Detection of Plasma Biomarkers Using Immunomagnetic Reduction: A Promising Method for the Early Diagnosis of Alzheimer’s Disease

The magnetic nanoparticles used are dextran-coated Fe₃O₄ particles (MF-DEX-0060, MagQu Co., Ltd.), as shown in Fig. 1. These nanoparticles are dispersed in phosphate-buffered saline (PBS) solution. The mean hydrodynamic diameter of the particles is 50–60 nm measured with laser dynamic scattering (Nanotrac 150, Microtrac). The diameter of core Fe₃O₄ is approximately 25–30 nm according to the θ−2θ X-ray powder diffraction pattern (D-500, Simens) for the (311) peak [55]. The dextran serves as a surfactant to achieve dispersion of the magnetic nanoparticles in the PBS and also acts as a linker between the Fe₃O₄ particles and antibodies. For antibodies to bind to dextran on the outermost shell of the magnetic nanoparticles, NaIO₄ solution is added into the magnetic solution to oxidize dextran to create aldehyde groups (–CHO) [63]. Then, dextran can react with the antibodies via the linking of –CH=N–. Thus, the antibody is bound covalently to dextran. Through magnetic separation, unbound antibodies are separated from the solution. In this work, two types of antibodies, targeting Aβ_1–42 and Tau protein, are separately immobilized onto magnetic nanoparticles. For the Aβ_1–42 reagent (MF-AB2-0060, MagQu Co., Ltd.), the antibody is monoclonal (A8354, Sigma). The antibody for Tau reagent (MF-TAU-0060, MagQu Co., Ltd.) is also monoclonal (T9450, Sigma) and is against the C terminal region of Tau protein. Thus, total Tau protein is measured. Hereafter, the total Tau protein is referred to as Tau protein in this study. The concentration of reagent is 8 mg Fe/ml, and both reagents demonstrate superparamagnetism. The reagents were stored at 2–8 °C and showed stability at 130 days.

The detailed mechanism of immunomagnetic reduction (IMR) using the antibody-functionalized magnetic nanoparticles is described here. The frequency-dependent ac magnetic susceptibility χ _ac of the reagent under an external magnetic field is expressed aswhere χ _o is the dc magnetic susceptibility, f is the frequency of the external magnetic field, and τ _eff is the effective time constant of magnetic relaxation of magnetic nanoparticles in reagent. τ _eff can be written aswhere τ _B and τ _N are the time constants of Brownian relaxation and Néel relaxation. τ _B and τ _N are expressed as [64, 65] where η is the viscosity of the water, V _H is the hydrodynamic volume of a nanoparticle, k _B is the Boltzmann constant, T is the temperature in Kelvin, κ is the anisotropy constant of nanoparticles, and V _M denotes the volume of the magnetic core of a nanoparticle. When the viscosity of water (=10⁻³ Pa-s), the hydrodynamic diameter of the magnetic nanoparticles (~55 nm), the measurement temperature (~293 K), the anisotropy constant of magnetic nanoparticles (~30 kJ m⁻³), and the core diameter of magnetic nanoparticles (~30 nm) are known, the τ _B is estimated to be microseconds and τ _N is approximately 1061 s. Since τ _N is much larger than τ _B , the second term on the right-hand side of Eq. (3) can be neglected. In the current case, τ _eff can be regarded as τ _B . Thus, the normalized amplitude of ac magnetic susceptibility, |χ _ac|/χ _o, in Eq. (2) as a function of frequency of an external magnetic field can be numerically analyzed with the known values of η, V _H, k _B and T in Eq. (4a). Figure 2 plots the relationship between the normalized amplitude of ac magnetic susceptibility and the frequency of the applied ac magnetic field, i.e., the |χ _ac|/χ _o–f curve. For a given mean hydrodynamic diameter of particles, say 50.8 nm, the |χ _ac|/χ _o continuously decreases with increasing frequency. On the other hand, as the mean hydrodynamic diameter of the particles increases, the |χ _ac|/χ _o–f curve moves downward. These results contribute to the reduction in the ac magnetic susceptibility of the reagent as antibody-functionalized magnetic nanoparticles associate with target molecules.

