The technical trends for the next-generation wireless network significantly extend the near-field region, necessitating a reevaluation for the performance of integrated sensing and communications (ISAC) to account for the effects introduced by the near field. In this paper, a near-field ISAC framework is proposed with a more accurate channel model than the three conventional models (TCMs): uniform plane wave, uniform spherical wave, and non-uniform spherical wave, in which the effective aperture of the antenna is considered. Based on the proposed model, sensing and communication (S&C) performance in both downlink and uplink scenarios are analyzed. For the downlink case, three distinct designs are studied: the communications-centric (C-C) design, the sensing-centric (S-C) design, and the Pareto optimal design. Regarding the uplink case, the C-C design, the S-C design and the time-sharing strategy are considered. Within each design, sensing rates (SRs) and communication rates (CRs) are derived. To gain further insights, high signal-to-noise ratio slopes and rate scaling laws concerning the number of antennas are also examined. Finally, the attainable SR-CR regions of the near-field ISAC are characterized. Numerical results reveal that 1) as the number of antennas grows, the SRs and CRs of the proposed model converges to constants, while those of the TCMs increase unboundedly; 2) ISAC achieves a more extensive rate region than the conventional frequency-division S&C in both downlink and uplink cases.