# Optical scattering coefficient measurement of blood plasma during clot formation

Lea Abi Nassif, Wadih Khater, Fabrice Pellen, Bernard Le Jeune, Marie Abboud, Marc Danguy Des Déserts, Benjamin Espinasse, Guy Le Brun

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Lea Abi Nassif, Wadih Khater, Fabrice Pellen, Bernard Le Jeune, Marie Abboud, et al. Optical scattering coefficient measurement of blood plasma during clot formation. Biomedical Physics & Engineering Express, 2025, 11 (6), pp.065015. 10.1088/2057-1976/ae103c. hal-05370183

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# Optical scattering coefficient measurement of blood plasma during clot formation

To cite this article: Lea Abi Nassif et al 2025 *Biomed. Phys. Eng. Express* 11 065015

View the [article online](#) for updates and enhancements.

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# Optical scattering coefficient measurement of blood plasma during clot formation

Lea Abi Nassif<fnref n="1" />,*, Wadih Khater<fnref n="1" />, Fabrice Pellen<fnref n="1" />, Bernard Le Jeune<fnref n="1" />, Marie Abboud<fnref n="2" />, Marc Danguy des Déserts<fnref n="3" />,<fnref n="4" />, Benjamin Espinasse<fnref n="3" />,<fnref n="5" /> and Guy Le Brun<fnref n="1" />

**E-mail:** lea.abinassif@univ-brest.fr

**Keywords:** biophotonics, laser, optics, human plasma, clot formation, scattering

## Abstract

**Objective.** Venous Thromboembolism (VTE) is a very dangerous and common disease. While approximately 50% of VTE can be attributed to identifiable causes, the remaining half has no known origin and about 30% of this group show recurrence. Monitoring the kinetics of optical scattering properties of plasma during clot formation can provide information on clot structure, which seems to be a relevant parameter to identify patients at risk of recurrence. **Approach.** This study aims to compare a sensitive and quantitative optical method based on the scattering coefficient $\mu_s$ measurement, never previously explored in the context of VTE, to the conventional optical density (OD) measurement obtained by a spectrophotometer. **Main results.** The evolution of eight characteristic parameters, extracted from clot formation curve signatures, was studied as a function of plasma concentration. **Significance.** Scattering coefficient measurements are sensitive to plasma concentration in the sample, more reproducible, more precise and provide access to new information compared to OD measurements.

## 1. Introduction

Venous thromboembolism (VTE), the third leading cause of cardiovascular death, is a significant health concern. It encompasses deep vein thrombosis (DVT) and pulmonary embolism (PE). Deep vein thrombo- sis occurs when a blood clot forms in the deep leg veins. If this clot then migrates through the blood- stream and occludes pulmonary arteries, it can result in a potentially fatal PE. Venous thromboembolism results in significant mortality, with PE having a 30% death rate (Cushman 2007). The estimated incidence rates of VTE among Europeans range from 104 to 183 per 100,000 person-years (Heit 2015) causing more than 30,000 deaths in Europe annually (Zabczyk et al 2017). After clinical investigation, nearly half of VTE cases can be explained (immobilization, cancer, inherited thrombophilia), but the other half has no known origin (known as idiopathic VTE). Among the

patients developing idiopathic/non-provoked VTE, about 30% of them have a recurrent thromboembolic event and 70% show no recurrence (Khan et al 2019). This leads to difficult decisions concerning the population with non-provoked VTE. Although antico- oagulation therapy used to treat VTE is very efficient, it also has major side effects, such as bleeding events, that can be deadly. A balance must be struck between the risks of recurrent thrombosis if anticoagulant treatment is stopped versus the risks of bleeding associated with ongoing anticoagulation therapy, which can continue for decades. Over the last 20 years, although research has helped in understanding clot formation dynamics (Piederrière et al 2004), devel- oped risk scores (Undas 2017) and made discoveries about the genetic basis of the disease (Undas and Ariëns 2011), VTE patient prognoses have not chan- ged (Piran and Schulman 2016). Such limited improvement in patient prognoses can be attributed