Equation (2) gives the ac magnetic susceptibility of the reagent under only one applied ac magnetic field. In IMR, two magnetic fields, H ₁ and H ₂, are applied to the reagent. These two applied magnetic fields have different frequencies, f ₁ and f ₂. The amplitudes of the two applied magnetic fields are weak, e.g., <1 Gauss. Thus, the effective ac magnetic susceptibility of the reagent can be expressed as [53]where χ _ac,_H1 is attributed to H ₁ with frequency f ₁, χ _ac,_H2 results from H ₂ with frequency f ₂, k _B is the Boltzmann constant, and T is the absolute temperature.

The frequencies shown in the first term on the right-hand side are f ₁ and f ₂, whereas the second term exhibits frequencies of f ₁, f ₂, 3f ₁, 3f ₂, f ₂−2f ₁, f ₂ + 2f ₁, f ₁−2f ₂, f ₁ + 2f ₂. One can select any linear combination of f ₁ and f ₂. In IMR, the frequency of f ₁ + 2f ₂ is of interest. Thus, the amplitude (denoted as χ _ac,_amp) for χ _ac,eff at f ₁ + 2f ₂ is proportional to the product of χ _ac,H1 at f ₁ and (χ _ac,H2)² at f ₂;

Once the antibody-functionalized magnetic nanoparticles associate with the target molecules, the hydrodynamic volume of the associated nanoparticles increases. Meanwhile, both χ _ac,_H1 and χ _ac,_H2 show a given frequency decrease. Thus, this results in a reduction in the ac magnetic susceptibility of the reagent [66].

The signal-channeled SQUID-based ac magnetometer was developed in 2008 [54]. The SQUID-based ac magnetosusceptometer consists of three parts: sample magnetization, flux coupling, and superconducting sensing, as shown in Fig. 3. The sample-magnetization component is a set of coils, including two excitation coils (referred to as excitation coil 1 and excitation coil 2, respectively) and one pick-up coil. The inductances and resistance of the three coils are listed in Table 1. The three coils are assembled coaxially, with the pick-up coil being innermost. Excitation coils are driven with an ac signal generator, generating two independent ac voltages at two different frequencies, f ₁ and f ₂, to excitation coils 1 and 2. The pick-up coil is an axial gradiometer. The ac magnetic signal from the sample is detected by the pick-up coil and is transmitted to the flux coupling component.

The flux-coupling component is a pair of twisted wires, as illustrated in Fig. 4. One end of the wires is connected to the pick-up coil. The other end of the wires is terminated with a coil. Once the output ac voltage of the pick-up coil is activated, an ac electric current I is induced along the wires, and an ac magnetic field B is generated at the coil terminal. The ac magnetic field B at the coil terminal is detected with the high-Tc SQUID magnetometer, which is the superconducting–sensing component. The mutual inductance between the coil terminal and the SQUID magnetometer is 1.6 µH. By utilizing the flux-coupling coil, the ac magnetic flux originally generated at the sample component is efficiently transferred to the sensor component of the SQUID-based ac magnetosusceptometer. With this setup, the SQUID magnetometer is not seriously disturbed by the two excitation fields, because the excitation fields are distant from the SQUID magnetometer. Thus, the system is very stable and is suitable for long-term operation. Note that the flux-coupling coil is enveloped with electromagnetically shielded shells.

The SQUID magnetometer and the coil terminal are immersed in liquid nitrogen. The dewar is placed inside an electromagnetically shielded box, showing 100 dB for the shielding factor at the operating frequency (~20 kHz). The SQUID magnetometer is controlled electronically, and the output signals are sent to a personal computer (PC).

