Processing pipeline for large optical coherence elastography datasets with quasi-static air-jet excitation: application to human brain tumor tissue

Abstract

Optical coherence elastography (OCE) is a powerful imaging modality for assessing the mechanical properties of biological tissues. We employed an OCE system based on an Optores OMES 3.2 MHz OCT platform combined with an in-house developed air-jet excitation source to characterize healthy and tumorous (meningioma) human brain tissue. This paper presents a comprehensive software framework for processing large OCE datasets, enabling robust extraction of characteristic features from phase-derived displacement data and calculation of mechanical proxy parameters for detailed tissue characterization. Feature detection is achieved using a modified triangle threshold algorithm applied to the displacement curves from the OCE phase data. Extensive pre- and post-processing steps, including percentile-based filtering and adaptive histogram equalization, are applied to mitigate phase unwrapping errors and enhance visualization of the high dynamic range of OCE data. Exemplary measurements on human brain tumor samples demonstrate the framework’s ability to differentiate between tissue types, highlighting its potential for future clinical and research applications.

1. Introduction

Optical Coherence Tomography (OCT) and its extension, Optical Coherence Elastography (OCE), have become powerful tools for biomedical and biomechanical tissue research [1–4]. Furthermore, both techniques are progressing toward intraoperative use for tumor margin detection [5–7].

Elastography in general determines the mechanical properties of materials by applying a known mechanical force (load) and measuring the resulting displacement. The excitation can be static (indentation, compression, tension), dynamic (shear wave propagation or oscillatory loading), or quasi-static, which combines aspects of both approaches [1–4]. In OCE, the displacement is measured using OCT, either via speckle tracking (intensity-based) or through the phase information of the complex OCT signal, providing micrometer-scale sensitivity. This project aims to establish OCE for neurosurgical applications, enabling quantitative assessment of brain tissue mechanics to support tumor delineation from healthy central nervous system (CNS) tissue and to complement existing intraoperative evaluation methods. This sub-project focuses on the development of a processing pipeline implemented as a software framework, capable of extracting phase-based displacement information, synchronizing it with the applied force, computing multiple mechanical parameters, and visualizing the results for up to 153,600 single displacement curves in parallel. The extracted parameters include the Normalized Bulk Displacement (NBD), representing the overall displacement response of the tissue; the Normalized Local Strain (NLS), describing local deformation gradients; the Creep Compliance Rate, quantifying time-dependent deformation under constant load; as well as Viscosity, indicating resistance to flow or internal friction, and Elasticity, reflecting the reversible stiffness of the material. Additionally, the Hysteresis-based Loss Energy characterizes the mechanical energy dissipated during one load–unload cycle and thus serves as a direct indicator of viscoelastic and plastic behavior. Together, these parameters form a comprehensive mechanical fingerprint of the investigated tissue. The overarching goal is to enable future AI-based differentiation between healthy and pathological regions.

Since currently only the total excitation force exiting the air-jet nozzles can be measured, absolute mechanical parameters cannot yet be derived. Therefore, the framework focuses on calculating proxy parameters that are assumed to be linearly proportional to the true mechanical properties and can serve as reliable descriptors of tissue mechanics. Which however, remains an assumption that will require future validation. However, the system’s high reproducibility allows consistent comparisons across samples, as all measurements share the same systematic offset and thus reflect true differences in sample properties.

The multi-parametric nature of the proposed measurement should enable a comprehensive mechanical characterization of the investigated tissue. Single parameters, most commonly elasticity, are often insufficient for robust tissue differentiation, particularly in complex, highly viscous, and heterogeneous biological samples. Incorporating multiple mechanical properties into the analysis should improve the robustness of tissue delineation across different tissue subtypes. Previous studies indicate that, while elastic parameters provide valid contrast, viscous and ductile properties related to stress-relaxation behavior can constitute more robust descriptors that complement the elastic response [8]. The presented approach further enables biomechanical research at optical resolution by providing a complete mechanical fingerprint for each tissue region and pixel within the scan data.

Brain tissue poses a particular challenge due to its pronounced viscoelastic and poroviscoelastic behavior [9–11]. We could not induce any measurable wave propagation using air-puff or piezo-based ultrasound excitations, indicating an overdamped, highly viscous system that dissipates dynamic forces. Consequently, wave-based OCE approaches were excluded in favor of a quasi-static excitation using elongated air-jet pulses, which provided stable and interpretable displacement data. This approach allows, within a single excitation cycle, the extraction of parameters corresponding to the primary mechanical properties: elasticity, viscosity, and ductility. The excitation is generated by a custom air-jet system [12], offering precise, contactless, and compact control of the applied force, corresponding to a uniaxial compression or indentation-based load. The OCT system provides high-resolution displacement maps but requires robust phase unwrapping to ensure noise-free data. Several approaches have been proposed [13,14]; here, a phase-based method was chosen for its superior displacement sensitivity and its ability to reveal subtle differences in the mechanical properties of different tissue types.

Most compression-based OCE studies generate volumetric displacement data to produce en face mechanical maps, which require either high sampling rates or separate acquisitions of unloaded and fully loaded states. This approach increases measurement time, limits temporal resolution, and makes the system sensitive to motion artifacts. Our approach reduces the measurement to a single line scan over time, sacrificing en face visualization for high temporal resolution and depth-resolved dynamics. This enables the extraction of both static and time-dependent parameters. While being less sensitive to motion artifacts. The line-scan method still provides approximately 4 mm of lateral coverage, and multiple line scans can be acquired to extend information along the second lateral axis. The method records displacement curves for every pixel in the B-scan at 2.45 kHz, fully resolving the excitation cycle and reducing the likelihood of multiple $2\pi$ phase jumps. Noise and motion, however, can still induce unwrapping errors, particularly in soft tissue with large displacements, although manual tuning of the excitation force mitigates these effects.

First ex vivo measurements demonstrated sufficient mechanical contrast even within healthy or tumor tissue to justify continuation despite residual unwrapping uncertainties, with the phase-based method. Phase unwrapping and displacement processing were developed as two complementary sub-projects; this paper focuses on the latter, while the unwrapping method was presented separately [15]. The processing framework assumes a largely unwrapping-error-free displacement volume and explores which mechanical parameters can be reliably extracted and visualized. Nevertheless, it incorporates several correction and compensation steps to address remaining phase artifacts when present.

The presented method, combining high-speed OCT with long-pulse excitation, offers a versatile basis for relative mechanical characterization of brain tissue. This paper outlines the core processing pipeline, from displacement and force preprocessing to mechanical parameter calculation and visualization, and presents the first steps toward quantitative, contactless analysis of brain tissue mechanics, highlighting the potential of this approach for future intraoperative applications.

The objective of this work, however, is not to present a comprehensive biomechanical analysis of brain tissue, but rather to introduce and demonstrate a processing framework and measurement approach that can serve as a versatile tool for such studies. For this reason, a pixelwise correlation between histological sections and mechanical data is not presented in the results. While an experimental image registration and transformation procedure was implemented [16], its application to mechanical contrast maps and inclusion would require extensive validation and introduce additional questions regarding spatial precision and methodological robustness that are beyond the scope of this work. Consequently, the histological sections shown here should be regarded as providing qualitative orientation and contextual reference rather than exact spatial correspondence with the mechanical measurements. For the same reason, we focus on a single sample to demonstrate the processing steps, rather than attempting a full mechanical characterization or comparison across multiple samples. Such analyses will be addressed in future publications.