<footnote n="1">¹ Laboratory of Optics and Magnetism OPTIMAG UR 938, IBSAM, Univ Brest, F-29200 Brest, France</footnote>

<footnote n="2">² Physics Department, UR TVA, Faculty of Science, Saint Joseph University, B.P. 11-514 Riad El Solh Beirut 1107 2050, Lebanon</footnote>

<footnote n="3">³ INSERM, UMR 1304, Groupe d'Etude de Thrombose de Bretagne Occidentale GETBO, Univ Brest, F-29200 Brest, France</footnote>

<footnote n="4">⁴ Department of anesthesia and intensive care, Clermont-Tonnerre Military Hospital, Brest, FCRIN INNOVTE, France</footnote>

<footnote n="5">⁵ Vascular medicine, Brest University Hospital, Brest, France</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
to the multifactorial aspect of this idiopathic pathology. It is therefore now vital to identify biomarkers that reveal abnormal clot structure.

A specific field of research has developed to study clotting *in vitro* using comprehensive physico-chemical, mechanical, and physical analysis techniques investigating the mesoscopic domain. These approaches involve macroscopic and microscopic analysis, including permeability measurement for fibrin fiber diameter estimation, turbidimetry measurement by photometric methods to determine lag phase (time to the start of protofibril aggregation), and average fibrin fiber thickness measurement by maximum absorption (Undas 2017), which also reflects the maximum number of fibrin fibers reached in a sample (Larsen and Hvas 2020). Imaging techniques have also been used for visual evaluation of pore size and clot density in the fiber network with promising results (Undas 2017). In brief, it appears that different patient phenotypes have different fibrin clot structures. Developing clot analysis based on physico-chemical properties appears promising for: 1. creating risk models for venous thromboembolic disease recurrence, 2. offering personalized treatments, and 3. enhancing understanding of pathophysiological mechanisms. Recent studies have demonstrated that low fibrin network permeability and resistance to lysis could help identify patients at risk of pulmonary embolism recurrence because VTE patients have denser *in vitro* fibrin clots (Undas 2021). While this clinical and physico-chemical context highlights the importance of characterizing clot structure, the aim of the present study is to focus mainly on optical methods for *in vitro* clot analysis. Existing physicochemical approaches are promising, showing similar trends for changes in network and fiber structure with regard to plasma concentration in samples, there were differences in the polymerization times and rates (Risman et al 2024). For example, Zeng et al demonstrated that optical density (OD) measurement and thromboelastography (TEG) have different strengths and weaknesses, so that both assays are necessary to form a comprehensive clot characterization under diverse condition (Zeng et al 2020). Moreover, OD measurements are not very reproducible since differences in optical configurations among different spectrophotometers make the largest contribution to observed differences (Matlock et al 2011). Matlock et al demonstrated that the distance between sample and detector, the size and focal length of any collector lens used, and the area and sensitivity of the detector can all affect the OD value measured. In addition, both the chosen wavelength and beam diameter can affect the values obtained by OD measurement. Furthermore, OD measurements provide information about the overall absorption of the sample, without differentiating transmitted or unabsorbed photons from scattered or multiply-scattered photons, combining the absorption and scattering properties. It is

therefore important to differentiate between the two kinds of information provided by this conventional analysis. To address this challenge, we propose a methodological approach that isolate the scattering-related optical properties by evaluating the scattering coefficient $\mu_s$ of plasma during *in vitro* clotting. This quantitative optical method measures only the transmitted photons and allows us to evaluate the evolution of $\mu_s$ over time. This work does not aim to directly solve clinical problems, but rather to improve the reliability and specificity of *in vitro* clot characterization methods, potentially contributing to better understanding clot structure in future biomedical studies. This approach provides direct insights into the structural properties of clots, offering a more detailed and reproducible analysis than standard OD measurement.

Our paper is organized as follows. In section 2 we first present the coagulation cascade and the commonly used optical density assay for clot formation analysis. We then describe the set-up we used to measure the scattering coefficient $\mu_s$ on plasma during clot formation and the sample preparation protocol used in this study. In section 3, we present the results obtained by this optical method compared with the classic optical density method before interpreting and discussing the results.