With the need for a high-throughput assay, the channel numbers of the SQUID-based ac magnetosusceptometer were increased to 4 in 2010 [67, 68], to 8 in 2014, and finally to 36 in 2016. An image of the 36-channel SQUID-based ac magnetosusceptometer is shown in Fig. 5. With increases in the channel numbers, more electrical technologies are integrated into the magnetosusceptometer. For example, to prevent electromagnetic crosstalk among coil sets, two neighboring coil sets are separated by 15 cm or each coil set is surrounded with an electromagnetic absorber. The coil sets are activated in sequence. Only one coil set is activated at one instance. To manipulate the activation of each coil set, low-noise electric switches are cascaded between the ac signal generator and excitation coils and between the pick-up coil and the flux-coupling coil component. A 105-channeled SQUID-based ac magnetosusceptometer is under development.

This article is based on previously conducted studies [22, 24, 28] and does not involve the performance of any new studies of human or animal subjects. In the previous studies, all subjects were recruited at National Taiwan University Hospital. AD subjects and healthy control volunteers were enrolled from a memory clinic and a mild-cognitive-impairment (MCI) project, respectively. The demographic information of the subjects is listed in Table 2. All subjects had completed primary-school education, and none displayed depressive symptoms, i.e., Geriatric Depression Scale score >8. Subjects with major systemic diseases possibly affecting cognitive function, such as cardiopulmonary failure, hepatic or renal failure, poorly controlled diabetes (HbA1C >8.5), head injury, stroke or other neurodegenerative disease, were excluded. All subjects have been diagnosed by experienced physicians at National Taiwan University Hospital.

Several clinical diagnostic tests were performed for the subjects to classify them as healthy controls, MCI due to AD, or AD. The clinical workup included medical history, physical and neurological examinations, laboratory tests, and neuroimaging studies. The neurological examinations included the Mini-Mental State Examination (MMSE) and Clinical Dementia Rating (CDR), the Activities of Daily Living (ADL) scale, the Instrumental ADL scale, and the Wechsler Memory Scale-III (WMS-III). Subjects with dementia meet the diagnostic guidelines for probable AD dementia proposed by the National Institute on Aging-Alzheimer’s Association (NIA-AA) workgroups in 2011. The diagnosis of MCI due to AD also follows the recommendations of the NIA-AA. For the diagnosis of MCI due to AD, a formal cognitive test is used, with a cutoff value at or below the fourth percentile (lower than 1.5 times the standard deviation) of the scale score for the age- and education-matched control. Additionally, all subjects with MCI due to AD demonstrated hippocampal atrophy as observed by magnetic resonance imaging [22].

As shown in Table 2, MMSE scores varied among groups. MMSE was 28.6 ± 1.1 for healthy controls, 24.6 ± 2.2 for MCI due to AD subjects, and 22.2 ± 2.9 for early-stage AD subjects. Significant group differences were observed between healthy controls and MCI due to AD or early-stage AD subjects (p < 0.01). Furthermore, significant group differences between MCI due to AD and early-stage AD subjects at a significance level of p < 0.01 were found.

Subjects were asked to provide a 10-mL non-fasting venous blood sample (K3 EDTA, lavender-top tube). Each sample was blinded to colleagues in the laboratory. The blood samples were centrifuged (2500 g for 15 min) within 1 h of draw, and plasma was aliquoted into cryotubes and stored at −20 °C.

Plasma (40–60 µL) was mixed with 80–60 µL reagent at room temperature for the detection of an immunomagnetic reduction signal, IMR (%). For each sample, IMR signal measurements were performed in duplicate. The IMR signals were converted into biomarker concentrations via standard curves. All plasma samples were blinded for IMR measurements.