2. Methods

2.1. Imaging system hardware and test sample data

2.1.1. Air-jet excitation source

The air-jet excitation source was developed in-house and presented in detail in a separate publication [12]. The system generates mechanical force pulses to induce tissue displacement and is capable of delivering force pulses ranging from $1\mu N$ to $40mN$ , with pulse durations between $5ms$ and $700ms$ . The excitation force reproducibility ranges from $\pm 3\mathrm{\%}$ at $4mN$ to $\pm 7\mathrm{\%}$ at $1\mu N$ . In this study, a force of $100\mu N$ with a pulse duration of 200 ms was applied. Additionally, the air-jet controller and OCT are collecting data $100ms$ beyond the actual air-jet excitation pulse to capture the relaxation phase, allowing for analysis of the tissue viscoelastic properties. Further details, especially concerning the force distribution and stability, can be found in the dedicated publication.

2.1.2. Optical coherence tomography system

The OCT component of the OCE system is an Optores OMES with A-scan rate of 3.2 MHz. The system operates at a center wavelength of 1310 nm with a spectral width of approximately 100 nm. The imaging lens used in the setup is the LSM04 from Thorlabs, Germany. The resolution is below 20 $\mathrm{\mu }$ m in both axis. The OCT system performs 2.45 kHz line scans or B-scans over time at a fixed position, producing an M-scan-like dataset. This dataset results in depth and width information in the first two dimensions, while the third dimension represents time. The system employs an self designed scan head equipped with adjustable nozzles for the air-jet excitation source, allowing for accurate control of the force application.

2.1.3. Processing server system

To efficiently store and process the large OCT and OCE datasets ( > 10 GB ) a processing server system was setup. The system contains three separate servers - two high performance processing servers and on primary storage server. The processing servers are connected via a 50 GBit/s Infiniband connection with the storage server, which is then connected to the standard 1 GBits/s network infrastructure. All OCT measurements are stored via the 1 GBit/s network to the storage server and from there, only the processing servers access the data via the fast Infiniband connection.

The processing servers contain two 64 core 3.3 GHz AMD EPYC CPUs and 8 Nvidia L40 GPUs with 46 GB VRAM each. Furthermore, the servers contain 1 TB RAM. Those hardware resources are then split into four Windows virtual machines (VMs) allowing the users with each VM, to access two of the L40 GPUs, 8 Cores of the CPUs and 256 GB RAM. All the presented processing is done on one single VM of this system.

2.1.4. Sample dataset

The data presented in this paper are all based on the same single resected human tumor sample, specifically a meningothelial meningioma CNS WHO grade 1. The sample was measured within 20 minutes after resection and kept at $0^{\circ }$ C in Ringer solution. Before measurement, the sample was punched out with a tissue punch of 12 mm diameter and placed in an agar filled tissue cassette with a fitting 12 mm diameter hole in the agar filling. Since the actual examined scan range was 4 mm, mechanical edge or boundary effects because of the sample geometry should be negligible. All processing steps, plots, diagrams, and mechanical maps are based on the OCE dataset of this sample. The detailed preparation and histological section generation steps are published in [15]. A detailed description of the registration process can be found in the study by Strenge et al. [16].

Figure 1 shows the camera image, the OCT data and the histological section of the sample, providing an overview of the tissue sample used in this paper. For the histological section the standard Hematoxylin & Eosin (H&E) stain was used for dying, the section was taken at the scan location of the OCE system.

Fig. 1.

Sample overview: A) Camera image of the sample in the agar cassette. The overlayed red line on the sample marks the OCE scan position. The real dark line underneath marks the cut marking for the pathology. B) OCT en face projection of the sample. C) Full H&E histological section of the sample. D) The full intensity B-scan at the OCE scan position in the en face volume. E) The OCE scan range in the histological section. F) The OCT intensity data of the actual OCE scan range.

The OCE dataset always consists of one OCT volume scan, scanned at one position over time. Therefore, the volume has the following dimensions (Table 1):

Table 1. Scan dimensions for the OCE line scan volume scans. Used to measure the displacement over time.

OCE Line Scan Volume Scan
Dimension	1st	2nd	3rd
OCT	A-scan Length	A-scans	B-scans
Representation	Depth	Scan Width	Time
Digital Units	250 pix	512 A-scans	800 B-scans
Real Units	3 mm	4 mm	300 ms

For every OCT volume one air-jet dataset exists containing all raw data to calculate the force over time over the full 300 ms.

Furthermore, for every sample two full-volume scans are taken for the measurement position correlation later on. One before the OCE measurement and one after (Table 2).

Table 2. Scan dimensions for the reference volume scans. Used for the position correlation later on.

Overview Two Axis Volume En Face Scan
Dimension	1st	2nd	3rd
OCT	A-scan Length	A-scans	B-scans
Representation	Depth	Scan Width	Scan Length
Digital Units	250 pix	2048 A-scans	2048 B-scans
Real Units	3 mm	12 mm	12 mm

2.2. Software framework

The processing pipeline was implemented as a fully object-orientated software framework in MATLAB (v2024b). The user is interacting with the framework through class and object-based method calls. The primary object the user is interacting with is the object derived from the OCEMechProcessor() class. It is designed to handle the processing of 3D displacement data from the OCE system, extracting characteristic features, and calculating mechanical parameters. All processing steps are applied to every pixel in the 3D volume in parallel, which significantly accelerates data processing. An example of the code is shown in Supplement 1 ^{(8.1MB, pdf)} S3. The main components of the software framework are:

• 1.Preconditioning and Preprocessing
• 2.Force profile correction
• 3.Feature Extraction
• 4.Mechanical Parameter Calculation
• 5.Result Data Postprocessing and Visualization

2.2.1. Preprocessing and preconditioning

The raw OCT data underwent phase unwrapping to obtain continuous phase values for subsequent mechanical property estimation. Several strategies were evaluated during development (see Supplement 1 ^{(8.1MB, pdf)} S1); in this study, the standard Matlab unwrapping algorithm was combined with a modified $atan2()$ function $\to atan{2}_{mod}()$ applied to the local phase difference estimated using the Kasai method, complex phase difference (Kasai): $\mathrm{\Delta }z=\overline{z}(t-1)\ast z(t)$ with phase angle: $\mathrm{\Delta }\varphi (t)=arg(\mathrm{\Delta }z(t))=atan{2}_{mod}(\frac{\mathrm{\Re }(\mathrm{\Delta }z(t))}{\mathrm{\Im }(\mathrm{\Delta }z(t))})$ . To reduce noise contributions, a moving-mean filter with a kernel size of [5 x 5 x 5] pixels was applied prior to integration, $\varphi (t)=\int movmean(\mathrm{\Delta }\varphi (t))dt$ . This procedure was used consistently for all analyses presented here.