## 2. Method

### 2.1. Coagulation cascade

Clot formation, the primary focus of our study, is a critical physiological process leading to hemostasis and represents the final step of a cascade of enzymatic reactions, as illustrated in figure 1 (Knesek et al 2012).

The coagulation cascade can be activated by different triggering factors leading to two distinct pathways, intrinsic and extrinsic, which ultimately converge at a common point leading to the transformation of fibrinogen proteins into fibrin monomers, in the presence of thrombin, as a transient intermediate. They then polymerize to protofibrils, which then associate laterally to form fibrin fibers that are cross-linked by Factor XIIIa, a coagulation factor activated by calcium chloride generating an insoluble network, known as the fibrin gel (De Cristofaro and Cera 1991). In our study, clot formation is activated through the extrinsic pathway by the addition of tissue factor, as done by Larsen et al (Larsen and Hvas 2020).

### 2.2. Sample preparation

In brief, *in vitro* clot formation was initiated by adding HEPES-buffered saline solution, commonly used to keep the media at a physiological pH of 7.4, tissue factor (TF) a clot initiator factor, and calcium chloride to cross-link the fibrin network. Research quality citrated platelet poor plasma (PPP) was obtained from
<figure><img src="image_6.png" /><figcaption>**Figure 1.** Coagulation cascade (Knesek, Peterson and Markel, 2012).</figcaption></figure>

<table><caption>**Table 1.** Concentrations in volume percentage of plasma, HEPES-buffered saline, tissue factor, and calcium chloride in clotting samples.</caption><thead><tr><th>Name of the sample</th><th>PPP<sub>51</sub>HE<sub>40</sub></th><th>PPP<sub>34</sub>HE<sub>57</sub></th><th>PPP<sub>25</sub>HE<sub>66</sub></th><th>PPP<sub>20</sub>HE<sub>71</sub></th><th>PPP<sub>13</sub>HE<sub>78</sub></th><th>PPP<sub>8</sub>HE<sub>83</sub></th></tr></thead><tbody><tr><td>Plasma (% v/v)</td><td>50.74%</td><td>33.83%</td><td>25.37%</td><td>20.30%</td><td>12.69%</td><td>8.45%</td></tr><tr><td>HEPES (% v/v)</td><td>40.46%</td><td>57.37%</td><td>65.83%</td><td>70.90%</td><td>78.51%</td><td>82.75%</td></tr><tr><td>Tissue Factor (% v/v)</td><td></td><td></td><td colspan="4">6.77%</td></tr><tr><td>CaCl<sub>2</sub> (% v/v)</td><td></td><td></td><td colspan="4">2.03% = 20 mM</td></tr></tbody></table>

EFS (Etablissement Français du Sang). This PPP, from healthy donors, was pooled, homogenized, centrifuged at 2500 g for 15 min at room temperature, and aliquoted in 5 ml volumes and stored at -80 °C. Different clots were initiated by the addition of HEPES-buffered saline solution (HEPES 20 mM, NaCl 150 mM pH 7.4, Ampliquon A/S, Odense M, Denmark), tissue factor (INNOVIN®, Siemens Health Care Diagnostics, Order No. DAB B4212-40), and calcium chloride hexahydrate (1M solution) for different concentrations of plasma ranging from 51% to 8%. The dilution was made by increasing the HEPES concentration while keeping concentrations of TF and calcium fixed, as shown in table 1. The name of each sample is represented by PPPₓHEᵧ, where x and y are the plasma and HEPES volume percentage in each sample, respectively.