Tau-PBS samples (100-pg/mL) were used for IMR detection by the 36-channel SQUID-based ac magnetosusceptometer. The IMR signal of each channel is plotted in Fig. 6. The maximum IMR signal is 5.14%, while the minimum IMR signal is 5.02%. The mean value and the standard deviation of the 36 IMR signals are 5.07% and 0.03%, respectively. The coefficient of variation in the 36 IMR signals is obtained as 0.62%, revealing the high consistency in IMR signals among channels.

Amyloid β 1–42 (Aβ_1–42) (10 µL of 0.1-mg/mL) (Cat. no. A9810; SIGMA-ALDRICH,) was spiked into 9990 µL of PBS (pH 7.4) to produce a 100 ng/mL (=100,000 pg/mL) Aβ_1–42-PBS stock-A sample. The stock-A sample (100 µL) was spiked into a 9900-µL PBS buffer pool to obtain a 1 ng/mL (=1000 pg/mL) Aβ_1–42-PBS stock-B sample. Stock-A and stock-B samples were mixed with PBS in various volume ratios to obtain nine Aβ_1–42-PBS samples of 1, 10, 50, 100, 1000, 2500, 5000, 20,000, and 50,000 pg/mL, which were used for IMR measurements. The IMR signals of these nine Aβ_1–42-PBS samples are plotted with dots in Fig. 7. Clearly, Fig. 7 shows the IMR signal increases as Aβ_1–42 concentration increases.

The IMR signals in Fig. 7 for Aβ_1–42 concentrations from 1 to 50,000 pg/mL are used for exploring the analytic relationship, which follows the logistic function [69, 70]where A, B, γ and ϕ _o are fitting parameters. By fitting the Aβ_1–42 concentration-dependent IMR signals in Fig. 7 to Eq. (18.1), the parameters are found to be A = 1.91, B = 8.09, γ = 0.49 and ϕ _o = 14,157. The parameter ϕ _Aβ1–42 is the Aβ_1–42 concentration. The fitted logistic function is plotted with a solid line in Fig. 7, with a coefficient of determination (R ²) of 0.999. Remarkably, significant IMR signals can could be detected for the 1-pg/mL Aβ_1–42-PBS sample. This implies that the minimal detection limit of assaying Aβ_1–42 using IMR is on the pg/mL level.

The IMR signal as a function of Tau-protein concentration from 1 to 5000 pg/mL, i.e., IMR (%)-ϕ _Tau curve, was measured. Samples of various concentrations of Tau protein were prepared by the following processes: 50 µL of purified human Tau protein ladder with six isoforms (30 µg/mL; Cat. no. T7951; SIGMA-ALDRICH) was mixed with 250 µL of PBS (pH 7.4) to reach a final concentration of 5 µg/mL Tau protein; 20 µL of Tau protein solution (5 µg/mL) is spiked into a 9980-µL PBS (pH 7.4) pool to reach a 10 ng/mL (=10,000 pg/mL) Tau-PBS stock-A sample; 1000 µL of the stock-A sample was spiked into a 9000-µL PBS pool to obtain a 1 ng/mL (=1000 pg/mL) Tau-PBS stock-B sample. Then, the stock-A and stock-B samples are mixed with PBS with various volume ratios to obtain Tau-PBS samples containing 0.1–2500 pg/mL of total Tau protein.

The detected IMR signals for Tau-PBS samples are plotted with crosses in Fig. 8. These experimental data are fitted to Eq. (7) by replacing ϕ _Aβ1–42 with ϕ _Tau. The values of the fitting parameters were found to be A = 2.28, B = 7.34, γ = 0.33 and ϕ _o = 39.03. The coefficient of determination (R ²) was 0.999. The fitted logistic function is plotted as the solid line in Fig. 8. Similar to the case in Fig. 7, the Tau-protein solution at pg/mL provides a significant IMR signal. The low-detection limit of assaying Tau protein using IMR at the level of pg/ml.

