To solve this optimization problem using Gurobi, we need to first define the variables and the objective function. Then, we will add the given constraints to the model.

The variables in this problem are:
- `x0`: milligrams of vitamin B3
- `x1`: grams of fiber
- `x2`: milligrams of vitamin K
- `x3`: grams of carbohydrates

The objective function is to minimize: 
4.8*x0^2 + 2.12*x0*x1 + 6.97*x0*x2 + 8.25*x1^2 + 7.81*x1*x2 + 3.96*x0 + 8.16*x1 + 7.57*x3

The constraints are:
- 1*x0 + 5*x1 + 2*x2 + 2*x3 <= 76 (cardiovascular support index constraint)
- x0 + x2 >= 17 (total combined cardiovascular support index from milligrams of vitamin B3 and milligrams of vitamin K)
- x2^2 + x3^2 >= 17 (total combined cardiovascular support index from milligrams of vitamin K squared and grams of carbohydrates squared)
- x0 + x1 >= 12 (total combined cardiovascular support index from milligrams of vitamin B3 and grams of fiber)
- x0 + x1 + x2 + x3 >= 12 (total combined cardiovascular support index from all variables)
- -5*x0 + 3*x1 >= 0
- -x0^2 + 2*x2^2 >= 0
- -2*x1 + 5*x2 + 2*x3 >= 0
- x0 + x3 <= 29 (total combined cardiovascular support index from milligrams of vitamin B3 and grams of carbohydrates)
- x0 + x1 <= 23 (total combined cardiovascular support index from milligrams of vitamin B3 and grams of fiber)

Here is the Gurobi code for this problem:
```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define the variables
x0 = m.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B3")
x1 = m.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="grams_of_fiber")
x2 = m.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_K")
x3 = m.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="grams_of_carbohydrates")

# Define the objective function
m.setObjective(4.8*x0**2 + 2.12*x0*x1 + 6.97*x0*x2 + 8.25*x1**2 + 7.81*x1*x2 + 3.96*x0 + 8.16*x1 + 7.57*x3, GRB.MINIMIZE)

# Add the constraints
m.addConstr(x0 + 5*x1 + 2*x2 + 2*x3 <= 76, name="cardiovascular_support_index")
m.addConstr(x0 + x2 >= 17, name="vitamin_B3_and_vitamin_K_index")
m.addConstr(x2**2 + x3**2 >= 17, name="vitamin_K_squared_and_carbohydrates_squared_index")
m.addConstr(x0 + x1 >= 12, name="vitamin_B3_and_fiber_index")
m.addConstr(x0 + x1 + x2 + x3 >= 12, name="total_combined_cardiovascular_support_index")
m.addConstr(-5*x0 + 3*x1 >= 0, name="constraint_1")
m.addConstr(-x0**2 + 2*x2**2 >= 0, name="constraint_2")
m.addConstr(-2*x1 + 5*x2 + 2*x3 >= 0, name="constraint_3")
m.addConstr(x0 + x3 <= 29, name="vitamin_B3_and_carbohydrates_index_max")
m.addConstr(x0 + x1 <= 23, name="vitamin_B3_and_fiber_index_max")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print("milligrams_of_vitamin_B3:", x0.x)
    print("grams_of_fiber:", x1.x)
    print("milligrams_of_vitamin_K:", x2.x)
    print("grams_of_carbohydrates:", x3.x)
else:
    print("No optimal solution found.")
```