Is it mathematically correct to fit AFM data (obtained on biological materials) to equations arising from Hertzian mechanics?

When testing soft biological samples using the Atomic Force Microscopy (AFM) nanoindentation method, the force-indentation data is usually fitted to the equations provided by Hertzian mechanics. Nevertheless, a significant question remains up to date; is this a correct approach from a mathematical perspective? Biological materials are heterogeneous, so 'what do we calculate' when using a classic fitting approach? In this paper, conclusive answers to the abovementioned questions are provided. In addition, a new tool for the nanomechanical characterization of biological samples, the depth-dependent mechanical properties maps, is introduced.

Is It Possible to Directly Determine the Radius of a Spherical Indenter Using Force Indentation Data on Soft Samples?

An important factor affecting the accuracy of Young's modulus calculation in Atomic Force Microscopy (AFM) indentation experiments is the determination of the dimensions of the indenter. This procedure is usually performed using AFM calibration gratings or Scanning Electron Microscopy (SEM) imaging. However, the aforementioned procedure is frequently omitted because it requires additional equipment. In this paper, a new approach is presented that focused on the calibration of spherical indenters without the need of special equipment but instead using force indentation data on soft samples. Firstly, the question whether it is mathematically possible to simultaneously calculate the indenter's radius and the Young's modulus of the tested sample (under the restriction that the sample presents a linear elastic response) using the same force indentation data is discussed. Using a simple mathematical approach, it was proved that the aforementioned procedure is theoretically valid. In addition, to test this method in real indentation experiments agarose gels were used. Multiple measurements on different agarose gels showed that the calibration of a spherical indenter is possible and can be accurately performed. Thus, the indenter's radius and the soft sample's Young's modulus can be determined using the same force indentation data. It is also important to note that the provided accuracy is similar to the accuracy obtained when using AFM calibration gratings. The major advantage of this paper is that it provides a method for the simultaneous determination of the indenter's radius and the sample's Young's modulus without requiring any additional equipment.

The Hertzian theory in AFM nanoindentation experiments regarding biological samples: Overcoming limitations in data processing.

Atomic Force Microscopy (AFM) nanoindentation is a powerful tool for the mechanical nano-characterization of biological samples. However, the range of Young's modulus values for the same type of samples usually varies significantly in the literature. This fact is partly related to the inhomogeneity of biological samples at the nanoscale and partly to significant mistakes during data processing. This review depicts that common errors related to (i) the real shape of the AFM tip, (ii) the range of data for which the sample presents an approximate linear elastic response, (iii) the sample's viscoelasticity, (iv) the sample's shape and (v) the substrate effects can be easily avoided without increasing the complexity of data processing. Thus, the present review paper focuses on the procedures that should be followed for the accurate processing of force-indentation curves regarding experiments on biological samples.

A New Approach for the AFM-Based Mechanical Characterization of Biological Samples.

The AFM nanoindentation technique is a powerful tool for the mechanical characterization of biological samples at the nanoscale. The data analysis of the experimentally obtained results is usually performed using the Hertzian contact mechanics. However, the aforementioned theory can be applied only in cases that the sample is homogeneous and isotropic and presents a linear elastic response. However, biological samples often present depth-dependent mechanical properties, and the Hertzian analysis cannot be used. Thus, in this paper, a different approach is presented, based on a new physical quantity used for the determination of the mechanical properties at the nanoscale. The aforementioned physical quantity is the work done by the indenter per unit volume. The advantages of the presented analysis are significant since the abovementioned magnitude can be used to examine if a sample can be approximated to an elastic half-space. If this approximation is valid, then the new proposed method enables the accurate calculation of Young's modulus. Additionally, it can be used to explore the mechanical properties of samples that are characterized by a depth-dependent mechanical behavior. In conclusion, the proposed analysis presents an accurate yet simple technique for the determination of the mechanical properties of biological samples at the nanoscale that can be also used beyond the Hertzian limit.

A simplified approach for the determination of fitting constants in Oliver-Pharr method regarding biological samples.

The atomic force microscopy (AFM) nanoindentation regarding biological samples is a challenging procedure. Biological samples at the nanoscale can be considered as purely elastic materials under the condition that the indentation depth is very small and the indenter is smooth. However, the indenters that are commonly used are pyramidal and in several cases the indentation depths are big comparing to the dimensions of the tip apex. Hence, pyramidal indenters usually cause a permanent damage to the sample. In this case, the best model that can be applied for the data processing is the Oliver-Pharr model which takes into account the elastic-plastic behavior of the sample. The Oliver-Pharr model is based on the fitting of the unloading load-indentation data to a power law equation. In this paper a simplified procedure which ensures the accurate fitting of the unloading load-indentation data to the Oliver-Pharr model is presented and validated on experimental data obtained from a human glioma cell line. It should be noted that the proposed method can be also applied for the data fitting in the case of purely elastic response.

Open-label randomized non-inferiority trial of a fixed-dose combination of glimepiride and atorvastatin for the treatment of people whose Type 2 diabetes is uncontrolled on metformin.