To reveal the ultra-high sensitivity of IMR, the Aβ_1–42 and Tau-protein concentration-dependent signals (OD450) were explored using the most frequently used laboratory assay, enzyme-linked immunosorbent assay (ELISA), which is plotted as dashed lines in Figs. 7 and 8 for Aβ_1–42 and Tau protein, respectively [59]. Clearly, for both Aβ_1–42 or Tau protein, the OD450 is trivial for concentrations lower than 100 pg/mL. The results in Figs. 7 and 8 provide evidence that the IMR assays are much more sensitive than ELISA. Samples with Aβ_1–42 or Tau-protein concentrations at several tens of pg/mL can be assayed with IMR, but not with ELISA.

For human plasma, many kinds of chemical and biological molecules co-exist with Aβ_1–42 and Tau protein. It is necessary to investigate the interference of these molecules in the detection of Aβ_1–42 and Tau protein using IMR. Some typical molecules were selected as interfering materials and mixed with Aβ_1–42 or Tau protein. For the interference tests on Aβ_1–42, a sample of pure 100-pg/mL Aβ_1–42 and samples of 100-pg/mL Aβ_1–42 with either 1000-µg/mL hemoglobin, 600-µg/mL conjugated bilirubin, 30,000-µg/mL intra lipid, 200-µg/mL uric acid, 500-IU/mL rheumatoid factor, 60,000-µg/mL albumin, 500-µg/mL acetylsalicylic acid, 300-µg/mL ascorbic acid, 1000-µg/mL ampicillin sodium, 100-pg/mL Aβ_1–40, or 1000-ng/mL heterophilic antibody were assayed using IMR. The measured concentration of the pure Aβ_1–42was 115.74 pg/mL. The detected Aβ_1–42 concentrations of other samples with interfering materials ranged between 104.31 and 123.80 pg/mL. The resulting recovery rates were 90.1%–108.7%. According to the FDA guideline, the accepted recovery rate is 90%–110%. Hence, there is no significant interference of these typical molecules with the assay of Aβ_1–42 using IMR.

For the interference tests on Tau protein, a sample of pure 100-pg/mL Tau protein and samples of 100-pg/mL Tau protein with either 1000-µg/mL hemoglobin, 600-µg/mL conjugated bilirubin, 30,000-µg/mL intra lipid, 200-µg/mL uric acid, 500-IU/mL rheumatoid factor, 60,000-µg/mL albumin, 500-µg/mL acetylsalicylic acid, 300-µg/mL ascorbic acid, 1000-µg/mL ampicillin sodium, or 1000-ng/mL heterophilic antibody were assayed using IMR. The measured concentration of the pure Tau protein was 99.85 pg/mL. The detected Tau-protein concentrations of the other samples with interfering materials ranged between 91.67 and 108.51 pg/mL. The resulting recovery rates were 91.8%–108.7%. Hence, there is no significant interference of these typical molecules with the assay of Tau protein using IMR.

The reason for the high specificity of the IMR assay is discussed in Ref. [70]. Interference with the assay is partly caused by non-specific binding between antibodies and non-target molecules. Once non-target molecules associate with antibodies immobilized on magnetic nanoparticles, the IMR signal is detectable and a false positive occurs. According to the mechanism of IMR, the magnetic nanoparticle is rotating regardless of whether non-target or target molecules associate with the magnetic nanoparticles via antibodies. The bound molecule is experiencing the centrifugal force because of particle rotation. The strength of the centrifugal force can be enhanced by increasing the rotation frequency of the nanoparticles. This can be done by adjusting the frequency of the applied ac magnetic fields. The binding force between the antibodies and non-target molecules is weaker than that between antibodies and target molecules. Hence, by suitably adjusting the rotating frequency of the applied ac magnetic fields, the strength of the centrifugal force is manipulated to be higher than the binding force for non-target molecules, but lower than that of target molecules. Thus, the binding between antibodies and non-target molecules is broken, whereas the binding between antibodies and target molecules is maintained. Therefore, the interference of non-target molecules is inhibited in IMR.