The effect of phase noise and phase errors in the raw OCT data on the final unwrapped phase is not yet fully understood and requires further investigation. There are indications that parts of the FDML OCT processing pipeline, originally optimized for magnitude data, may introduce additional phase errors. Because such artifacts can propagate into the estimation of mechanical properties, phase unwrapping remains a sensitive step in the workflow. Development of a more robust and generally applicable algorithm is ongoing and will be essential for further improving the reliability of the method.

Finally, to convert the phase angle $\varphi (t)$ in radians to displacement $L(t)$ in meter, the following equation is used:

$$L(t)=\varphi (t)\cdot \frac{{\lambda }_c}{4\pi \cdot n}=\varphi (t)\cdot \frac{1310nm}{4\pi \cdot 1.36}$$ (1)

with $n=1.36$ as the refractive index of brain tissue [17] and $1310nm$ as the central wavelength of the OCT system. These values are the framework standard but can be changed by the user.

The result of Eq. (1) are visualized as a video in the supplement Visualization 1 ^{(99.6MB, mp4)} . With a full excitation cycle over time for three selected pixels.

Unwrapping Error Detection

The unwrapping algorithm was developed in parallel with the mechanical data processing, requiring, especially in the beginning, a comprehensive error compensation step to remove pixels affected by unwrapping errors. Although the final unwrapping algorithm is not error-free, it provides reasonably reliable phase data. Major unwrapping errors are typically confined to sample edges due to scanning artifacts (e.g., scanner turning points) and signal loss at greater depths. Most detection and correction functions from earlier iterations have been retained in the final mechanical processing framework, but are not applied to its full extent on the example data set presented in this paper.

Percentile Thresholding Filter

A simple error compensation step was implemented using a percentile thresholding filter. For each feature matrix, values below the 5th percentile or above the 95th percentile were removed to suppress extreme outliers and processing artifacts, thereby improving overall data quality. This filtering procedure was applied to all final contrast maps. In the case of the Kasai-based unwrapping approach, the threshold range could be extended to the 1st–99th percentile without noticeable loss of contrast, as outlier noise was substantially reduced.

2.2.2. Force preconditioning and profile correction

The force data always contains a constant offset and an undershoot at the end of the falling edge. The undershoot artifact in the data is caused by the system design details see [12]. This undershoot is not a real force reaching the sample. Therefore, for processing all values after the first zero value of the falling edge are set to the initial offset of the force. Whether the offset force is interacting with the sample causing a pre-loading state is not clear. However, this offset is not subtracted to incorporate any possible influence on the measurement. The offset is caused by the fast-switching valves since they seem not to fully close after a certain amount of switching cycles. In the example data set the offset is around 4 $\mathrm{\mu }$ N around 6 % of the maximum force of 67 $\mathrm{\mu }$ N. It is not visible in the plots in this paper since they are plotted with the ’tight’ option of Matlab which automatically scales the axis of the plot based on the minimum and maximum value of the plot.

Furthermore, since the air-jet samples with 1.4 kHz and the OCT system with 2.45 kHz, there is not one force value for each captured B-scan. However, the air-jet counts the B-scan trigger of the OCT system and therefore, every force value in time can be assigned to a corresponding B-scan. The missing force values are then interpolated to generate a force value for every B-scan or displacement value in time.

Additionally, the force data from the air-jet needs to be corrected for the force distribution on the sample: The air-jet delivers a Gaussian-shaped profile, causing an uneven load on the sample. To correct this, a reference beam profile measured on a mechanically homogeneous polyvinyl alcohol (PVA) phantom is used to weight the force applied to the sample. Furthermore, the parameter of the Gaussian correction profile can be fine-tuned if necessary (width: $2\sigma$ , center position on sample: ${\mu }_0$ and strength: $A_0$ ).

The force matrix for the mechanical calculations is built by replicating the force-over-time curve delivered by the air-jet for every pixel in the OCT data set. This results in a 3D matrix with a force-over-time curve for every displacement curve. This matrix is then weighted by the 1D Gaussian reference profile over the width and depth dimensions of the 3D force matrix. The steps are shown in Fig. 2.

Fig. 2.

Force Matrix: (A) the raw force over time / B-scan from the air-jet. (B) the replicated force curve over the width of the OCT displacement volume / matrix. (C) The corrected 2D force Matrix. (D) the reference profile from the PVA phantom. (E) The uncorrected 2D force matrix data is equivalent to a slice to the 3D matrix at a fixed depth. (F) The 2D force matrix slice after correction with the reference profile.

This approach reduces most of the mechanical calculations later on to simple matrix operations between the force matrix from the air-jet and the displacement matrix from the unwrapped OCT data. However, an ideal solution to determine the absolute force on the surface of the sample with full spatial resolution could not be implemented, since the 2D force distribution at low force values can not be reliably measured as discussed in [12]. Therefore, the absolute force value as well as the force dissipation over the depth of the sample during the compression is not corrected and the force over the depth per A-scan is assumed constant, which is a common simplification of uniaxial compression [4]. Therefore, all calculated values are normalized to the total excitation force exiting the air-jet nozzle system and not absolute physically correct values. However, this still allows the comparability of the different measurements taken with our specific system.

2.2.3. Feature extraction

Due to the high sampling rate of the OCT system the displacement propagation through the sample over time can be resolved. This reveals that each displacement curve per pixel is slightly shifted in time the further the pixel is away from the excitation center. This can be resolved either by detecting the rising edge or the overshoot position in the per-pixel displacement curves and shifting each curve to a common reference point. This has the advantage that all the following calculation can then be made for the full displacement matrix. However, because of high noise, weak signals or strongly deformed displacement curves, the detection of these feature positions in each displacement curve, is not always reliable, causing asynchronous displacement curves after shifting.

Therefore, the framework detects the primary feature positions (Fig. 3) in time for a reference curve. This is determined by first calculating the "intensity centroid" of the intensity B-scan and then searching for the maximum intensity pixel around the centroid position in a 10 x 10 pixel window. The assumption is that the high intensity pixels have a lower probability to go to zero during excitation (dark Speckle) and therefore, will deliver a clean displacement curve as a reference curve. Based on this curve the framework then searches the same feature positions in all the other displacement curves in a B-scan range around the reference curve positions. The feature position and the corresponding displacement values for each pixel are stored in a 2D matrix which is then used for the actual calculations of the mechanical parameters. This process basically collects the displacement values for each feature position in time for every displacement curve into a single 2D matrix per feature with the dimensions of the B-scan, thereby reducing the mechanical value calculation per feature to an operation between two 2D matrices.

Fig. 3.

Main Feature Positions: Right: The pixel position (White cross) where the force curve (top left) and the displacement curve bottom left are extracted. Bottom right: the unscaled displacement curve. In the two curves on the left the found feature positions are marked.

