Glioblastoma multiforme (GBM) is one of the most malignant primary tumors in the central nervous system (CNS). The incidence of GBM worldwide varies depending on the report and country, from 0.59 cases per 100,000 person-years to 5 per 100,000 person-years [22, 27, 29, 33]. The prognosis of GBM remains poor, despite medical progress in therapy. As it is a highly invasive and fast-growing tumor of the brain’s glia, the treatment strategy usually includes three pillars, microsurgical resection, radiotherapy, and chemotherapy. In addition, newer procedures, such as tumor treating fields or immunotherapy, may be used. Microsurgical resection, if feasible, is considered a highly important component of therapy.

Quality of life and survival rates depend significantly on resection radicality while sparing healthy and especially eloquent areas [41, 43]. If possible, a gross-total or even supramarginal resection should be aimed to achieve [6, 30]. Meningiomas and brain metastases can generally be distinguished from healthy brain tissue intraoperatively. However, even experienced neurosurgeons can face significant challenges distinguishing gliomas from healthy brain tissue.

For this purpose, the neurosurgical toolbox offers a wide range of technical aids, like neuro-navigation, fluorescent dyes, intraoperative 3D-Ultrasound, Confocal Laser Imaging, and Raman technology [4, 12, 13, 18, 21, 24, 26, 31, 34, 37, 39, 42] In recent years, the surgical landscape in neurosurgery has evolved toward multimodality to balance the error rates of individual systems.

Aside from technical methods, tactile feedback is employed to distinguish between healthy brain tissue and tumorous tissue during the early stages of not only neurosurgical but also tumor resections in general. Experienced neurosurgeons utilize haptic perception, whether consciously or unconsciously, in order to obtain additional information regarding the tissue’s condition. Mechanical properties, such as tissue elasticity significantly contribute to this process.

Elasticity and stress relaxation behavior of brain tissue

Since there is little data on the intraoperative mechanical characteristics of different brain tumors, this project aimed to investigate the suitability of these very properties for distinguishing between glioblastoma (GBM) and non-tumorous tissue in particular. Biological tissues, including brain tissues, are usually viscoelastic [7,8,9,10, 40]. Both elasticity and viscosity are quantitatively measurable variables.

Elasticity describes the time-independent deformability of a tissue when a force is applied to it. Brain tissue is one of the softest tissues in the body, along with fatty tissue. Newer studies and our own research have shown that the elasticity values of brain tissue are in the range of 800—1400 Pa [10]. This means brain tissue is extremely soft and sensitive.

Viscosity describes the damping behavior of a tissue. Because viscosity is difficult to determine in biological tissues due to desiccation, stress-relaxation behavior was determined instead in this work.

In the stress-relaxation experiment, the course of the force or load development for maintaining a deformation is recorded over time. Various studies in recent years have shown that changes in the microenvironment of tumors can lead to a stiffening of the extracellular matrix. Factors such as tenascin-C, overexpression of hyaluronic acid, fibronectin, and brevican play decisive roles here. As a result, tumors usually appear firmer than the surrounding healthy tissue. This also applies to GBMs. [3, 20, 25, 38]

This project aimed to investigate how GBMs differ from healthy brain tissue in terms of elasticity and stress-relaxation behavior, providing the neurosurgeon with additional information about the tissue to be resected in cases of uncertainty.

Materials and methods


19 patients with initially diagnosed GBM (n = 10) or recurring GBM (n = 9) were included. All recurring GBM patients received chemo- and radiotherapy. Inclusion criteria were: age over 18 years, capable of consent, tumor in supratentorial location, tumor in non-eloquent area. Exclusion criteria were: serious comorbidities, coagulation disorders or blood thinner intake, and pregnancy.

This project was approved by the local ethics committee (Ethics Committee University of Luebeck, AZ 19-319) and carried out according to the Declaration of Helsinki. Patient recruitment and sample selection are illustrated in Fig. 1.

Fig. 1
figure 1

Flow chart of patient recruitment and sample selection

Patient enrolment was carried out as part of regular clinical practice. All patients underwent tumor resection according to current international neurosurgical guidelines and were followed up as part of standard care. In addition, a close-meshed complication screening of the study patients was performed. No complications attributable to study-related procedures were identified. All patients received detailed study information and gave their written informed consent. Detailed patient information is presented in Table 1, 2 and 3.