The IMR assay is applied to detect the concentrations of Aβ_1–42 and Tau protein in human plasma. According to the clinical diagnosis, there were 68 healthy controls, 24 subjects with MCI due to AD, and 31 early-stage-AD subjects. MCI due to AD is the transition stage from health to early-stage AD [22, 24, 48]. Figure 9a gives the age-dependent Aβ_1–42 concentration for healthy controls and subjects suffering from either MCI due to AD or early-stage AD. Each point in Fig. 9a denotes the Aβ_1–42 concentration of one subject. For healthy controls, the Aβ_1–42 concentration in human plasma is 15.82 ± 0.73 pg/mL. Note that the plasma Aβ_1–42 concentration (plotted with dots) in healthy controls truly exists below the low-detection limit of ELISA but above that of IMR. This explains why IMR is suitable for application to the assay of ultra-low-concentration biomarkers of AD in human plasma. Once subjects present with MCI due to AD or early-stage AD, the concentration of plasma Aβ_1–42 (plotted with crosses) increases (18.14 ± 1.51 pg/mL). A significant difference (p < 0.001) in plasma Aβ_1–42 concentration between healthy controls and subjects is observed in Fig. 9a. Through analysis of the receiver operating characteristic (ROC) curve shown in Fig. 9b, the cut-off value of the plasma Aβ_1–42 concentration for discriminating subjects and healthy controls was found to be 16.42 pg/mL. The corresponding clinical sensitivity and specificity were 0.945 and 0.926, respectively. The area under the curve (AUC) was 0.976, as listed in Table 3.

As shown in Fig. 10a, using IMR, the detected concentration for the Tau protein in human plasma was (13.38 ± 6.85) pg/mL for healthy controls and (40.74 ± 13.72) pg/mL for subjects. An increase in plasma Tau protein in subjects with either MCI due to AD or early-stage AD was clearly observed. Through t test analysis, the p value in terms of concentration of plasma Tau protein differentiating healthy controls from subjects was smaller than 0.001, revealing a significant difference in the concentration of Tau protein in human plasma between subjects and healthy controls. According to analysis of the ROC shown in Fig. 10b, the cut-off value of plasma Tau-protein concentration for differentiating subjects with MCI due to AD or early-stage AD from healthy controls was found to be 25.20 pg/mL. The corresponding clinical sensitivity and specificity were 0.964 and 0.956, respectively. The AUC was 0.993, as listed in Table 3.

The results of t test and ROC-curve analyses show the high consistency between the levels of plasma Aβ_1–42 and Tau protein and clinical diagnosis for discriminating healthy controls and subjects with early-stage AD or MCI due to AD. This implies a blood test via IMR is promising as an initial step before performing complicated and high-cost clinical diagnosis.

In the past, several research groups have applied ELISA or modified ELISA to assay plasma Aβ_1–42 and Tau protein [71‐76]. The results demonstrated no significant difference between healthy controls and AD subjects, possibly due to the ELISA technique’s lack of ultra-sensitivity. The results shown in Figs. 9a and 10a evidence that the levels of plasma Aβ_1–42 and Tau protein are lower than 100 pg/mL, which is below the low-detection limit of ELISA.

In addition to demonstrating the feasibility of differentiating healthy controls from AD subjects, the discrimination between MCI due to AD from early-stage AD using plasma biomarkers was investigated. Remarkably, the subjects in this study with a high degree of AD severity showed lower scores on the MMSE. Hence, the relationship between plasma biomarker levels and MMSE score was investigated.

For plasma Aβ_1–42, the subjects with MCI due to AD showed a concentration of (17.52 ± 1.22) pg/mL, while (18.61 ± 1.55) pg/mL was found for subjects with early-stage AD. The p value of the plasma Aβ_1–42 concentration between MCI due to AD and early-stage AD was calculated to be 0.003, indicating a significant difference between MCI due to AD and early-stage AD when using plasma Aβ_1–42 as a diagnostic parameter. Through ROC analysis shown in Fig. 11a, the cut-off value to differentiate early-stage AD from MCI due to AD was 17.68 pg/mL. The clinical sensitivity and specificity were 0.742 and 0.750, respectively. The area under the curve was 0.762, as listed in Table 3. These results reveal an accuracy of identifying disease severity of approximately 75% based on the Aβ_1–42 plasma concentration.