## 2.3. Optical density measurement

After thawing to 37 °C, plasma was transferred into an individual well of a 96-well microliter plate (Nunc ImmunoPlate, Thermo Fisher Scientific). Clot formation was induced in HEPES-buffered saline by a clot induction mix (CIM) consisting of tissue factor and calcium chloride with the concentrations shown in table 1, resulting in a final volume of 200 µl per well. The final induction mixture was obtained by an automatic injection of calcium and a shaking of the microliter plate at 120 rpm for 5 seconds, ensuring uniform distribution of all components. Six replicates of each sample were tested. Optical density was

monitored at 37 °C on a spectrophotometer (Thermo Scientific Varioskan® Flash with SkanIT software), measuring every 20 seconds for 350 reads (i.e., up to 120 min) at a 405 nm wavelength with a settle delay of 50 ms. The 405 nm wavelength was selected for two reasons: its high sensitivity to changes in fibrin structure (Wolberg et al 2002) and its linear correlation with the fiber mass-length ratio, as reflected in the optical density measurements (Carr and Zekert 1990).

A well containing only HEPES-buffered saline was included as a background control, and the OD value obtained from this well was subtracted from the readings of all experimental wells to correct baseline absorbance. Figure 2. represents the optical configuration of a spectrophotometer.

## 2.4. Scattering coefficient measurement set-up

Figure 3 illustrates the experimental set-up used for optical scattering coefficient measurement. A linearly polarized He-Ne laser beam (15 mW) with a coherence length of 20 cm, operating at a wavelength of 632.8 nm was directed onto the sample. The He-Ne laser was used in this study for its excellent beam quality, a main factor for μₛ measurements. Numerous studies investigated the optical properties of human blood and human plasma (Friebel et al 2006, Meinke et al 2007, Bosschaart et al 2014, Saiko et al 2025). At a wavelength of 632.8 nm, absorption coefficient μₐ was negligible making the attenuated light beam directly associated with scattering. Clot
<figure><img src="image_7.png" /><figcaption>Figure 2. Optical configuration of a spectrophotometer.</figcaption></figure>

formation being a polymerization process of fibrinogen into fibrin fibers, forming a network that would only increase the scattering coefficient without altering the absorbent chemical component. Hajjarian et al also showed that absorption was negligible compared to scattering before and after clot formation (Hajjarian et al 2015). Thus, the attenuated signal is directly associated with scattering. The laser intensity was controlled by a half-wave plate (λ/2) and polarizer. The sample temperature was set at 37 °C, and spatial filtering by a converging lens (CL) and optical diaphragm (D) was applied between the sample and detector, with D positioned at the CL focal length in order to only detect non-scattered photons. The non-scattered light was captured by a power meter console (PM100D, Thorlabs, Newton, NJ, USA). The detector was linked to a computer via an interface allowing continuous measurement of the transmitted power through the sample during clot formation with a measurement taken every 10 s, each measurement point being the average of 1000 power measurements.

The study was based on the Beer–Lambert law for collimated transmission:

$$P(t) = P_0 e^{-\mu_s(t)d} \qquad (1)$$

Where $\mu_s$ is the scattering coefficient and d is the thickness of the spectroscopic cuvette made of special optical glass. The thickness of the glass, d, was chosen in order to stay in a single scattering regime i.e., d ≈ l_s with the mean free path l_s = 1/μ_s representative of the average distance between successive scattering events. P_0 is the optical power measured for the HEPES-

buffered saline in the cuvette and P(t) is the transmitted beam's optical power through the sample. The total sample volume used for each scattering coefficient measurement was 2500 µl. The final induction mixture was obtained by gently pipetting up and down, ensuring uniform distribution of all components. Four replicates of each sample were tested for the μ_s measurement set-up. This set-up was calibrated beforehand using suspensions of Polybead® polystyrene microspheres (Polysciences Europe GmbH, 69493 Hirschberg an der Bergstrasse, Germany), with the scattering coefficient predetermined by controlling the size and concentration of scatterers in the sample. An error of 0.3% was obtained between reference and measured value for the microsphere's suspension.