The feature positions of the displacement curve and the force curve are shown in Fig. 3. The pronounced feature positions Rising Edge and Falling Edge are detected by searching for the maximum and minimum values in the first derivative of the displacement curve. The Center position is then the center between these two edges. Based on those positions the displacement curve can be split in three ranges: the High Dynamic Range which spans from the rising edge to the end of the overshoot, followed by the Classical Quasi Static Range until the beginning of the final indentation feature Max and finally the Tail or Viscose Range with the load free tail of the displacement curve. In this ranges the less pronounced features are searched (Overshoot, Undershoot, 2nd Overshoot, Plateau Start and Max) based on a modified Triangle Threshold Algorithm (TTA).

The standard triangle threshold algorithm operates by identifying the point on a histogram that maximizes the distance to a line drawn between the histogram’s peak and the end of the histogram [18]. In our framework, instead of a histogram, the displacement curve of the tissue per pixel is used. The algorithm is applied to the different loading state sections of the displacement curve, detecting the strongest "bend points" which correspond to significant features in the tissue’s mechanical response. An example for the search of the "Max" feature position is shown in Fig. 4

Fig. 4.

Example of the triangle thresholding algorithm to search the max indentation feature. The blue curve is the normalized displacement curve $\mathrm{\Delta }L(x)$ with x as the whole number B-scan index. Start (yellow) and End (light blue) are the limits of the search range (purple). The red curve is the linear curve $g(x)$ connecting the start and end points of the search range, on the displacement curve. The orange curve is the difference between the linear curve and the displacement curve $\mathrm{\Delta }L(x)-g(x)$ . Searching for the maximum of $|\mathrm{\Delta }L(x)-g(x)|$ (gray line) directly results in the index of the point with the largest distance between the linear curve and the displacement curve and therefore the maximum bend in the curve in the search range.

This method has been proven highly reliable by identifying i.e. the final (maximum static Max) displacement in the displacement curve. The final (Max) and overshoot position usually need to be further refined by searching the actual maximum value in the range around the position found by the TTA. The framework standard range is $\pm 10$ data points in time.

This approach allows for the detection of the points of maximum bend above and below the reference curve $g(x)$ , even in displacement curves which are heavily diverting from the standard displacement curve shown in Fig. 3. Consequently, the algorithm is also utilized later to divide the tail of the displacement curve into two sections for the viscosity calculations, see section 2.3.4

2.3. Mechanical parameter calculation

During development the focus for the calculation of mechanical parameters shifted towards extracting characteristic or proxy parameters, rather than technically exact parameters as defined by continuum mechanics. However, the classical definitions were used as a starting point but then simplified if necessary. The mechanical parameter calculation module comprises five main subsections: stiffness, elasticity, hysteresis (loss energy), viscosity and creep. The stiffness and elasticity parameters are calculated for each feature position. The viscosity, creep compliance rate and hysteresis are calculated per pixel. All calculations are done on all pixels in parallel on a GPU. In our system, the elasticity represents the high dynamic behavior, while the stiffness represents the behavior under constant load. The resulting maps are fairly similar, indicating a high correlation between stiffness and elasticity, but the two different properties allow for a better classification of the tissue later on. We tried to apply the technical definitions for the different mechanical properties to our data. However, some definitions had to be adapted to the specific case, either because of the tissue exhibiting no clear technical behavior or due to limitations of the hardware system. For example, as already mentioned in section 2.2.2, the mechanical parameters are normalized to the total nozzle force and not to the actual local force applied to the sample.

2.3.1. Elasticity calculation

Elasticity $E$ reflects the ability of a material to deform and return to its initial shape. The approach is the same as with the Young’s modulus in the linear elastic range of the Hook stress-strain curve,

$$E=\frac{\sigma }{\epsilon }=\frac{\frac{F}{A}}{\frac{\mathrm{\Delta }L-L_0}{L_0}}$$ (2)

With $F$ as the force, $A$ as the area the force is applied to, $L_0$ the initial length of the sample, $\mathrm{\Delta }L$ the change in length. $\sigma$ is the stress in the material and $\epsilon$ is the displacement. Therefore, our adaptation is: The force and displacement on the rising edge is basically linear as well. However, since the exact local force and the absolute position $L_0$ is unknown, the slope of the force and displacement data is used for the calculation. With the assumption that the resulting parameter is proportional to the actual Young’s Modulus it is possible to represent the elastic component of the sample with this parameter.

The framework calculates the elastic parameter by linear fitting the initial slope (rising edge feature) in a range around the maximum rising slope of $\pm 10$ points in both the displacement and in the force curve (see Fig. 5). The fit over this range reduces noise and outlier issues. The elasticity parameter is then the result of the division of both slopes:

$$E=\frac{\mathrm{\Delta }F}{\mathrm{\Delta }L}=\frac{F_{i+10}-F_{i-10}}{L_{i+10}-L_{i-10}}\text{;}[E]=\frac{N}{m}$$ (3)

with $i$ as the index of the feature (B-scan).

Fig. 5.

Force curve on the top and the displacement curve on the bottom. In orange the values for the elasticity calculation. The position for the elasticity calculation is the point of the maximum slope. From this position 10 values before and after are used to extract the differential value for the calculation to better include the curve shape.

2.3.2. Normalized bulk displacement calculation (NBD)

Normalized Bulk Displacement Calculation (NBD) is a simple normalization of the absolute displacement per pixel to the applied total force.

$$NBD=\frac{F_{total}}{\mathrm{\Delta }L}\text{;}[NBD]=\frac{N}{m}$$ (4)

$\mathrm{\Delta }L$ is the absolute displacement of each pixel. The force $F_{total}$ is the total force exiting the nozzles of the air-jet system. Further details concerning the total force concept can be found in [12]. This very simple parameter allows the compensation of the air-jet beam profile as well as a general normalization of the measurement for comparison with other measurements. The resulting contrast maps are pixel-wise and more detailed since no windowing is applied.

2.3.3. Normalized weighted local strain calculation (NWLS)

The Normalized Weighted Local Strain Calculation (NWLS) method, first calculates the weighted local strain (WLS) ${ϵ}_i^w$ based on a Savitzky-Golay differentiation filter, first presented by F. Kennedy et. al. [19] and then applies the same normalization as for the NBD Eq. (4) to compensate for the air-jet profile. This approach provides a calculation of the actual local strain, reflecting a more precise and localized mechanical behavior, but with the disadvantage of lower resolution because of the windowing necessary for the calculation. The window size is set fixed to 10 pixel in depth.

$$NWLS=\frac{F_{total}}{{ϵ}_i^w};[NWLS]=\frac{N}{\mathrm{\mu }\epsilon }$$ (5)

2.3.4. Regression parameters

The Regression Parameters are proxy parameters for the viscosity which is the measure of a tissue’s ability to return to its original shape after deformation over time. The framework represents the viscosity by a the regression constant of the subsiding part of the displacement curve captured after the air-jet pulse and without a load. The system captures an additional 100 ms post-excitation to record this subsiding displacement. The tail is split in two sections (Fig. 6) pre pr (blue range) and post po (orange range) the point of maximum bend, determined by the TTA algorithm. The two sections are fitted independently with a weighted exponential decay model of the form $\mathrm{\Delta }l(t)=a\cdot e^{b\cdot t}$ .

Fig. 6.