Regarding the plasma Tau protein, subjects with MCI due to AD and early-stage AD showed concentrations of (33.33 ± 7.77) pg/mL and (53.57 ± 22.87) pg/mL, respectively. A clear increase in the concentration of plasma Tau protein for early-stage AD compared to MCI due to AD resulted. The p value in terms of plasma Tau-protein concentration for these two groups was calculated to be smaller than 0.001, showing a definite difference in plasma Tau-protein concentration between MCI due to AD and early-stage AD. By performing ROC analysis shown in Fig. 11b, the cut-off value of Tau-protein concentration to discriminate MCI due to AD and early-stage AD was 37.93 pg/mL. The clinical sensitivity and specificity were 0.742 and 0.792, respectively. The area under the curve was 0.822. Compared to plasma Aβ_1–42, plasma Tau protein showed higher accuracy in determining disease severity for prodromal AD. This suggests that plasma Tau protein is a promising biomarker not only to discriminate healthy controls and AD subjects but also to identify disease severity for prodromal AD. However, according to published papers [70, 77‐80], elevations of Tau protein in CSF were found for other types of neurodegenerative diseases, such as Parkinson’s disease, frontotemporal dementia, vascular dementia, and brain injuries. The degree of specificity of Tau protein to AD is not high enough. If Tau protein were to be used as the sole parameter for diagnosing prodromal AD, the false-positive occurrence due to other types of dementia or brain injuries would be more than negligible. Fortunately, Aβ_1–42 is highly correlated to the pathology of AD. Aβ_1–42 should be considered a parameter for diagnosing prodromal AD. To achieve high specificity and accuracy, the combination of Aβ_1–42 and Tau protein is suggested as a possible biomarker. In Figs. 9a and 10a, the levels of Aβ_1–42 and Tau protein become higher for AD subjects. To enhance the increased biomarker level, the product of Aβ_1–42 concentration and Tau-protein concentration, denoted as ϕ _Aβ1–42xϕ _Tau, is proposed as a diagnostic parameter [49]. The distributions of ϕ _Aβ1–42xϕ _Tau for healthy controls, MCI due to AD, and early-stage AD are plotted in Fig. 12. The solid lines in Fig. 12 denote the Gaussian distribution.

Figure 12 clearly shows that the values of ϕ _Aβ1–42xϕ _Tau for healthy controls range between zero and 400 (pg/mL)². The ϕ _Aβ1–42xϕ _Tau values increase for MCI due to AD and are much higher for early-stage AD. Obviously, ϕ _Aβ1–42xϕ _Tau is promising as a diagnostic parameter not only for discriminating AD subjects but also for identifying disease severity. In this study, MMSE scores decreased with disease severity. Hence, ϕ _Aβ1–42xϕ _Tau increased with decreasing MMSE score for subjects in this study. Through analysis of the ROC shown in Fig. 13a, the cut-off value for discriminating healthy controls and AD subjects was found to be 455.49 (pg/mL)², with the corresponding clinical sensitivity and specificity being 0.945 and 0.971, respectively. The area under the curve was 0.995. The cut-off value is plotted with a thinly dashed line in Fig. 12. On the other hand, the cut-off value for differentiating early-stage AD from MCI due to AD was obtained as 643.96 (pg/mL)² via the ROC analysis shown in Fig. 13b. The clinical sensitivity and specificity and area under the curve were 0.774, 0.837, and 0.841, respectively.

This implies an accuracy of determining the severity of prodromal AD of nearly 85%, which is absolutely applicable in clinics.