## 2.5. Statistical analysis of data

Matlab® for Windows (Version R2010b, The MathWorks, Inc., USA) was used to perform all statistical analyses of the data. The Kolmogorov-Smirnov test was applied to assess the normality distribution of continuous variables (characteristic parameters of clot formation kinetics obtained from both OD and μ_s measurements). For group comparison, a two-sample t-test was used for normally distributed variables, while the Mann-Whitney test was applied for non-normally distributed ones. A significant level of p-value ≤ 0.05 was considered statistically significant. Confidence intervals at 95% were computed on the mean for normally distributed variables and on the median for non-normally distributed variables. Effect sizes were also assessed: Cohen's d was used for parametric comparison and effect size r for non-parametric ones. Sample sizes for OD measurement group was n₁ = 6 and n₂ = 4 for μ_s measurement group, as detailed in the Method section.

## 3. Results

The measured OD and calculated μ_s (t) were plotted as a function of time for each tested sample during clot formation. By measuring the transmitted power over time, the evolution of the scattering properties was calculated using the equation:

$$\mu_s(t) = \frac{\ln\left(\frac{P_0}{P(t)}\right)}{d} \qquad (2)$$

The evolution of the curves reflecting the kinetics of clot formation has a similar overall pattern whether obtained by the measurement of μ_s or OD. An example of experimental data curves for different plasma concentrations is shown in figure 4.

Although, at first glance, clot formation curves look the same, the scattering coefficient measurements reveal a pronounced temporal shift among them as a function of plasma concentration, which does not occur with OD measurements.
<figure><img src="image_8.png" /><figcaption>**Figure 3.** Experimental set-up used to measure the scattering coefficient of plasma during clot formation. CL: converging lens with a 150 mm focal distance. D: Diaphragm with a 200 µm diameter. λ/2: half wave plate associated with an optical polarizer for intensity control.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 4.** Optical density (a) and scattering coefficient (b) measurements as a function of time during clot formation for all samples represented in table 1.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 5.** Example of an experimental scattering coefficient plot during clot formation showing the sigmoid fit, deviation between the experimental and fit curve, and eight characteristic parameters of the clot formation curve, here corresponding to a PPP₅₁HE₄₀ sample.</figcaption></figure>

Figure 5 shows an example of scattering coefficient kinetics during a clot formation test. As observed, the evolution curves of the scattering coefficient show slight measurement noise. The initial plateau (from 0 to 4 min) reflects the liquid state of the plasma/HEPES ratio, with slight amplitude fluctuations arising from scatterer Brownian movement in the sample. The final plateau (starting at 8 min) corresponds to the structured

gel-like state of the clot, which is sensitive to low-frequency mechanical vibrations. To reduce measurement noise and enhance data accuracy, experimental curves were adjusted to filter out these fluctuations.

Thus, the curves obtained from μs and OD measurements were fitted using a logistic function (equation (3)), a model commonly used to describe how biological systems that initially grow exponentially, then slow down,
and finally stabilize when a limit is reached.

$$f(t) = \frac{K}{1 + ae^{-rt}} \quad (3)$$

What makes this model relevant is its ability to capture the characteristic stages of clot formation: an initial latent phase, followed by a rapid transformation, and then an ultimate stable plateau corresponding to the gel phase. The difference between the experimental curve and fit as a function of time were also calculated. The measurement/model residual showed fluctuations but little bias, which confirms the relevance of the model chosen to denoise the measurements. Finally, eight characteristic parameters were extracted from the clotting kinetics curves, as described by (Posch et al 2020) Characteristic parameters were calculated on raw experimental data as well as on filtered data adjusted by the logistic fit for curves obtained by OD analysis and the scattering coefficient measurement. The first parameter is the average value of the scattering coefficient when plasma is still in the liquid phase. In the literature, this parameter is called baseline absorbance in the case of OD measurements. The second parameter is the average value when plasma is clotted and in the gel phase and is referred to as the maximum absorbance for OD measurements. The amplitude, which is the difference between the two states of plasma was then calculated as a third parameter. Times to 10% (lag-phase), 50% and 90% (time to maximum clot formation rate) of clotting were also calculated. Δt was calculated as the difference between time at 90% and time at 10% of clotting. The clot formation rate (CFR) was calculated as the ratio between the amplitude and Δt.

An analysis and comparison of the evolution of the eight characteristic parameters as a function of plasma concentration is proposed in figures 6 and 7.

