The Things in the smart Internet of Things (IoT) depend more on self decision making abilities instead of relying on human interventions. In the IoT, static security mechanisms are not well suited to handle all security risks sufficiently. A security mechanism can be considered static if it is developed with fixed security measures whereas an adaptive security mechanism can be considered dynamic if it can continuously monitor, analyse, and reassess a security risk at runtime. Adaptive security mechanisms can be a better choice to secure dynamic and heterogeneous computing systems in the IoT. This paper presents a patient monitoring scenario using the smart IoT and aims at highlighting all important assets, vulnerabilities, and threats that can harm assets and disrupt eHealth systems. We describe adaptive security and introduce a concept of adaptive security countermeasures for the smart IoT in eHealth.