Relaxation fit: The raw extracted tail curve separated in two sections at the point of the strongest bend (pre-bend dark blue and post-bend brown) and the fit for both sections (light blue and dark brown). As well as the weights range (transparent light blue and light yellow range) for the two sections with a focus on the range around the strongest curvature.

Matrix Fitting Algorithm

To accurately fit the subsiding tail of the displacement curve, the exponential decay is linearized, and the pr and po part of the tail are fitted using a linear regression algorithm based on the method published by Kenney and Keeping [20]. This method is applied because it can be easily adapted to the GPU-based volume processing of the OCE framework. The linearization simplifies the computation, allowing for efficient parallel processing and accurate fitting of the decay characteristics of the tissue. The beginning and the end of the tail sections are weighted less heavily than the center, prioritizing the fit of the strong slope parts of each section. This approach ensures that the primary decay characteristics, are accurately captured. The algorithm allows the parallel fit of at least 153,600 displacement curves in one batch operation, only limited by the VRAM of the GPU, significantly accelerating the data processing.

The results are the fit coefficients of two separate exponential functions:

$$\mathrm{\Delta }{L}_{pr}(t)=a_{pr}\cdot e^{{\tau }_{pr}\cdot t}$$ (6)

$$\mathrm{\Delta }{L}_{po}(t)=a_{po}\cdot e^{{\tau }_{po}\cdot t}$$ (7)

The factors ${\tau }_{pr}$ and ${\tau }_{po}$ in $\frac{m}{s}$ represent the characteristic time dependence of the regression of the tissue to the initial position, ${\tau }_{pr}$ for the range before and ${\tau }_{po}$ after the split of the tail range. The higher the value the faster the regression and therefore the lower the viscosity of the sample. It is important to note that standard viscosity is usually defined the other way around high value $\to$ high viscosity $\to$ low regression and low value $\to$ low viscosity $\to$ high regression. However, displacement per time unit as a result is correct based on the fit and the resulting units. Therefore, the framework is working with the non-standard definition. The final contrast map however, is displayed as the inverse of the calculated parameters to fit the standard definition. $a_{pr}$ and $a_{po}$ are the start points of the decay all four factors can be visualized for each pixel in the B-scan. A normalized version which normalizes the regression factors to the maximum indentation under constant load is also calculated.

$${\tau }_{pr,po}^{norm}=\frac{{\tau }_{pr,po}}{\mathrm{\Delta }{L}_{max}}\text{;}[{\tau }_{pr,po}^{norm}]=\frac{1}{s}$$ (8)

This version compensates for faster regeneration due a high elastic component and a higher stored deformation energy, optimizing the viscosity factors for a more precise representation of the actual relaxation.

2.3.5. Deformation energy dissipation and hysteresis

The deformation energy dissipated in the tissue indicates how much energy is dissipated as the tissue deforms due to internal friction and other dissipative processes within the tissue. This energy dissipation is the area of the hysteresis loop during the air-jet excitation and subsequent relaxation phase, which is given by:

$$W_d={\int }_{l_{Start}}^{l_{End}}Fdl\text{;}[W_d]=J$$ (9)

The hysteresis loop is the X-Y plot of the force (Y-axis) and the displacement (X-axis). The overview is shown in Fig. 7. This approach was already demonstrated on OCE data by [21]. Based on their work we also calculate the load area $W_l$ (Fig. 7 blue area + yellow area) and the loss ratio, the ratio between the two areas where a value of zero represents an ideal elastic material and a value of one an ideal viscous material.

$$LR=\frac{W_d}{W_l}$$ (10)

Fig. 7.

Deformation Energy: The per pixel plot of the force (top left) vs. the displacement (bottom left) results in a hysteresis curve (blue dotted). The dissipated energy in the material is the hysteresis loop area (blue) while the total introduced energy is the blue area plus the orange area encased by the red dashed line. The ratio of the two areas is the loss ratio [21].

For the calculation the polyarea() MATLAB function is applied, which builds a polygon between two curves and returns the area of the polygon. The function is GPU-ready and multi-thread capable which allows the calculation for every pixel in the B-scan in one function call.

It should be noted that, for tissue with pronounced viscous behavior or high inertia, the hysteresis curve may cross itself, as shown in Fig. 13 (I) as well as in 14 (I) and (K). In such cases, the calculated loss ratio and loss energy values become invalid. This situation is currently not handled separately within the processing framework. Further investigation is required to determine whether this effect can be reliably detected and potentially used as an additional indicator of strongly viscous or high inertia tissue behavior.

Fig. 13.

A: The histological section of the scan range. B: The Normalized Bulk Displacement (Stiffness) map of the same range as the histological section. C-E: The Fingerprint plot of the positions marked in A and B. (F, H, J) the displacement (blue) and the force (orange) for the spider plots above at the positions marked in A and B. G, I, K the hysteresis loops of (F, H, J). The position 1 and fingerprint plot C is in poroviscous tumor tissue, the position 2 plot D is collagen-rich blood vessel walls and the position 3 plot E is dense tumor tissue. The different Fingerprint plots show a distinct distribution for each position. In the plots (F to K) the axis label are not plotted for better visibility. Since only the curve shapes are of interest. However, in i.e. F. the x axis is time and the y axis is force and displacement. In the hysteresis i.e. G. the x axis is the displacement and the y axis is the force.

Fig. 14.

Fingerprint plot of the healthy histological section. The positions are only very roughly correlated and should only be seen as orientation, since the sample detached during histological processing, which makes an exact correlation impossible. The shown range in (A.) is at least twice as large as the actual scan range in (B. red rectangle), to include the detached parts and the two distinct tissue types, as well as the homogeneous gray matter on the sample surface. All other elements of the figure are identical to those of the tumor sample shown in Fig. 13.

2.3.6. Creep compliance rate

The creep compliance ( $J(t)$ ) of the tissue in general is a measure of how the tissue continues to deform (strain $\epsilon (t)$ ) under a constant load (stress ${\sigma }_0$ ) over time. This behavior is indicative of the tissue’s viscoelastic, ductile properties and long-term stability under mechanical stress.

$$J(t)=\frac{\epsilon (t)}{{\sigma }_0}\text{;}[J(t)]=\frac{1}{Pa}$$ (11)

The standard creep compliance is defined as a function. However, to be able to represent the creep behavior of the sample with a single parameter, we define the basic creep compliance rate by dividing the absolute displacement change $\mathrm{\Delta }L$ during constant load application (plateau) by the applied force $F_{max}$ and the load duration. The plateau start is determined by the end of the second overshoot feature position $pStart$ and the max indentation feature position $pEnd$ . The feature positions are shown in the Fig. 8

$$J^{\ast }=\frac{|L_{pEnd}-L_{pStart}|}{(F_{max}+(F_{pEnd}-F_{pStart}))\ast (t_{pEnd}-t_{pStart})}=\frac{|\mathrm{\Delta }L|}{(F_{max}+\mathrm{\Delta }F)\ast \mathrm{\Delta }t}\text{;}[J^{\ast }]=\frac{m}{N\ast s}$$ (12)

Fig. 8.

Feature and value determination for the creep constant calculation. The start feature of the plateau (constant load) is the end of the second overshoot and the end is the maximum force before the drop off into the tail end of the displacement curve.