Figure 6(a) shows how the optical density measured by spectrophotometry increased with plasma concentration in the sample when the plasma was still in the liquid phase (coagulation had not yet started). The optical density was lowest for PPP₈HE₈₃, with a value of 0.12, and was highest for PPP₅₁HE₄₀, with a value of 0.62. Moreover, the OD was proportional to plasma concentration in the samples, as shown by the equation representing the evolution of OD in relation to plasma concentration. The linear regression equation (figure 6(a)) was calculated on raw as well as adjusted data with no significant difference. When plasma was in the gel phase, the fibrin network was fully formed. (Pieters et al 2020) OD also increased when plasma concentration increased (figure 6(b)). The lowest value of OD = 0.27 corresponded to the least concentrated sample (PPP₈HE₈₃) and the highest value of OD = 1.33 corresponded to the most concentrated sample. The linear regression equation linking OD values to plasma concentration for this state of plasma (figure 6(b)), showed a clear proportionality between the two terms. The amplitude, indicative of plasma transition from liquid to gel state, was also

proportional to plasma concentration, with the lowest value reflecting the least concentrated clot (figure 6(c)). The time to reach 10% of clotting, shown in figure 6(d), decreased as the plasma concentration increased. The plot for this temporal parameter followed a power law with the highest value of 7.61 min corresponding to the sample with the lowest plasma concentration, PPP₈HE₈₃, and the lowest t₁₀% value 5.61 min to the sample with the highest plasma concentration PPP₅₁HE₄₀. The lag phase time represents the initiation of the enzymatic interaction phase and is therefore influenced by plasma concentration. The lower the plasma concentration, the greater the time required to initiate clot formation. The times to 50% and 90% of clotting did not follow a clear pattern in relation to plasma concentration, as shown in figures 6(e) and (f): taking the error bars into account, these parameters remained constant regardless of plasma concentration. There was a dispersion of values around 7.46 ± 0.60 min for t₅₀% and around 8.96 ± 0.64 min for t₉₀%. The parameter Δt = t₉₀% - t₁₀% increased with plasma concentration in the sample (figure 6(g)). This increase was governed solely by the evolution of plasma concentration, showing a corresponding linear evolution with values going from 2.44 to 4.50 min. Finally, CFR increased following a power law with regard to plasma concentration in the sample as shown in figure 6(h). It is important to note that the data dispersion for each sample, represented by the error bars in figure 6, was only noticeable for the time parameters.

For comparison, the evolution of the characteristic parameters derived from optical scattering coefficient measurements is presented in figure 7. Figures 7(a)–(c), show that samples with low plasma concentration had lower scattering coefficients while high concentration samples showed higher scattering coefficients. When plasma was still in the liquid phase (figure 7(a)), the scattering coefficient increased with its concentration in the sample. Figure 7(b) shows the same linear evolution of the scattering coefficient as figure 7(a). Figure 7(c) shows the amplitude linearly increasing as a function of plasma concentration. The amplitude was thus proportional to the plasma concentration in the samples, since μs followed a linear evolution. The evolution of these first three parameters is in accordance with the results obtained by OD measurements.

Moreover, the uncertainty of the slope for these three characteristic parameters following a linear evolution as a function of plasma concentration was calculated using ordinary least squares calculations to compare the sensitivity of each analysis (Montgomery et al 2012). Thus, OD measurements had slope uncertainties of 9.17%, 12.02%, and 15.10% for plasma in a liquid state, gel state, and for the amplitude, respectively. Slope uncertainties calculated for the μs measurement set-up were 8.56%, 6.80%, and 7.03%, respectively.

