**4. Discussion**

Practically, cancer markers must be measured precisely in relation to the clinical criterion values. Here, we discuss the detection results for PSA and CEA using human serums from a practical and critical point of view.

Table 1 lists published information on PSA and CEA detections [6–17] and the present results. The dynamic range in Table 1 is defined according to a strict criterion, as is stated in Section 3.1.1. Apart from the claims in the previous reports, the published experimental data were reviewed whether the detection is dynamical, i.e., one concentration is clearly discriminated from the others; for example, if a detected signal at a concentration is overlapped with the other within 1*σ*, the discrimination is judged to be failure, and the concentration is excluded from the dynamical range in Table 1.

There are mainly two types in the previous reports: one is excessive claims of the dynamical ranges and LODs [7–14,17], and the others are focusing on too low target concentrations in practical senses [6,15]. We here discuss the former cases from a practical viewpoint; the latter does not show any experimental data to support the validity around the clinical criteria. The detections using the electrochemical (EC) methods showed exponential responses, i.e., and most measured data were linearly changed by a factor of 3–5 times and plotted for logarithmic target concentrations, which indicated that narrow signal ranges to the wide target concentrations. Due to such deep sublinear responses, it is generally difficult to discriminate nearest-neighbor concentrations. For example, detection signals at target concentrations of 1 ng/mL and 10 ng/mL cannot be distinguished. This property will be an issue in the practical clinical diagnoses, where definite values should be determined. Thus, it is crucial that signals have a wide dynamic range. It is for this reason that FL detection is considered to be a practically feasible method of detection [33].

For the PSA detections, [8,10,11,13], the dynamic ranges are evaluated to be one or two orders of target concentrations from the strict criterion. In contrast, the present metasurface biosensors provide almost four orders of target concentrations and, furthermore, exhibit robustness for human serums (Figure 2c,e).

The CEA detections based on the EC methods in Table 1 tend to reduce the signals when the target CEA was put in human serums. As an example, the LOD in PBS was claimed to be 0.5 ng/mL, while the CEA detection in human serums was limited to the concentrations at 100 ng/mL and more [6]. A similar reduction in the detection of CEA was reported in an EC method using gold nanoparticles and protein A [34]; the dynamic range was claimed to be from 1 pg/mL to 100 ng/mL; however, the detection range of CEA in rat serum was substantially reduced to a range of 1–50 ng/mL. In the optical sensing [14,16], such heavy reductions were not observed. In this study, although some FL-signal reduction was observed, the reduction was not substantial. Importantly, the metasurface biosensors offer most precise detection among the related reports [6,9,12,14,16,17] and enable parallel detection, even when PSA coexists (Figure 4). It is referred to that optical nanostructured biosensors, such as metasurface biosensors, are extensively explored [35–38]; so far, better performance and robustness for PSA and CEA than those of the present metasurface biosensors are not found.

**Table 1.** PSA and CEA detections in human serums. EC and NP stand for electrochemical and nanoparticle, respectively. AD-MSB denotes an all-dielectric metasurface biosensor. PlC denotes plasmonic crystal. NS means the sample diluent NS buffer. The dynamic ranges in this Table are not based on the claims in the references, but on the strict criterion described in the text because the ranges were sometimes overestimated.


#### **5. Conclusions**

We have tested the detections of two cancer markers, PSA and CEA, using the metasurface biosensors. In the sample diluent buffer and human serums, the target makers were successfully detected in similar manners. The dynamic ranges were almost four orders of target concentrations of PSA and CEA. Furthermore, the metasurface biosensors were hardly affected by the impeding biomolecules in human serums, demonstrating their robustness. Thus, the all-dielectric metasurface biosensors demonstrated highly sensitive and robust detections of the cancer markers.