In our framework, we added a term to account for the eventual remaining change in the force $\mathrm{\Delta }F$ during the constant excitation load phase of the displacement curve. This additional term compensates for small changes in the excitation force, ensuring a better comparable calculation of the creep compliance rate.

The creep compliance rate results in positive and negative values. Therefore, the corresponding contrast maps can be scaled in the original range or as absolute values. The latter one is the standard visualization. Details see section: 2.4.1

2.4. Post-processing and visualization

The final step in the software framework involves post-processing and visualization of the results. The mechanical maps resulting from the mechanical parameter calculations are filtered for visualization, first by removing all outlier pixels using Matlabs filloutliers function with the parameters movmedian and a window of 5 pixels. In a second filtering step remaining values above the 95th percentile and below the 5th percentile are filtered out. This step is necessary because the mechanical property differences in the tissue are very small, but the outliers due to processing artifacts (division by zero) create a huge value range. Therefore, the outliers need to be suppressed, and the value difference of the mechanical properties needs to be enhanced for visualization. The enhancement is done by an adaptive histogram thresholding algorithm ( adapthisteq(), Matlab) to even out the high dynamic range of the mechanical data maps. This ensures the visual representation of the data is clear and interpretable. However, it’s important to note that the actual numerical values are lost during this process, as the data range is rescaled between 0 and 1.

For visualization purposes in Fig. 9 the mechanical maps are displayed as images before and after each post-processing step. It illustrates the impact of outlier removal and adaptive histogram thresholding on the mechanical property maps. For the visualization of the first steps a very "aggressive" color map is used to visualize the high dynamic nature of the data. The main images are:

Fig. 9.

Visualization steps for mechanical maps. (A) Raw Mechanical NBD-Map of the example sample, with outliers: Initial data showing high dynamic range and outliers. (B) After Applying Intensity Mask: Reduces noise but retains outliers. (C) After Clearing All Infinite Values: Removes infinite values, yet outliers remain. (D) After Outlier and Percentile Filtering and Rescaling: Removes extreme outliers using Matlab filloutliers() function and percentile filtering, rescaling data between 0 and 1. (E) After Adaptive Histogram Filtering: Enhances subtle differences in mechanical properties by evening out high dynamic range. (F) Rescaling to Initial Value Range: Returns data to the original range for comparison. The white dots in each plot represent outliers below the 1st and above the 99th percentile.

Raw Mechanical Map: This image shows the initial mechanical map with all data points, including outliers and high dynamic range values. Filtered Mechanical Map: This image illustrates the mechanical map after the removal of outliers, showcasing the cleaned-up data without extreme values. Enhanced Mechanical Map: This image presents the final mechanical map after applying adaptive histogram thresholding, which enhances the visualization of subtle mechanical property differences.

These post-processing steps are essential to ensure that the mechanical maps can be visualized as an image and allow for a visual distinction between different tissue types. The suppression of outliers and enhancement of data visualization are particularly important given the small differences in mechanical properties and the potential artifacts introduced during data processing.

2.4.1. Contrast map scaling

The displacement data allow for positive as well as negative values, resulting in i.e. negative stiffness or creep values. The simple plotting of the resulting contrast maps equates negative values to low values and positive values as high values. Therefore, it is not possible to distinguish whether the pixel value in the map has i.e. a low stiffness or is negative. However, the contrast maps can be scaled either as absolute value or to the actual range. The first one is easier to conceive if only the actual mechanical value is of interest. The later one adds the additional information of the deformation direction either towards or away from the OCT scan head.

However, the adapthisteq() function applied to enhance the contrast map, only accepts positive values since it is intended for the use with image data. Therefore, the positive and negative ranges need to be processed separately and then stitched back together into one map. This is done by splitting the two ranges by their sign. Then the absolute value of the negative data is processed by the adapthisteq() function and the result is then rescaled to the initial negative range and recombined with the positive range into one contrast map. The corresponding processing function allows the user to choose whether the negative range should be rescaled to its initial range or added to the positive range as absolute values (positive values). All contrast maps in this paper are scaled in the absolute range. Since this is the more intuitive visualization.

2.4.2. Spectral Visualization approach

In search for the ideal visualization of the complex mechanical data and to address the loss of precise quantitative values, we also display a histogram of the original value distribution of the raw mechanical map before the enhancement step. This approach allows for a numerical representation of the data parallel to the spatial visualization of the data in the B-scan. By showing both the color-coded and enhanced mechanical maps along with the histogram, one can better conceive the underlying data distribution and the mechanical properties of the tissue. The results are shown in Fig. 10. The binning of the histogram is done via a k-means algorithm to adapt the binning to the unevenly distributed data values.

Fig. 10.

Visualization of loss energy contrast map on the left-hand side. On the right-hand side the value distribution of the underlying raw data. Since the direct correlation between contrast map and number value is lost during the contrast adjustment the histogram visualization adds more context to the contrast map. Allowing a spatial localization of the data and a value context. The binning of the spectrum is done via a k-means algorithm to adapt the binning to the unevenly distributed raw values. The highlighted numbers in the histogram are: bin value in parameter units and [counts in %]

2.4.3. Fingerprint plot

As a final summary visualization, in addition to the mechanical maps and histogram data, we employ a spider plot to depict the primary mechanical properties of the sample at a selected pixel position. This "fingerprint" representation provides an intuitive overview of key parameters, offering a concise characterization of the tissue’s mechanical behavior. The approach complements both spatial and numerical analyses, thereby facilitating the identification of tissue-specific mechanical signatures and enabling straightforward comparison across tissue types.

All values are normalized to depict a high characteristic of the parameter as a larger radius on the circle. Therefore, i.e. the viscosity is shown as the inverse of the calculated value.

All axes are scaled to the range determined by the complete database of measured samples, ensuring standardized comparisons. If the current sample establishes a new minimum or maximum for a given property, the corresponding point is highlighted with a red circle. In the example shown in Fig. 11, representing a full tumor position, the creep compliance ( $J^{\ast }$ ) reaches the highest value recorded in the database to date. Such new extrema are automatically stored in the database.

Fig. 11.

The fingerprint plot (left) displays the primary mechanical properties of the pixel marked in the Loss Energy map (top right red dot), scaled to the range of all measured samples. This plot highlights the dominant properties of the selected position relative to the database. The middle-right panel shows raw displacement and excitation force, while the bottom-right panel presents the synchronized hysteresis curve of force versus displacement. The black cross marks the centroid of the hysteresis, the orange triangle the rising edge, and the green triangle the falling edge of the hysteresis curve.