Table 1 Patient's characteristics I
Table 2 Patient's characteristics II
Table 3 Patient's characteristics in detail

Tissue samples

For this project, samples of tumor tissue and, if possible, non-tumorous brain tissue were taken during tumor resections and mechanically measured by indentation. Non-tumorous brain tissue was collected only if it was affected by the resection from the access path or the resection cavity and was not located in eloquent areas. All samples were gathered using a 5 mm grasping forceps (see Fig. 2B). Sampling was initially based on the surgeon's assessment of whether the tissue was tumor or non-tumor.

Fig. 2
figure 2

A MR-images of a GBM in three axes. B Sample collection in the surgical setting using a 5mm tumor grasping forceps. C Sample of solid tumor portion placed under the indenter tip

After sampling, the fresh preparations were measured immediately. Subsequently, all samples were preserved in formalin solution, sectioned, H&E-stained (hematoxylin and eosin) and examined histopathologically by a neuropathologist. The neuropathologist classified all samples into non-tumor (no tumor cells detectable) and tumor (over 60% tumor cells). Samples containing up to 60% tumor cells were excluded. In seven cases, tissue that was considered tumorous by the surgeon was subsequently diagnosed as non-tumorous by the neuropathologist.

Test setting

After collection, all samples were immediately measured in the operation room to avoid desiccation effects. The Mach-1 v500c® device from Biomomentum (Montreal, Canada) was used to determine the mechanical properties. The mechanical tester is equipped with a vertical single-axial load cell (up to 0.25N). Using a plane-ended cylindrical test rod (with a diameter of 1 mm), samples were loaded unconfined at a rate of 0.1 mm/s up to a load of 0.3 g (see Fig. 3). Furthermore, the reached position was held for 30 s to determine the stress-relaxation behavior of the tissue.

Fig. 3
figure 3

A The mechanical tester, which was used to estimate elastic modulus and relaxation behavior. B A schematic representation of the measurements

Before every measurement course, a height calibration was performed. Each indentation measurement resulted in a load-indentation diagram (see example in Fig. 4) and a corresponding stress-relaxation curve. The Elastic Modulus was evaluated at 200 μm indentation by determining the slope in the load-indentation diagram.

Fig. 4
figure 4

Left: Example of a load-indentation curve. The position represents the vertical position of the indenter. The dashed lines indicate (from left to right): Initial contact to the wet sample surface with an overshoot resulting from a suction effect (red), the estimated tissue contact (green) and at 200μm of indentation. (blue) Right: Example of a relaxation curve

Each sample was measured three times in different locations. The arithmetic mean value of these measurements was calculated for further analysis. Room temperature was held at 20 °C during the whole experiment. Measurements with a resulting deformation of more than 30% of the initial sample height, as well as measurements where the indenter tip punctured the tissue, were discarded from further analysis to avoid unwanted effects. Elasticity and stress-relaxation behavior of 35 (10 non-tumorous, 25 GBM) samples were examined by indentation.

Elasticity and relaxation

The following formula was used to calculate the respective Elastic Modulus (Young’s Modulus [E]) proposed by Zhang et al. [44] with the Poisson ratio being ν = 0.5. A Poisson ration of ν = 0.5 was chosen due to the quasi incompressibility of brain tissue [19] and as a result of our own previous experiments on porcine brain tissue:

$$E=P*\frac{(1-{\nu }^{2})}{2*a*w*\kappa (\nu \frac{a}{h})}$$

P is the applied force and w the indentation depth. The numerical function 2aκ is a correction term proposed by Hayes et al. [23] with a = 1 mm being the indenter diameter. Values for κ for plane-ended cylindrical indenters can be taken directly from Hayes et al.

The stress relaxation behavior was observed in a relaxation experiment over 30 s and fitted into the following two-term prony series adapted from Sasaki et al. [36]:

$$f\left(x\right)= {G}_{1}*{e}^{(-t*{\tau }_{1})}+ {G}_{2}*{e}^{(-t*{\tau }_{2})}+{G}_{0}$$

Statistical analysis and data over-sampling

Statistical analysis was conducted using the open-source statistical software R (version 4.3.2 binary for macOS). The Wilcoxon Rank Sum Test was utilized with alpha = 0.05 to examine group differences, while the Spearman Rank Coefficient (r) was applied to determine correlations.

Due to the restrictive requirements for the samples and the limited amount of non-tumorous brain tissue that could be obtained, the current data set is small and somewhat unbalanced. For this reason, the training data was artificially over-sampled and balanced to facilitate the application of machine learning algorithms for classification. The available data set was split randomly into 250 test and training sets (stratified by class). Each test set consists of 4 non-tumorous samples and 10 GBM samples. The data sets for training were subsequently utilized in a logistic regression training process.

