optimization of the configuration of a spatially resolved spectroscopy sensor for milk analysis

A global optimizer has been developed, capable of computing the optimal configuration in a probe for spatially resolved reflectance spectroscopy (SRS). The main objective is to minimize the number of detection fibers, while maintaining an accurate estimation of both absorption and scattering profiles. Multiple fibers are necessary to robustify the estimation of optical properties against noise, which is typically present in the measured signals and influences the accuracy of the inverse estimation. The optimizer is based on a robust metamodel-based inverse estimation of the absorption coefficient and a reduced scattering coefficient from the acquired SRS signals. A genetic algorithm is used to evaluate the effect of the fiber placement on the performance of the inverse estimator to find the bulk optical properties of raw milk. The algorithm to find the optimal fiber placement was repeatedly executed for cases with a different number of detection fibers, ranging from 3 to 30. Afterwards, the optimal designs for each considered number of fibers were compared based on their performance in separating the absorption and scattering properties, and the significance of the differences was tested. A sensor configuration with 13 detection fibers was found to be the combination with the lowest number of fibers which provided an estimation performance which was not significantly worse than the one obtained with the best design (30 detection fibers). This design resulted in the root mean squared error of prediction (RMSEP) of 1.411 cm(-1) (R(2) = 0.965) for the estimation of the bulk absorption coefficient values, and 0.382 cm(-1) (R(2) = 0.996) for the reduced scattering coefficient values.

Three-dimensional microscale modelling of CO2 transport and light propagation in tomato leaves enlightens photosynthesis

We present a combined three-dimensional (3-D) model of light propagation, CO2 diffusion and photosynthesis in tomato (Solanum lycopersicum L.) leaves. The model incorporates a geometrical representation of the actual leaf microstructure that we obtained with synchrotron radiation X-ray laminography, and was evaluated using measurements of gas exchange and leaf optical properties. The combination of the 3-D microstructure of leaf tissue and chloroplast movement induced by changes in light intensity affects the simulated CO2 transport within the leaf. The model predicts extensive reassimilation of CO2 produced by respiration and photorespiration. Simulations also suggest that carbonic anhydrase could enhance photosynthesis at low CO2 levels but had little impact on photosynthesis at high CO2 levels. The model confirms that scaling of photosynthetic capacity with absorbed light would improve efficiency of CO2 fixation in the leaf, especially at low light intensity.

Robust metamodel-based inverse estimation of bulk optical properties of turbid media from spatially resolved diffuse reflectance measurements

Estimation of the bulk optical properties of turbid samples from spatially resolved reflectance measurements remains challenging, as the relation between the bulk optical properties and the acquired spatially resolved reflectance profiles is influenced by wavelength-dependent properties of the measurement system. The resulting measurement noise is apparent in the estimation of the bulk optical properties. In this study, a constrained inverse metamodeling approach is proposed to overcome these problems. First, a metamodel has been trained on a set of intralipid phantoms covering a wide range of optical properties to link the acquired spatially resolved reflectance profiles to the respective combinations of bulk optical properties (absorption coefficient and reduced scattering coefficient). In this metamodel, the wavelength (500 - 1700 nm) is considered as a third input parameter for the model to account for the wavelength dependent effects introduced by the measurement system. Secondly, a smoothness constraint on the reduced scattering coefficient spectra was implemented in the iterative inverse estimation procedure to robustify it against measurement noise and increase the reliability of the obtained bulk absorption and reduced scattering coefficient spectra. As the estimated values in some regions may be more reliable than others, the difference between simulated and measured values as a function of the evaluated absorption and scattering coefficients was combined in a 2D cost function. This cost function was used as a weight in the fitting procedure to find the parameters of the µ(s)' function giving the lowest cost over all the wavelengths together. In accordance with previous research, an exponential function was considered to represent the µ(s)' spectra of intralipid phantoms. The fitting procedure also provides an absorption coefficient spectrum which is in accordance with the measurements and the estimated parameters of the exponential function. This robust inverse estimation algorithm was validated on an independent set of intralipid® phantoms and its performance was also compared to that of a classical single-wavelength inverse estimation algorithm. While its performance in estimating µ(a) was comparable (R2 of 0.844 vs. 0.862), it resulted in a large improvement in the estimation of µ(s)' (R2 of 0.987 vs. 0.681). The change in performance is more apparent in the improvement of RMSE of µ(s)', which decreases from 10.36 cm(-1) to 2.10 cm(-1). The SRS profiles change more sensitively as a function of µ(a). As a result, there is a large range of µ(s)' and a small range of µa resulting in a good fit between measurement and simulation. The robust inverse estimator incorporates information over the different wavelengths, to increase the accuracy of µ(s)'estimations and robustify the estimation process.