The time to 10%, 50%, and 90% of clotting decreased as plasma concentration increased. For samples with a low plasma concentration, the clotting
<figure><img src="image_11.png" /><figcaption>**Figure 6.** Eight characteristic parameters of the optical density measurement plotted as a function of plasma concentration (a) optical density for liquid-phase plasma, (b) optical density for gel-phase plasma, (c) optical density as plasma passes from one phase to the other, (d) time to 10% of clotting, (e) time to 50% of clotting, (f) time to 90% of clotting, (g) Δt, (h) clot formation rate.</figcaption></figure>

cascade took longer to initiate (figure 7(d)), going from 4 min for PPP₅₁HE₄₀ to 12 min for PPP₈HE₈₃. We could clearly see by comparing figures 7(d) and (d) that the evolution of t₁₀% in relation to plasma concentration was much more pronounced in the case of the scattering coefficient analysis. The times to 50% and 90% of clotting extracted from μs measurements, presented in figures 7(e) and (f), also decreased as plasma concentration increased, unlike the times extracted from the OD measurements, which remained constant with no clear evolution. Δt, presented in figure 7(g), decreased following a power law, which is in complete contradiction with the OD measurement results. Clot formation rate, presented in figure 7(h), increased with

plasma concentration. The evolution of this last parameter depends on the amplitude and Δt.

Statistical analysis revealed that all characteristic parameters of clot formation kinetics were significantly different between OD and μs measurements (p-value ≤ 0.01) for all plasma concentrations.

## 4. Discussion

The first half of characteristic parameters for OD measurements (figures 6(a)–(d)) followed the same linear evolution as those extracted from μs measurements (figures 7(a)–(d)), keeping in mind that μs
<figure><img src="image_12.png" /><figcaption>**Figure 7.** Eight characteristic parameters of the scattering coefficient measurement plotted as a function of plasma concentration (a) scattering coefficient for liquid-phase plasma, (b) scattering coefficient for gel-phase plasma, (c) scattering coefficient as plasma passes from one phase to the other, (d) time to 10% of clotting, (e) time to 50% of clotting, (f) time to 90% of clotting, (g) Δt, (h) clot formation rate.</figcaption></figure>

reflects the size and concentration of scatterers in the sample. It is thus proportional to their evolution and the slopes clearly show that the µs set-up used in our study is sensitive to plasma concentration. The first parameter, presented in figure 7(a), is indicative of the concentration of scatterers, such as fibrinogen protein, platelet debris, etc The second parameter, shown in figure 7(b), represents the sample structured by a network of fibrin fibers and maximum concentration of fibrin fibers reached (Pieters et al 2020). The third parameter (figure 7(c)) reflects the transition of the sample from liquid state to gel state, which in turn represents the aggregation of fibrin fibers. Time to 10% of clotting, referred to as lag time in the literature (Marchi et al 2021), reflects the beginning of the enzymatic stage when the reaction between thrombin and fibrinogen starts. The evolution of these four

characteristic parameters is in accordance with the results of Risman et al, who found increases in maximum absorbance and CFR and a decrease of lag time for human pooled plasma clots with increasing fibrinogen concentration (Risman et al 2024). It is important to note that the OD measurement method, frequently associated with absorbance and turbidimetry, takes into account the absorbed, scattered and non-scattered/transmitted light, as shown by (Yeromonahos et al 2010). Furthermore, scattering coefficient measurements are quantitative, which is not the case for OD measurements as these are instrument dependent, making it difficult to compare values obtained on different spectrophotometers or by different teams. The ability of the Beer-Lambert based set-up to distinguish and quantitatively measure only the non-scattered/transmitted light is particularly
relevant for studying clot formation, highlighting one of the key advantages of using the scattering coefficient measurement method. The slope uncertainty calculated for the first three characteristic parameters clearly proves that the scattering coefficient measurement set-up based on the Beer-Lambert law for a collimated transmission is more sensitive than classic OD analysis, especially for gel state plasma and µs amplitude measurements. Pathological clots, because of their abnormal structure, can be distinguished by the µs set-up due to the extraction of quantifiable physical parameters reflecting, for example, the thickness and density of fibrin fibers.