AIMS: To evaluate, in a randomized, open-label study, the non-inferiority of a bioequivalent fixed-dose combination of glimepiride and atorvastatin vs. separately co-administered tablets in people with Type 2 diabetes mellitus. METHODS: Participants with HbA1c ≥ 53 to < 80 mmol/mol (≥ 7.0 to < 9.5%), average fasting blood glucose > 7.0 mmol/l, who were on metformin for ≥ 3 months, were randomized to combination (n = 215) or co-administered glimepiride and atorvastatin (n = 212) once daily for 20 weeks. Up-titration of glimepiride (1-4 mg) and atorvastatin (10-20 mg) were based on average fasting blood glucose and LDL cholesterol, respectively. Co-primary endpoints were change from baseline to week 20 in HbA1c and LDL cholesterol. RESULTS: Non-inferiority was demonstrated for both co-primary endpoints: the upper limits of 95% CIs for differences (combination-reference) were less than the prespecified margins of 3.3 mmol/mol (0.3%) for change from baseline in HbA1c [difference 0.1 mmol/mol (95% CI -1.6, 1.9); 0.01% (95% CI -0.15, 0.17)] and 6% for percentage change from baseline in LDL cholesterol [difference 0.87% (95% CI -2.47, 4.21)]. Similar proportions of participants on combination and reference had treatment-emergent adverse events (64 vs. 61%). More participants on combination had hypoglycaemia (21 vs. 13%); most events were considered by the treating physician to be unrelated to study drug. CONCLUSIONS: The combination was non-inferior to separately co-administered tablets and the safety profile was consistent with the known profiles of glimepiride and atorvastatin. The observed increase in hypoglycaemia on the combination cannot be explained, but may be attributable to non-systematic collectiof glucose readings and may have been influenced by reporting bias in this open-label trial.

[Preoperative MR mammography in breast carcinoma. Effect on operative treatment from the surgical viewpoint]. / Präoperative MR-Mammographie beim Mammacarcinom. Einfluss auf die operative Behandlung aus chirurgischer Sicht.

INTRODUCTION: In a prospective study the diagnostic validity of magnetic resonance mammography (MRM) as well as its impact on the choice of the operative procedure in the treatment of breast cancer was examined. In 125 patients who were suspected of having breast cancer by clinical examination, ultrasound, and X-ray mammography, additional bilateral MRM was performed. Of special interest was the diagnostic potential of MRM with regard to multifocal, multicentric and contralateral lesions. METHODS: After a complete resection all lesions diagnosed by the various conventional methods were examined patho-histologically. In 112 patients, complete data were available to calculate the sensitivity and the specificity of each method as well as to correlate its results with the pathohistological findings. RESULTS: In 91 cases, a breast carcinoma was diagnosed by conventional methods, with a sensitivity/specificity of 73%/67% for clinical examination, of 58%/86% for ultrasound, and of 89%/20% for X-ray mammography. In this preselected series of patients with a prevalence of 81.25% the diagnosis established by the various methods was confirmed by MRM with sensitivity of 96.7% and specificity of 19%. Forty-six additional suspicious lesions were found only by MRM, of which 28 were malignant (25 multifocal or multicentric and 3 contralateral carcinomas), and 18 benign. The rate of false-positive MRM results was 18%. Due to the MRM findings, the therapeutic procedure was changed from breast preservation to mastectomy in 14.3%. CONCLUSION: Not only for the differential diagnosis of discrepant findings between X-ray mammography and ultrasound, but especially for the diagnosis of multifocal or multicentric lesions, MRM seems to be the method of choice. Consequently, MRM plays an important role in planning the operative procedure in breast cancer patients, especially in the context of breast preservation. To ensure optimal use of this new diagnostic tool high technical standards, proper expertise on the part of the examining radiologist, and effective cooperation among the involved disciplines (radiology, pathology, surgery) must be guaranteed.

Apoptosis regulator bcl-w is essential for spermatogenesis but appears otherwise redundant.

Proteins of the Bcl-2 family are important regulators of apoptosis in many tissues of the embryo and adult. The recently isolated bcl-w gene encodes a pro-survival member of the Bcl-2 family, which is widely expressed. To explore its physiological role, we have inactivated the bcl-w gene in the mouse by homologous recombination. Mice that lack Bcl-w were viable, healthy, and normal in appearance. Most tissues exhibited typical histology, and hematopoiesis was unaffected, presumably due to redundant function with other pro-survival family members. Although female reproductive function was normal, the males were infertile. The testes developed normally, and the initial, prepubertal wave of spermatogenesis was largely unaffected. The seminiferous tubules of adult males, however, were disorganized, contained numerous apoptotic cells, and produced no mature sperm. Both Sertoli cells and germ cells of all types were reduced in number, the most mature germ cells being the most severely depleted. The bcl-w-/- mouse provides a unique model of failed spermatogenesis in the adult that may be relevant to some cases of human male sterility.

[Effect of MR mammography on surgical procedure in operative treatment of breast cancer]. / Einfluss der MR-Mammographie auf das chirurgische Vorgehen bei der operativen Behandlung des Mammakarzinoms.

In addition to conventional imaging techniques, magnetic resonance (MR) mammography is an important tool in the diagnosis of breast cancer. It has proved to be the method of choice especially for the differential diagnosis of discrepant findings between mammography and ultrasound as well as the detection of multifocal and multicentric disease. In this context MR mammography is a meaningful method for the planning of breast preserving surgery and seems likely to become routine practice as long as the preconditions for high quality performance are guaranteed.