diff --git a/fastapi/concurrency.py b/fastapi/concurrency.py
index 25aa705f4..0a7aebc99 100644
--- a/fastapi/concurrency.py
+++ b/fastapi/concurrency.py
@@ -11,7 +11,6 @@ else:  # pragma: no cover
 import anyio
 from anyio import CapacityLimiter
 from starlette.concurrency import iterate_in_threadpool as iterate_in_threadpool  # noqa
-from starlette.concurrency import run_in_threadpool as run_in_threadpool  # noqa
 from starlette.concurrency import (  # noqa
     run_until_first_complete as run_until_first_complete,
 )
diff --git a/fastapi/param_functions.py b/fastapi/param_functions.py
index 77accd9f6..86c3c22e8 100644
--- a/fastapi/param_functions.py
+++ b/fastapi/param_functions.py
@@ -2246,7 +2246,7 @@ def Depends(  # noqa: N802
         ),
     ] = True,
     limiter: Annotated[
-        anyio.CapacityLimiter,
+        Optional[anyio.CapacityLimiter],
         Doc(
             """
             By default, synchronous dependencies will be run in a threadpool
@@ -2337,7 +2337,7 @@ def Security(  # noqa: N802
         ),
     ] = True,
     limiter: Annotated[
-        anyio.CapacityLimiter,
+        Optional[anyio.CapacityLimiter],
         Doc(
             """
             By default, synchronous dependencies will be run in a threadpool
diff --git a/fastapi/params.py b/fastapi/params.py
index 499c2d66f..41494044f 100644
--- a/fastapi/params.py
+++ b/fastapi/params.py
@@ -763,7 +763,7 @@ class Depends:
     def __init__(
         self, dependency: Optional[Callable[..., Any]] = None, *,
         use_cache: bool = True,
-        limiter: anyio.CapacityLimiter | None = None,
+        limiter: Optional[anyio.CapacityLimiter] = None,
     ):
         self.dependency = dependency
         self.use_cache = use_cache
@@ -784,7 +784,7 @@ class Security(Depends):
         *,
         scopes: Optional[Sequence[str]] = None,
         use_cache: bool = True,
-        limiter: anyio.CapacityLimiter | None = None,
+        limiter: Optional[anyio.CapacityLimiter] = None,
     ):
         super().__init__(dependency=dependency, use_cache=use_cache, limiter=limiter)
         self.scopes = scopes or []