Oversampling was performed using a method called’Adaptive Synthetic Sampling Approach for Imbalanced Learning’ in combination with a downstream use of the Tomek-Link algorithm. This process resulted in an individual training set size of 15 non-tumorous and 15 GBM samples each. The over-sampling of the training data itself took place in the cross-validation phase of the machine learning process to avoid positive bias [35]. Principal component analysis was performed to determine which variables from the indentation measurement were useful for classification purposes. Therefore, neither the Elastic Modulus nor the parameter G0 were considered during the classification process. The classification was based on the material-specific constants of each sample (G1, G2, τ1, τ2) extracted from the relaxation behavior fit.

To evaluate model performance, the parameters precision and recall were used. With

$$Precision= \frac{True\;Positives}{True\;Positives+False\;Positives}$$


$$Recall/Sensitivity= \frac{True\;Positives}{True\;Positives+False\;Negatives}$$



No statistically significant differences were found between the two groups (non-tumor, GBM) with respect to elasticity values. See Table 4 and Fig. 5(A). The GBM group showed a higher spread in Elastic Modulus than the non-tumorous samples and the recurrence group showed a higher spread than the initial diagnosis group (both not significant).

Table 4 Results Elasticity
Fig. 5
figure 5

A Distribution of Elastic Modulus measurements in recurring (green) and non-recurring GBM (blue) and non-tumorous tissue (red). B Elastic Modulus over tumor volume in recurring (blue) and non-recurring GBM (red)

Additionally, a correlation was found between tumor size and Elastic Modulus (with r = 0.48), which was not statistically significant (p = 0.052). Small tumors tend to be softer than larger ones. See Fig. 5(B).

Relaxation behavior

The individual relaxation parameters show partially significant group differences. Thus, the differences in G1, τ1, τ2 and G0 between non-tumorous tissue and GBM tissue are significant in the Wilcoxon Rank Sum Test with p = 0.0005 (W = 215) for G1, p = 0.001 (W = 211) for τ1, p = 0.01 (W = 189) for τ2 and p = 0.01 (W = 61) for G0. See Table 5 and Fig. 6.

Table 5 Results Relaxation Behavior
Fig. 6
figure 6

AE Distribution of G1, τ1, G1, τ2 and G0 between non-tumorous tissue (red) and GBM tissue (recurring (green) and non-recurring (blue))

In the stress-relaxation experiment, the course of the force or load development for maintaining a deformation is recorded over time. Non-tumorous tissue appears to relax somewhat faster than GBM tissue. At 15 s, deformation maintenance values are mean = 50% (median = 49%) for non-tumorous tissue and mean = 56% (median = 56%) for GBM tissue of the initial weight load of 0.3 g. See Fig. 7. Group differences in the Wilcoxon Rank Sum Test are significant with p = 0.006 (W = 199). See Fig. 7.

Fig. 7
figure 7

A Relaxation behavior measurements in tumorous (blue) and non-tumorous tissue (red). The relaxation behavior experiment was performed over the course of 30s. B Relaxation behavior measurements at 15s. Shown is the distribution of relative load in recurring (green) and non-recurring GBM (blue) and non-tumorous tissue (red)

In addition, the height of the samples was examined for group differences (see Table 6). A Wilcoxon Rank Sum Test showed no significant differences in sample height between the two groups.

Table 6 Distribution of sample height in non-tumorous and tumorous samples


The aim of classification by logistic regression was to determine, whether a sample is tumorous or non-tumorous tissue, based only on the stress-relaxation behavior of each sample. Recall for the tumorous class was estimated with 0.83 with a standard deviation of SD=0.12 and precision was estimated with 0.87 with a standard deviation of 0.09 (see Fig. 8).

Fig. 8
figure 8

Distribution of Precision and Recall over 250 different test data sets


Haptic information serves as a crucial intraoperative information source for surgeons from varied surgical disciplines as it enables them to accurately distinguish between healthy and diseased tissue. Neurosurgeons can easily differentiate tactilely between tumors such as meningiomas, metastases, and other clearly defined brain tumors. However, haptic tactile findings in the border region between glial tumors and healthy brain tissue are more intricate. The interpretation of this sensory stimulus necessitates extensive surgical expertise. Nevertheless, haptics, coupled with other advanced visual measures such as fluorescent dyes, MRI, and intraoperative ultrasound, serve as a crucial augmented source of intraoperative information for the surgeon. The mechanical indentation measurements outlined herein reveal the first direct intraoperative data on elastographic measurements of human CNS tissue, as well as GBM tissue. This study stands in distinction to previously published data on ex vivo indentation measurements of animal CNS samples or post-mortem human CNS tissue [7,8,9,10, 17, 40].