The times to 50% and 90% of clotting, derived from the scattering coefficient measurement set-up, did not follow the same evolution as those derived from OD which remained constant with no clear evolution. By taking a closer look into the evolution of t₁₀% and t₅₀%, we could clearly see that both parameters followed the same power law. t₅₀% and t₉₀% were conditioned by the value of t₁₀%, as shown in figures 7(e) and (f). This was first demonstrated by (De Cristofaro and Cera 1991) on OD measurements. This can be explained by the fact that both t₅₀% and t₉₀% are linearly dependent on the values of t₁₀% for each sample as well as being linearly dependent on each other due to the localized screening of the µs set-up. The µs set-up is thus much more sensitive than OD measurements to variation in time parameters. This could be because OD is not very accurate for highly concentrated samples, (Thermo Fisher Scientific - FR 2025) or because OD results can mix information about the absorbed, scattered, and non-scattered/transmitted light or that the results obtained by this conventional analysis are very dependent on the optical configuration of the instrument used, which affects its dynamic range (Matlock et al 2011). By looking at figures 7(d)–(f) in closer detail, we could clearly see that characteristic temporal parameters presented asymptotic behaviour for high plasma concentrations. It is therefore advisable to work with diluted samples in order to remain within the range where the evolution of temporal parameters shows a strong dependence on plasma concentration.

To conclude, the comprehensive analysis of the scattering coefficient, time parameters, and CFR as a function of plasma concentration revealed the efficiency of this optical analysis to quantitatively measure the optical scattering coefficient and thus study clot formation kinetics. µs is thus more suitable for the studied samples since only the non-scattered light is measured. This parameter provides quantitative data that is independent of the spectrophotometer used and yields more detailed and nuanced information than that typically obtained. The differences observed between the two methods tested in this study arose because spectrophotometers were originally designed for the measurement of losses due to

absorption and should be used with caution for studying clot formation kinetics.

## 5. Conclusion

In our work, we conducted a detailed investigation of clot formation process as a function of plasma concentration using a scattering coefficient measurement set-up based on the Beer-Lambert law. A comparative analysis was performed with the conventional OD measurement method widely used by the scientific community. The results provided valuable insights into the non-scattered/transmitted signal during clot formation, indirectly reflecting structural changes in the clot during its formation. When plasma was still in its liquid phase, clots with low plasma concentrations, presenting low scattering coefficients were considered to have fewer scatterers than samples with high values of scattering coefficient, representing high plasma concentrations. In contrast, samples with higher plasma concentrations showed smaller values for time parameters, which were attributed to localized screening effects during clot formation using the scattering coefficient measurement set-up. While µs results aligned with OD measurements in assessing the liquid phase, gel phase, and the amplitude, they offered distinct advantages. Unlike OD, which is highly dependent on the optical configuration of the spectrophotometer, thus making the comparison of results from different teams risky, µs measurements are quantitative and more reproducible. In addition, µs measurements are more precise, with lower uncertainties in slope estimation compared with OD. Moreover, scattering coefficient measurements provide access to new information, such as the evolution of t₅₀%, t₉₀%, Δt, and CFR, which offer significant potential for identifying new biomarkers.

Through this research, we introduced a straightforward and quantitative optical approach for studying the evolution of the optical scattering properties of plasma during clot formation. This method enabled the analysis of characteristic parameters of clot formation kinetics as a function of plasma concentration. In future work, we plan to assess the sensitivity of our set-up to altered clots, by doping healthy plasma with factor VIII, an anti-hemophilic factor. Further investigations will also explore the angular dependence of scatterers and coherence properties of light during clot formation (Hajjarian and Nadkarni 2020). Finally, applying these optical methods to patient plasma exhibiting pronounced thrombophilia phenotypes will be extremely valuable and of significant clinical interest.

## Acknowledgments

This project has received funding from the European Union's Horizon 2020 research and innovation
program under the Marie Skłodowska-Curie grant agreement No 899546. All authors acknowledge IBSAM (Institut Brestois Santé Agro Matière) for financial support, Le Roux for technical assistance and Delabrosse, Frigout and Trimech for their assistance with data collection and analysis.

## Data availability statement

All data that support the findings of this study are included within the article (and any supplementary files).

## Ethical statement

The project was led according to the highest ethical standards: biological samples were obtained from certified structures via ‘Etablissement Français du Sang’ (EFS Rennes) with plasma samples specially dedicated to scientific research, that are not impacting the plasma dedicated and available to patients.

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