The nine mechanical properties are grouped into three sectors and arranged clockwise on the plot, with each sector assigned a distinct background color:

• 1.
  Elastic Sector (Red):

  • •
    Elasticity ( $E$ ): Represents the sample’s ability to deform and regress back into its initial shape. Eq. (3)
  • •
    Normalized Weighted Local Strain ( $NLS$ ): Indicates the sample’s local resistance to compression. Eq. (5)
  • •
    Normalized Bulk Displacement ( $NBD$ ): Indicates the sample’s bulk resistance to compression. The closest proxy value for the Stiffness. Eq. (4)
• 2.
  Viscous Sector (Green):

  • •
    Creep Compliance Rate ( $J^{\ast }$ ): Reflects time-dependent deformation under sustained force. Eq. (11)
  • •
    Inverse of the First Viscoelastic Parameter ( ${\tau }_{pr}^{-1}$ ): Describes the initial relaxation and dampening behavior. Eq. (6)
  • •
    Inverse of the Second Viscoelastic Parameter ( ${\tau }_{po}^{-1}$ ): Represents longer-term relaxation and dampening behavior. Eq. (7)
  • •
    for both parameters the inverse is used to represent a large value as a slow regeneration.
• 3.
  Ductile Sector (Blue):

  • •
    Remaining Sample Deformation ( $pD)$ : Shows permanent deformation after force application. At least on the timescale of the measurement.
  • •
    Width of the Hysteresis ( $H{y}_W)$ : Indicates the extent of energy dispersion during the deformation cycle.
  • •
    Ratio hysteresis loading area vs. loop area ( $LR$ ): Is the ratio between total introduced energy and loss energy. [21]. Eq. (9)

Additionally, the centroid of the property distribution is calculated. This provides a numerical summary of the mechanical behavior at the analyzed position and enables a basic classification into the three groups or sectors in the spider plot (Elastic, Viscous, and Ductile). It has to be noted that since Matlab does not provide a spider plot function. The following GitHub repository was employed and modified to fit our specific needs i.e. sector visualization and centroid calculation: https://github.com/NewGuy012/spider_plot The result is a mechanical visualizer class in Matlab, as a wrapper for the spider plot class of the mentioned repository. The class takes our standard mechanical results and returns a handle to the final "fingerprint plot".

3. Results

3.1. Proxy parameter contrast maps

Figure 12 presents the main proxy parameter contrast maps. All feature-dependent parameters were extracted at the Max feature position in time. Each map was contrast-adjusted and rescaled to the initial value range of the raw data, and all parameters are shown as absolute values. The first column displays parameters derived directly from displacement data, the second column shows force-normalized parameters, and the third column presents parameters related to time-dependent or viscoelastic-to-ductile behavior. The first image corresponds to the histological section, followed by the OCT intensity image of the sample. Complete parameter maps together with their value distributions are provided in the Supplement 1 ^{(8.1MB, pdf)} S4. Figure 12 is intended to provide an overview and direct comparison of all primary parameters.

Fig. 12.

$u$ : The raw displacement value at the max feature position. $WLS$ : The Weighted Local Strain. $u_{end}$ : The last displacement value of the measurement per pixel. $NBD$ : The Normalized Bulk Displacement at feature position max. $NWLS$ : Normalized Weighted Local Strain the Local Strain normalized by the force distribution. $|E|$ : The Elasticity as the ratio of the slopes of the rising edge in the force and the displacement curve. $J$ : This is the absolute value of the creep compliance rate. $W$ : Is the dissipated energy. ${\tau }_{pre}^{-1}$ : Is the pre maximum bend viscosity or regression parameter. ${\tau }_{post}^{-1}$ : Is the post maximum bend viscosity or regression parameter. All values are the absolute values so that in all maps red equals a high value and blue equals a low value.

The viscosity is shown as the inverse of the calculated parameter to fit the technical definition of high viscosity $\to$ less fluid and low viscosity $\to$ more fluid.

3.2. Fingerprint plot

The fingerprint plots in Fig. 13 represent a very comprehensive visualization of the tissue per pixel position. The distinction between full poroviscous tumor, connective tissue and dense tumor tissue is fairly obvious just based on those plots. Furthermore, these plots deliver the primary characteristic of the tissue position based on the centroid of the sample.

The full poroviscous tumor tissue tends to lean heavily into the viscous and ductile sector of the plot, while the dense tumor tissue is more evenly distributed over all sectors, but still leans into the ductile sector. Blood vessel tissue leans more into the elastic sector of the fingerprint plot and less into the ductile sector. An initial interpretation of the observed distributions suggests that the fully poroviscous tumor tissue exhibits pronounced ductile and poroviscoelastic behavior, as it is permeated by extracellular fluid. Under compression, this fluid is displaced, resulting in strong creep compliance and limited regression after unloading, since the liquid must be expelled from, and subsequently drawn back into, the tissue cavities. The high flow resistance within these microchannels leads to significant damping effects.

The denser tumor regions also display creep behavior, though to a lesser extent, as the solid tissue matrix itself is compressed under load. Regression is more pronounced in these areas, as they lack fluid-filled cavities requiring refilling during relaxation. The blood vessel tissue represents the most elastic component, consistent with the expectation that collagen-rich structures must deform elastically to accommodate blood pressure variations.

Figure 14 shows the spider plots for three positions on the only healthy sample that could be measured during the project. The healthy region was part of a human tumor sample (meningioma CNS WHO grade 2) containing a small area of gray matter. Unfortunately, the sample detached during histological processing, making precise spatial correlation between OCE and histology impossible. The detachment was likely promoted by the presence of several small blood vessels (position one) and one large vessel (between position one and two) in the scanned region, which may have weakened the tissue structure at this site. Therefore, the measurement positions shown are only approximate. However, the large vessel can be seen in the stiffenss contrast map as the large low stiffness area in the center, indicating a sufficient localization of the scan area in the histological section.

The histological image cutout is about twice the size of the OCE scan area to include both tissue types and the detached healthy area. Nevertheless, the scanned region can be considered predominantly healthy tissue, and its spider plots differ clearly from those of the full tumor sample. The parameters tend toward the elastic sector rather than the ductile or viscoelastic sectors. Positions one and two, which include blood vessels, show mixed mechanical characteristics, whereas position three, representing pure healthy tissue, exhibits almost no ductile behavior and primarily stiffer, more elastic properties.

It should be noted that further processing of the complete dataset will modify the fingerprint visualization, as additional samples will rescale the axes of the fingerprint plots. The current scaling is based solely on the two presented samples; therefore, the fingerprint plots shown here serve primarily to illustrate the concept and methodology, and the mechanical interpretation of the results remains preliminary.

3.3. Discussion

Our OCE processing software framework can be integrated into Matlab as a library, with the OCEMechProcessor object serving as the core component for data processing. The framework operates via object-based method calls. For feature detection, the modified triangle threshold algorithm effectively identifies key points in the displacement curves, supporting accurate mechanical parameter extraction. The dual stiffness calculation provides both bulk and localized mechanical insights. Furthermore, the analysis of elasticity, viscosity, mechanical energy dissipation, and creep behavior enables detailed tissue characterization. The results are visualized as mechanical contrast maps, highlighting differences between tissue types for improved interpretation. The Fingerprint plot offers a fast, intuitive representation of the sample’s mechanical properties on a per-pixel basis, further supported by the hysteresis curve of the selected pixel, which provides context for local mechanical behavior.

It should be emphasized that the use of the Kasai estimator (complex phase difference) for raw phase retrieval is essential, as it substantially improves accuracy while maintaining computational efficiency.