Despite the small size of the data set, the results suggest that the information on elasticity and stress relaxation behavior can be used as an additional factor in distinguishing tumorous from non-tumorous tissue. The sensitivity/recall values achieved in the classification (83%) are similar to the known values for 5-ALA (approx. 85%) and exceed those of sodium fluorescein (42–80.8%) [1, 5, 28, 32].

However, although the ranges of elasticity values and stress relaxation behavior partially overlap, trends can be derived that indicate that tumor and peritumoral, non-tumorous tissue differ in their mechanical behavior. Differences between various brain areas in the healthy brain were not considered here, as well as the transition zones from healthy to tumor tissue (which contained less than 60% tumor cells).

The relatively high standard deviations of precision and recall may be due to noise in the measurement and subsequent neuropathological evaluation of the samples. This could be attributed to inconsistencies in the histological analysis of the samples, which did not allow for a 1:1 assignment of the measuring range.

The tissue samples obtained are not regular, healthy brain tissue, but rather from the peritumoral area. However, it is crucial to be able to distinguish this tissue from the tumor tissue during the tumor resection and to spare it. Intraoperative information on the mechanical parameters of the tissue can provide valuable additional information to the surgeon, thus potentially increasing the extent of the resection and prolonging the survival time and the recurrence-free period [6, 30].

In seven cases, tissue that was considered tumorous by the surgeon was subsequently diagnosed as non-tumorous by the neuropathologist. This might be due to inaccuracies of the neuro-navigation and leakage of fluorescein into the peritumoral tissue and also shows the importance of a multimodal intraoperative classification of tumor and non-tumor.

One significant issue with neuro-navigation is its growing inaccuracy during the advancement of surgical interventions and manipulations. Changing of intracranial pressure (brain shift), escaping cerebrospinal fluid (CSF) after dura opening, and manipulations during the resection itself push the accuracy of neuro-navigation to its limits. [37, 39]

To compensate for this problem, the possibility of intraoperative MRI exists. However, this requires high equipment, logistical, and time expenditure. Newer 3D ultrasound systems, developed in recent years, can assist with adapting preoperative MRIs to the surgical site based on the intraoperative situation, by employing anatomical landmarks, such as vessels and other brain structures. The use of ultrasound requires the surgeon to undergo an extended learning process and is relatively time-consuming. [12, 13] One of the latest commercially available techniques for tissue differentiation in neurosurgery is intraoperative confocal laser endoscopy. It also requires a high level of equipment and personnel effort and the use of fluorescein. [4, 34, 42]

Beyond that, Raman technology is currently under investigation on an exclusively experimental scale to determine its potential in differentiating brain tumor tissue from healthy tissue [18, 24, 31]. For improved resection accuracy, additional fluorescent dyes such as fluorescein and 5-aminolevulinic acid can be utilized. These dyes accumulate in tumorous tissue under specific conditions allowing for visualization under special light sources. These dyes are largely ineffective in low-grade gliomas, as they do not typically absorb either contrast medium or the aforementioned dyes [21, 26].

In addition, these substances may not always be free of adverse effects. Uneven aggregation, leakages while excising, and physiological degradation of the dyes over time further complicate intraoperative interpretation.

This study shows similar results to those from previous MRE studies [2]. Despite the similarity of these results, the dependence of the values on the measurement parameters and the preoperative versus intraoperative approach should be emphasized. Other load parameters, such as the load speed and depth, produce different results in viscoelastic tissues, due to their nonlinear behavior, particularly with regard to relaxation behavior.

An interesting future step would be the implementation of an intraoperative method, eliminating the need for biopsies. Successful and precise application could support resection radicality and accuracy. This type of measurement is already available in the form of intraoperative ultrasound elastography. However, the disadvantage is that, as with most ultrasound imaging, a high level of experience is required to interpret the images. Despite promising research findings, the accuracy of this method is directly related to the skills of the surgeon. Moreover, the employment of this technology entails a significant investment in sophisticated equipment and logistical resources. [12, 13] Additionally, the device’s low spatial resolution compromises its precision, rendering it inadequate for microsurgical excision of CNS tumors.

In recent years, Detrez et al. and Burhan et al. have also delivered promising, contactless approaches using optical coherence elastography for tumor delineation in the field of neurosurgery [11, 14,15,16].

Further research will be needed, especially to consider the variations in mechanical properties of specific brain areas, especially white and grey matter.