Estimation of bulk optical properties of turbid media from hyperspectral scatter imaging measurements: metamodeling approach

In many research areas and application domains, the bulk optical properties of biological materials are of great interest. Unfortunately, these properties cannot be obtained easily for complex turbid media. In this study, a metamodeling approach has been proposed and applied for the fast and accurate estimation of the bulk optical properties from contactless and non-destructive hyperspectral scatter imaging (HSI) measurements. A set of liquid optical phantoms, based on intralipid, methylene blue and water, were prepared and the Vis/NIR bulk optical properties were characterized with a double integrating sphere and unscattered transmittance setup. Accordingly, the phantoms were measured with the HSI technique and metamodels were constructed, relating the Vis/NIR reflectance images to the reference bulk optical properties of the samples. The independent inverse validation showed good prediction performance for the absorption coefficient and the reduced scattering coefficient, with R(2)(p) values of 0.980 and 0.998, and RMSE(P) values of 0.032 cm(-1) and 0.197 cm(-1) respectively. The results clearly support the potential of this approach for fast and accurate estimation of the bulk optical properties of turbid media from contactless HSI measurements.

Modeling the propagation of light in realistic tissue structures with MMC-fpf: a meshed Monte Carlo method with free phase function

Monte Carlo methods commonly used in tissue optics are limited to a layered tissue geometry and thus provide only a very rough approximation for many complex media such as biological structures. To overcome these limitations, a Meshed Monte Carlo method with flexible phase function choice (fpf-MC) has been developed to function in a mesh. This algorithm can model the light propagation in any complexly shaped structure, by attributing optical properties to the different mesh elements. Furthermore, this code allows the use of different discretized phase functions for each tissue type, which can be simulated from the microstructural properties of the tissue, in combination with a tool for simulating the bulk optical properties of polydisperse suspensions. As a result, the scattering properties of tissues can be estimated from information on the microstructural properties of the tissue. This is important for the estimation of the bulk optical properties that can be used for the light propagation model, since many types of tissue have never been characterized in literature. The combination of these contributions, made it possible to use the MMC-fpf for modeling the light porapagation in plant tissue. The developed Meshed Monte Carlo code with flexible phase function choice (MMC-fpf) was successfully validated in simulation through comparison with the Monte Carlo code in Multi-Layered tissues (R2 > 0.9999) and experimentally by comparing the measured and simulated reflectance (RMSE = 0.015%) and transmittance (RMSE = 0.0815%) values for tomato leaves.

Flexible tool for simulating the bulk optical properties of polydisperse spherical particles in an absorbing host: experimental validation

In this study, a flexible tool to simulate the bulk optical properties of polydisperse spherical particles in an absorbing host medium is described. The generalized Mie solution for Maxwell's equations is consulted to simulate the optical properties for a spherical particle in an absorbing host, while polydispersity of the particle systems is supported by discretization of the provided particle size distributions. The number of intervals is optimized automatically in an efficient iterative procedure. The developed tool is validated by simulating the bulk optical properties for two aqueous nanoparticle systems and an oil-in-water emulsion in the visible and near-infrared wavelength range, taking into account the representative particle sizes and refractive indices. The simulated bulk optical properties matched closely (R2 ≥ 0.899) with those obtained by reference measurements.

Dependent scattering in Intralipid® phantoms in the 600-1850 nm range

The effect of dependent scattering on the bulk scattering properties of intralipid phantoms in the 600-1850 nm wavelength range has been investigated. A set of 57 liquid optical phantoms, covering a wide range of intralipid concentrations (1-100% v/v), was prepared and the bulk optical properties were accurately determined. The bulk scattering coefficient as a function of the particle density could be well described with Twersky's packing factor (R(2) > 0.990). A general model was elaborated taking into account the wavelength dependency and the effect of the concentration of scattering particles (R(2) = 0.999). Additionally, an empirical approach was followed to characterize the effect of dense packing of scattering particles on the anisotropy factor (R(2) = 0.992) and the reduced scattering coefficient (R(2) = 0.999) of the phantoms. The derived equations can be consulted in future research for the calculation of the bulk scattering properties of intralipid dilutions in the 600-1850 nm range, or for the validation of theories that describe the effects of dependent scattering on the scattering properties of intralipid-like systems.

Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements

A metamodeling approach is introduced and applied to efficiently estimate the bulk optical properties of turbid media from spatially resolved spectroscopy (SRS) measurements. The model has been trained on a set of liquid phantoms covering a wide range of optical properties representative for food and agricultural products and was successfully validated in forward and inverse mode on phantoms not used for training the model. With relative prediction errors of 10% for the estimated bulk optical properties the potential of this metamodeling approach for the estimation of the optical properties of turbid media from spatially resolved spectroscopy measurements has been demonstrated.

Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range

A supercontinuum laser based double integrating sphere setup in combination with an unscattered transmittance measurement setup was developed and carefully validated for optical characterization of turbid samples in the 500-2250 nm wavelength range. A set of 57 liquid optical phantoms, covering a wide range of absorption and scattering properties, were prepared and measured at two sample thicknesses. The estimated bulk optical properties matched well for both thicknesses, and with theory and literature, without significant crosstalk between absorption and scattering. Equations were derived for the bulk scattering properties μ(s), μ(s)' and g of Intralipid® 20% which can be used to calculate the bulk scattering properties of intralipid-dilutions in the 500-2250 nm range.