In the first interpretation of the results, high elastic parameters correlate well with collagen-rich vessel walls and connective tissue in the histological sections. This agrees with theoretical expectations that collagen and connective tissue exhibit high elasticity with lower viscoelastic damping. In contrast, elevated viscous values correlate with liquid-permeated tissue.

Tumor tissue, in general, shows high creep compliance and elevated displacement energy, indicating strong and slow deformability under constant load. These characteristics, together with the viscoelastic parameters, appear to be the most distinctive mechanical features of tumor tissue. This behavior is further reflected in the hysteresis curves: tumor tissue exhibits wide hysteresis loops with permanent deformation, whereas connective tissue shows narrow loops with almost ideal elastic behavior. Accordingly, in the fingerprint plots, tumor tissue clusters predominantly within the ductile and viscoelastic sectors, while connective, vessel, and healthy tissue, display a distribution leaning more into the elastic sector.

It is noteworthy that the pure elastic parameter $E$ is very homogeneously distributed, indicating that the rising edge of the displacement curve is almost identical across all pixels and tissue types. This supports our hypothesis that the initial rising edge and overshoot are mainly driven by the excitation force, particularly in soft or highly viscoelastic tissue such as brain. Thus, this parameter may not reflect a true intrinsic local property of the sample but rather a system response of the whole sample. Furthermore, all parameters except the NLS are strongly bulk-dependent, meaning that each measurement point is influenced by surrounding tissue and structure. The extent of these bulk effects, and how distinctly the fingerprint plots separate different tissues, will be analyzed further in the full dataset collected during the project. These results will be published separately.

The hysteresis loop crossing effect is currently not explicitly handled within the processing framework, and only a general elastic model is applied in these cases. A reliable detection of loop crossings and an appropriate treatment of this effect may enable the definition of an additional proxy parameter related to the inertia of the material.

In general, loop crossings arise from a temporal delay between displacement and force, indicating damping or inertia effects. In the presented data, this behavior appears primarily in connective tissue within the tumor sample and in two of the three example positions in healthy tissue, suggesting a possible association with inertia rather than viscosity alone. This interpretation is consistent with the observation that all examined positions exhibit predominantly elastic characteristics, as pronounced ductile behavior would be expected to coincide with broader hysteresis loops. Nevertheless, this hypothesis remains tentative and requires further investigation.

It is noteworthy that this effect does not substantially influence the fingerprint plots. A loop crossing is associated with a small enclosed hysteresis area, which leads to artificially low loss ratio and hysteresis width values and therefore to a low ductile contribution in the fingerprint representation.

Furthermore, we observe a slight but consistent decrease in the maximum displacement with depth in very homogeneous phantoms, which may indicate a reduction in effective force transmission at greater depths. However, local displacement variations consistently dominate this depth-dependent effect, as shown in the Results section. In general, this is a well-known phenomenon in compression OCE and is typically mitigated using differential parameters, such as the WLS. For non-differential parameters, we evaluated a depth-dependent weighting approach to compensate for this effect. However, because the effect is relatively minor, such weighting tends to overcompensate rather than mitigate it. Therefore, although the current framework allows for compensation of this effect, it is not applied to the data presented here.

With respect to tissue mechanics, the exact correlation between OCE-derived parameters and the underlying histological structures requires further investigation. The observation that different tissue types, even within the tumor tissue, are associated with distinct mechanical signatures suggests a meaningful relationship between tissue morphology, tissue type, and mechanical behavior. Open questions remain regarding the extent to which tissue microstructure (e.g., fiber orientation), interactions between components (e.g., frictional effects), and extracellular fluid content (e.g., necrotic or edematous regions leading to a porous, compliant behavior) contribute to the measured mechanical response.

Addressing these aspects will require a dedicated study systematically comparing OCE-derived mechanical data with corresponding histological analyses, in close collaboration with pathologists, biologists, and experts in soft-tissue mechanical modeling.

Overall, the current results are consistent with the latest findings in tissue mechanics, supporting the validity and correct performance of the developed software framework.

4. Conclusion and outlook

We have developed a comprehensive processing pipeline and software framework for processing large OCE datasets acquired with an air-jet excitation system. The framework enables robust extraction of characteristic features and the calculation of mechanical proxy parameters, providing detailed insights into tissue mechanics and supporting the differentiation between healthy and pathological brain tissues. Validation on human brain tumor samples demonstrates the framework’s potential for clinical application in tissue characterization and diagnostic support, as well as for advancing basic research in tissue mechanics.

Furthermore, we introduced a fingerprint-based visualization system intended to support interdisciplinary collaboration, particularly with biological and medical experts. The sector-based representation of the primary mechanical properties (elastic, viscous, and ductile) is designed to provide an intuitive overview and a preliminary mechanical characterization of tissue, while requiring only limited prior expertise in mechanics.

The next step in software development is the implementation of a graphical user interface to create an intuitive and easy-to-use system. The primary technical challenges remain the accurate and efficient phase retrieval from large OCT datasets and the precise measurement of the excitation force beam profile. While the predictive approach for phase unwrapping is highly promising, it requires further refinement, particularly through stabilizing mechanisms that mitigate unwrapping errors arising from the algorithm’s high sensitivity to nonphysical phase noise in the raw data. Likewise, quantitative characterization of the excitation beam profile represents an essential next step toward enabling accurate determination of the local excitation force and, consequently, true quantitative mechanical measurements.

The complete dataset collected during the current project will be processed and analyzed in full, with the results to be published separately. Furthermore, the current experimental software framework will undergo full validation and optimization using this dataset, and once it has been further proven robust and reliable, it will be published independently. Building on this foundation, future work will focus on a large interdisciplinary study involving clinicians, pathologists, biologists, physicists, and mechanical engineers, aimed at systematically investigating the correlations between OCE-derived and classically measured mechanical properties (e.g., indenter or rheometric data), microstructural organization, and genetic markers of different tissue and tumor types. We also plan to incorporate artificial intelligence and deep learning methods for feature extraction, advanced data processing, and processing time acceleration.

Finally, an in situ study is planned to validate the technique during neurosurgical procedures, assessing its applicability for real-time tissue differentiation and intraoperative decision support.

Funding

Bundesministerium für Forschung, Technologie und Raumfahrt https://ror.org/04pz7b180 ( 13N14665, 13N14664, 01KD2424, 13N14663, 13N14661, 13GW0227C); Deutsche Forschungsgemeinschaft https://ror.org/018mejw64 ( EXC 2167-390884018); University of Lübeck https://ror.org/00t3r8h32; Christian-Albrechts-Universität zu Kiel https://ror.org/04v76ef78; State of Schleswig-Holstein, Germany, (Excellence Chair Program by the Universities of Kiel and Luebeck).

Disclosures

R. Huber: University of Lübeck (P), Ludwig Maximilian University of Munich (P), Optores GmbH (I, P, R), Optovue Inc. (I, R), Abott (I, R).

Data availability

Due to its size, the full dataset used to generate the results reported in this paper is not publicly available. However, upon reasonable request, the authors can provide it.

Supplemental document

See Supplement 1 ^{(8.1MB, pdf)} for supporting content.